id	sid	tid	token	lemma	pos
cana-5235	1	1	communications	communication	NOUN
cana-5235	1	2	on	on	ADP
cana-5235	1	3	applied	apply	VERB
cana-5235	1	4	nonlinear	nonlinear	ADJ
cana-5235	1	5	analysis	analysis	NOUN
cana-5235	1	6	issn	issn	NOUN
cana-5235	1	7	:	:	PUNCT
cana-5235	1	8	1074	1074	NUM
cana-5235	1	9	-	-	PUNCT
cana-5235	1	10	133x	133x	NUM
cana-5235	1	11	vol	vol	VERB
cana-5235	1	12	32	32	NUM
cana-5235	1	13	no	no	NOUN
cana-5235	1	14	.	.	PUNCT
cana-5235	2	1	10s	10	NOUN
cana-5235	2	2	(	(	PUNCT
cana-5235	2	3	2025	2025	NUM
cana-5235	2	4	)	)	PUNCT
cana-5235	2	5	1323	1323	NUM
cana-5235	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5235	2	7	nonlinear	nonlinear	ADJ
cana-5235	2	8	hydrodynamic	hydrodynamic	ADJ
cana-5235	2	9	instability	instability	NOUN
cana-5235	2	10	control	control	NOUN
cana-5235	2	11	on	on	ADP
cana-5235	2	12	a	a	DET
cana-5235	2	13	shear	shear	NOUN
cana-5235	2	14	-	-	PUNCT
cana-5235	2	15	imposed	impose	VERB
cana-5235	2	16	two	two	NUM
cana-5235	2	17	-	-	PUNCT
cana-5235	2	18	layer	layer	NOUN
cana-5235	2	19	film	film	NOUN
cana-5235	2	20	flow	flow	NOUN
cana-5235	2	21	by	by	ADP
cana-5235	2	22	means	mean	NOUN
cana-5235	2	23	of	of	ADP
cana-5235	2	24	velocity	velocity	NOUN
cana-5235	2	25	slip	slip	NOUN
cana-5235	2	26	and	and	CCONJ
cana-5235	2	27	insoluble	insoluble	ADJ
cana-5235	2	28	surfactant	surfactant	NOUN
cana-5235	2	29	1muhammad	1muhammad	NUM
cana-5235	2	30	sani	sani	PROPN
cana-5235	2	31	,	,	PUNCT
cana-5235	2	32	2s	2s	PROPN
cana-5235	2	33	.	.	PUNCT
cana-5235	2	34	karthick	karthick	PROPN
cana-5235	2	35	*	*	PROPN
cana-5235	2	36	,	,	PUNCT
cana-5235	2	37	1iliyasu	1iliyasu	NUM
cana-5235	2	38	bello	bello	PROPN
cana-5235	2	39	,	,	PUNCT
cana-5235	2	40	1james	1james	NUM
cana-5235	2	41	andrawus	andrawus	NOUN
cana-5235	2	42	,	,	PUNCT
cana-5235	2	43	3	3	NUM
cana-5235	2	44	g.	g.	NOUN
cana-5235	2	45	jayaraman	jayaraman	NOUN
cana-5235	2	46	.	.	PUNCT
cana-5235	3	1	1	1	NUM
cana-5235	3	2	department	department	NOUN
cana-5235	3	3	of	of	ADP
cana-5235	3	4	mathematics	mathematic	NOUN
cana-5235	3	5	,	,	PUNCT
cana-5235	3	6	faculty	faculty	NOUN
cana-5235	3	7	of	of	ADP
cana-5235	3	8	physical	physical	ADJ
cana-5235	3	9	sciences	science	NOUN
cana-5235	3	10	,	,	PUNCT
cana-5235	3	11	federal	federal	ADJ
cana-5235	3	12	university	university	NOUN
cana-5235	3	13	dutse-7156	dutse-7156	NOUN
cana-5235	3	14	,	,	PUNCT
cana-5235	3	15	jigawa	jigawa	PROPN
cana-5235	3	16	state	state	PROPN
cana-5235	3	17	,	,	PUNCT
cana-5235	3	18	nigeria	nigeria	PROPN
cana-5235	3	19	.	.	PUNCT
cana-5235	4	1	msdjunior9@gmail.com	msdjunior9@gmail.com	PROPN
cana-5235	4	2	,	,	PUNCT
cana-5235	4	3	iliyasubello13@gmail.com	iliyasubello13@gmail.com	X
cana-5235	4	4	,	,	PUNCT
cana-5235	4	5	jamesandy7772@gmail.com	jamesandy7772@gmail.com	X
cana-5235	4	6	2	2	NUM
cana-5235	4	7	*	*	PROPN
cana-5235	4	8	department	department	NOUN
cana-5235	4	9	of	of	ADP
cana-5235	4	10	mathematics	mathematics	PROPN
cana-5235	4	11	,	,	PUNCT
cana-5235	4	12	college	college	NOUN
cana-5235	4	13	of	of	ADP
cana-5235	4	14	engineering	engineering	NOUN
cana-5235	4	15	and	and	CCONJ
cana-5235	4	16	technology	technology	NOUN
cana-5235	4	17	,	,	PUNCT
cana-5235	4	18	srm	srm	PROPN
cana-5235	4	19	institute	institute	PROPN
cana-5235	4	20	of	of	ADP
cana-5235	4	21	science	science	NOUN
cana-5235	4	22	and	and	CCONJ
cana-5235	4	23	technology	technology	NOUN
cana-5235	4	24	,	,	PUNCT
cana-5235	4	25	kattankulathur-603203	kattankulathur-603203	NOUN
cana-5235	4	26	,	,	PUNCT
cana-5235	4	27	tamilnadu	tamilnadu	NOUN
cana-5235	4	28	,	,	PUNCT
cana-5235	4	29	india	india	PROPN
cana-5235	4	30	.	.	PUNCT
cana-5235	5	1	karthickmaths007@gmail.com	karthickmaths007@gmail.com	X
cana-5235	5	2	3	3	NUM
cana-5235	5	3	department	department	NOUN
cana-5235	5	4	of	of	ADP
cana-5235	5	5	mathematics	mathematic	NOUN
cana-5235	5	6	,	,	PUNCT
cana-5235	5	7	vels	vels	PROPN
cana-5235	5	8	institute	institute	PROPN
cana-5235	5	9	of	of	ADP
cana-5235	5	10	science	science	NOUN
cana-5235	5	11	,	,	PUNCT
cana-5235	5	12	technology	technology	NOUN
cana-5235	5	13	and	and	CCONJ
cana-5235	5	14	advanced	advanced	ADJ
cana-5235	5	15	studies	study	NOUN
cana-5235	5	16	,	,	PUNCT
cana-5235	5	17	chennai	chennai	PROPN
cana-5235	5	18	,	,	PUNCT
cana-5235	5	19	tamilnadu	tamilnadu	NOUN
cana-5235	5	20	,	,	PUNCT
cana-5235	5	21	india	india	PROPN
cana-5235	5	22	.	.	PROPN
cana-5235	5	23	jayaram07maths@gmail.com	jayaram07maths@gmail.com	X
cana-5235	6	1	corresponding	correspond	VERB
cana-5235	6	2	author	author	NOUN
cana-5235	6	3	:	:	PUNCT
cana-5235	6	4	karthickmaths007@gmail.com	karthickmaths007@gmail.com	X
cana-5235	6	5	article	article	NOUN
cana-5235	6	6	history	history	NOUN
cana-5235	6	7	:	:	PUNCT
cana-5235	6	8	received	receive	VERB
cana-5235	6	9	:	:	PUNCT
cana-5235	6	10	12	12	NUM
cana-5235	6	11	-	-	SYM
cana-5235	6	12	01	01	NUM
cana-5235	6	13	-	-	PUNCT
cana-5235	6	14	2025	2025	NUM
cana-5235	6	15	revised	revise	VERB
cana-5235	6	16	:	:	PUNCT
cana-5235	6	17	15	15	NUM
cana-5235	6	18	-	-	NUM
cana-5235	6	19	02	02	NUM
cana-5235	6	20	-	-	PUNCT
cana-5235	6	21	2025	2025	NUM
cana-5235	6	22	accepted	accept	VERB
cana-5235	6	23	:	:	PUNCT
cana-5235	6	24	01	01	NUM
cana-5235	6	25	-	-	SYM
cana-5235	6	26	03	03	NUM
cana-5235	6	27	-	-	PUNCT
cana-5235	6	28	2025	2025	NUM
cana-5235	6	29	abstract	abstract	NOUN
cana-5235	6	30	:	:	PUNCT
cana-5235	6	31	the	the	DET
cana-5235	6	32	impact	impact	NOUN
cana-5235	6	33	of	of	ADP
cana-5235	6	34	an	an	DET
cana-5235	6	35	insoluble	insoluble	ADJ
cana-5235	6	36	surfactant	surfactant	NOUN
cana-5235	6	37	on	on	ADP
cana-5235	6	38	the	the	DET
cana-5235	6	39	free	free	ADJ
cana-5235	6	40	surface	surface	NOUN
cana-5235	6	41	of	of	ADP
cana-5235	6	42	a	a	DET
cana-5235	6	43	two	two	NUM
cana-5235	6	44	-	-	PUNCT
cana-5235	6	45	layer	layer	NOUN
cana-5235	6	46	fluid	fluid	NOUN
cana-5235	6	47	flowing	flow	VERB
cana-5235	6	48	down	down	ADP
cana-5235	6	49	an	an	DET
cana-5235	6	50	inclined	inclined	ADJ
cana-5235	6	51	slippery	slippery	ADJ
cana-5235	6	52	plane	plane	NOUN
cana-5235	6	53	is	be	AUX
cana-5235	6	54	analyzed	analyze	VERB
cana-5235	6	55	under	under	ADP
cana-5235	6	56	external	external	ADJ
cana-5235	6	57	shear	shear	NOUN
cana-5235	6	58	stress	stress	NOUN
cana-5235	6	59	.	.	PUNCT
cana-5235	7	1	the	the	DET
cana-5235	7	2	flow	flow	NOUN
cana-5235	7	3	dynamics	dynamic	NOUN
cana-5235	7	4	in	in	ADP
cana-5235	7	5	both	both	DET
cana-5235	7	6	layers	layer	NOUN
cana-5235	7	7	are	be	AUX
cana-5235	7	8	governed	govern	VERB
cana-5235	7	9	by	by	ADP
cana-5235	7	10	the	the	DET
cana-5235	7	11	navier	navier	NOUN
cana-5235	7	12	-	-	PUNCT
cana-5235	7	13	stokes	stoke	NOUN
cana-5235	7	14	equations	equation	NOUN
cana-5235	7	15	,	,	PUNCT
cana-5235	7	16	with	with	SCONJ
cana-5235	7	17	shear	shear	NOUN
cana-5235	7	18	stress	stress	NOUN
cana-5235	7	19	applied	apply	VERB
cana-5235	7	20	to	to	ADP
cana-5235	7	21	the	the	DET
cana-5235	7	22	upper	upper	ADJ
cana-5235	7	23	layer	layer	NOUN
cana-5235	7	24	.	.	PUNCT
cana-5235	8	1	using	use	VERB
cana-5235	8	2	perturbation	perturbation	NOUN
cana-5235	8	3	and	and	CCONJ
cana-5235	8	4	normal	normal	ADJ
cana-5235	8	5	-	-	PUNCT
cana-5235	8	6	mode	mode	NOUN
cana-5235	8	7	analysis	analysis	NOUN
cana-5235	8	8	,	,	PUNCT
cana-5235	8	9	the	the	DET
cana-5235	8	10	governing	govern	VERB
cana-5235	8	11	equations	equation	NOUN
cana-5235	8	12	and	and	CCONJ
cana-5235	8	13	boundary	boundary	ADJ
cana-5235	8	14	conditions	condition	NOUN
cana-5235	8	15	are	be	AUX
cana-5235	8	16	transformed	transform	VERB
cana-5235	8	17	into	into	ADP
cana-5235	8	18	the	the	DET
cana-5235	8	19	orr	orr	PROPN
cana-5235	8	20	-	-	PUNCT
cana-5235	8	21	sommerfeld	sommerfeld	ADJ
cana-5235	8	22	system	system	NOUN
cana-5235	8	23	and	and	CCONJ
cana-5235	8	24	solved	solve	VERB
cana-5235	8	25	via	via	ADP
cana-5235	8	26	the	the	DET
cana-5235	8	27	spectral	spectral	ADJ
cana-5235	8	28	collocation	collocation	NOUN
cana-5235	8	29	method	method	NOUN
cana-5235	8	30	.	.	PUNCT
cana-5235	9	1	the	the	DET
cana-5235	9	2	study	study	NOUN
cana-5235	9	3	reveals	reveal	VERB
cana-5235	9	4	the	the	DET
cana-5235	9	5	presence	presence	NOUN
cana-5235	9	6	of	of	ADP
cana-5235	9	7	an	an	DET
cana-5235	9	8	unstable	unstable	ADJ
cana-5235	9	9	yih	yih	NOUN
cana-5235	9	10	mode	mode	NOUN
cana-5235	9	11	due	due	ADP
cana-5235	9	12	to	to	ADP
cana-5235	9	13	the	the	DET
cana-5235	9	14	free	free	ADJ
cana-5235	9	15	surface	surface	NOUN
cana-5235	9	16	.	.	PUNCT
cana-5235	10	1	this	this	DET
cana-5235	10	2	instability	instability	NOUN
cana-5235	10	3	is	be	AUX
cana-5235	10	4	suppressed	suppress	VERB
cana-5235	10	5	by	by	ADP
cana-5235	10	6	the	the	DET
cana-5235	10	7	marangoni	marangoni	NOUN
cana-5235	10	8	effect	effect	NOUN
cana-5235	10	9	,	,	PUNCT
cana-5235	10	10	which	which	PRON
cana-5235	10	11	arises	arise	VERB
cana-5235	10	12	from	from	ADP
cana-5235	10	13	the	the	DET
cana-5235	10	14	surfactant	surfactant	NOUN
cana-5235	10	15	-	-	PUNCT
cana-5235	10	16	induced	induce	VERB
cana-5235	10	17	surface	surface	NOUN
cana-5235	10	18	tension	tension	NOUN
cana-5235	10	19	gradient	gradient	NOUN
cana-5235	10	20	.	.	PUNCT
cana-5235	11	1	the	the	DET
cana-5235	11	2	marangoni	marangoni	NOUN
cana-5235	11	3	mode	mode	NOUN
cana-5235	11	4	stabilizes	stabilize	VERB
cana-5235	11	5	the	the	DET
cana-5235	11	6	interface	interface	NOUN
cana-5235	11	7	by	by	ADP
cana-5235	11	8	counteracting	counteract	VERB
cana-5235	11	9	perturbations	perturbation	NOUN
cana-5235	11	10	.	.	PUNCT
cana-5235	12	1	however	however	ADV
cana-5235	12	2	,	,	PUNCT
cana-5235	12	3	as	as	ADP
cana-5235	12	4	the	the	DET
cana-5235	12	5	external	external	ADJ
cana-5235	12	6	shear	shear	NOUN
cana-5235	12	7	stress	stress	NOUN
cana-5235	12	8	increases	increase	NOUN
cana-5235	12	9	,	,	PUNCT
cana-5235	12	10	the	the	DET
cana-5235	12	11	stabilizing	stabilize	VERB
cana-5235	12	12	effect	effect	NOUN
cana-5235	12	13	of	of	ADP
cana-5235	12	14	the	the	DET
cana-5235	12	15	marangoni	marangoni	NOUN
cana-5235	12	16	mode	mode	NOUN
cana-5235	12	17	weakens	weaken	VERB
cana-5235	12	18	.	.	PUNCT
cana-5235	13	1	beyond	beyond	ADP
cana-5235	13	2	a	a	DET
cana-5235	13	3	certain	certain	ADJ
cana-5235	13	4	threshold	threshold	NOUN
cana-5235	13	5	,	,	PUNCT
cana-5235	13	6	the	the	DET
cana-5235	13	7	marangoni	marangoni	NOUN
cana-5235	13	8	mode	mode	NOUN
cana-5235	13	9	destabilizes	destabilize	VERB
cana-5235	13	10	,	,	PUNCT
cana-5235	13	11	leading	lead	VERB
cana-5235	13	12	to	to	ADP
cana-5235	13	13	interfacial	interfacial	ADJ
cana-5235	13	14	disturbances	disturbance	NOUN
cana-5235	13	15	.	.	PUNCT
cana-5235	14	1	this	this	DET
cana-5235	14	2	study	study	NOUN
cana-5235	14	3	highlights	highlight	VERB
cana-5235	14	4	the	the	DET
cana-5235	14	5	interplay	interplay	NOUN
cana-5235	14	6	between	between	ADP
cana-5235	14	7	surfactants	surfactant	NOUN
cana-5235	14	8	,	,	PUNCT
cana-5235	14	9	shear	shear	NOUN
cana-5235	14	10	stress	stress	NOUN
cana-5235	14	11	,	,	PUNCT
cana-5235	14	12	and	and	CCONJ
cana-5235	14	13	hydrodynamic	hydrodynamic	ADJ
cana-5235	14	14	stability	stability	NOUN
cana-5235	14	15	.	.	PUNCT
cana-5235	15	1	the	the	DET
cana-5235	15	2	findings	finding	NOUN
cana-5235	15	3	have	have	VERB
cana-5235	15	4	applications	application	NOUN
cana-5235	15	5	in	in	ADP
cana-5235	15	6	coating	coating	NOUN
cana-5235	15	7	processes	process	NOUN
cana-5235	15	8	,	,	PUNCT
cana-5235	15	9	microfluidics	microfluidic	NOUN
cana-5235	15	10	,	,	PUNCT
cana-5235	15	11	and	and	CCONJ
cana-5235	15	12	geophysical	geophysical	ADJ
cana-5235	15	13	fluid	fluid	NOUN
cana-5235	15	14	dynamics	dynamic	NOUN
cana-5235	15	15	.	.	PUNCT
cana-5235	16	1	keywords	keyword	NOUN
cana-5235	16	2	:	:	PUNCT
cana-5235	16	3	hydrodynamic	hydrodynamic	ADJ
cana-5235	16	4	stability	stability	NOUN
cana-5235	16	5	,	,	PUNCT
cana-5235	16	6	two	two	NUM
cana-5235	16	7	-	-	PUNCT
cana-5235	16	8	layer	layer	NOUN
cana-5235	16	9	fluid	fluid	NOUN
cana-5235	16	10	,	,	PUNCT
cana-5235	16	11	insoluble	insoluble	ADJ
cana-5235	16	12	surfactant	surfactant	NOUN
cana-5235	16	13	,	,	PUNCT
cana-5235	16	14	orrsommerfeld	orrsommerfeld	NOUN
cana-5235	16	15	,	,	PUNCT
cana-5235	16	16	marangoni	marangoni	ADJ
cana-5235	16	17	number	number	NOUN
cana-5235	16	18	,	,	PUNCT
cana-5235	16	19	shear	shear	NOUN
cana-5235	16	20	stress	stress	NOUN
cana-5235	16	21	.	.	PUNCT
cana-5235	17	1	ams	am	NOUN
cana-5235	17	2	subject	subject	ADJ
cana-5235	17	3	classification	classification	NOUN
cana-5235	17	4	:	:	PUNCT
cana-5235	17	5	76e05	76e05	NUM
cana-5235	17	6	,	,	PUNCT
cana-5235	17	7	76e06	76e06	NUM
cana-5235	17	8	,	,	PUNCT
cana-5235	17	9	76e09	76e09	NUM
cana-5235	17	10	,	,	PUNCT
cana-5235	17	11	76e25	76e25	NUM
cana-5235	17	12	,	,	PUNCT
cana-5235	17	13	76e30	76e30	NUM
cana-5235	17	14	1	1	NUM
cana-5235	17	15	.	.	PUNCT
cana-5235	17	16	introduction	introduction	NOUN
cana-5235	17	17	the	the	DET
cana-5235	17	18	hydrodynamic	hydrodynamic	ADJ
cana-5235	17	19	instability	instability	NOUN
cana-5235	17	20	of	of	ADP
cana-5235	17	21	falling	fall	VERB
cana-5235	17	22	flow	flow	NOUN
cana-5235	17	23	models	model	NOUN
cana-5235	17	24	is	be	AUX
cana-5235	17	25	a	a	DET
cana-5235	17	26	topic	topic	NOUN
cana-5235	17	27	of	of	ADP
cana-5235	17	28	much	much	ADJ
cana-5235	17	29	interest	interest	NOUN
cana-5235	17	30	because	because	SCONJ
cana-5235	17	31	of	of	ADP
cana-5235	17	32	its	its	PRON
cana-5235	17	33	wide	wide	ADJ
cana-5235	17	34	range	range	NOUN
cana-5235	17	35	of	of	ADP
cana-5235	17	36	applications	application	NOUN
cana-5235	17	37	in	in	ADP
cana-5235	17	38	the	the	DET
cana-5235	17	39	chemical	chemical	NOUN
cana-5235	17	40	and	and	CCONJ
cana-5235	17	41	coating	coating	NOUN
cana-5235	17	42	industries	industry	NOUN
cana-5235	18	1	[	[	X
cana-5235	18	2	6	6	NUM
cana-5235	18	3	,	,	PUNCT
cana-5235	18	4	26	26	NUM
cana-5235	18	5	]	]	PUNCT
cana-5235	18	6	,	,	PUNCT
cana-5235	18	7	as	as	ADV
cana-5235	18	8	well	well	ADV
cana-5235	18	9	as	as	ADP
cana-5235	18	10	in	in	ADP
cana-5235	18	11	countless	countless	ADJ
cana-5235	18	12	other	other	ADJ
cana-5235	18	13	industrial	industrial	ADJ
cana-5235	18	14	and	and	CCONJ
cana-5235	18	15	natural	natural	ADJ
cana-5235	18	16	settings	setting	NOUN
cana-5235	18	17	[	[	X
cana-5235	18	18	27	27	NUM
cana-5235	18	19	,	,	PUNCT
cana-5235	18	20	31	31	NUM
cana-5235	18	21	]	]	PUNCT
cana-5235	18	22	.	.	PUNCT
cana-5235	19	1	in	in	ADP
cana-5235	19	2	order	order	NOUN
cana-5235	19	3	to	to	PART
cana-5235	19	4	increase	increase	VERB
cana-5235	19	5	the	the	DET
cana-5235	19	6	heat	heat	NOUN
cana-5235	19	7	and	and	CCONJ
cana-5235	19	8	mass	mass	NOUN
cana-5235	19	9	transfer	transfer	NOUN
cana-5235	19	10	rates	rate	NOUN
cana-5235	19	11	in	in	ADP
cana-5235	19	12	process	process	NOUN
cana-5235	19	13	equipment	equipment	NOUN
cana-5235	19	14	,	,	PUNCT
cana-5235	19	15	the	the	DET
cana-5235	19	16	surface	surface	NOUN
cana-5235	19	17	wave	wave	NOUN
cana-5235	19	18	is	be	AUX
cana-5235	19	19	essential	essential	ADJ
cana-5235	19	20	.	.	PUNCT
cana-5235	20	1	different	different	ADJ
cana-5235	20	2	dynamical	dynamical	ADJ
cana-5235	20	3	features	feature	NOUN
cana-5235	20	4	,	,	PUNCT
cana-5235	20	5	referred	refer	VERB
cana-5235	20	6	to	to	ADP
cana-5235	20	7	as	as	ADP
cana-5235	20	8	free	free	ADJ
cana-5235	20	9	surface	surface	NOUN
cana-5235	20	10	instabilities	instability	NOUN
cana-5235	20	11	,	,	PUNCT
cana-5235	20	12	are	be	AUX
cana-5235	20	13	observed	observe	VERB
cana-5235	20	14	on	on	ADP
cana-5235	20	15	the	the	DET
cana-5235	20	16	surface	surface	NOUN
cana-5235	20	17	of	of	ADP
cana-5235	20	18	a	a	DET
cana-5235	20	19	liquid	liquid	ADJ
cana-5235	20	20	film	film	NOUN
cana-5235	20	21	[	[	X
cana-5235	20	22	19	19	NUM
cana-5235	20	23	]	]	PUNCT
cana-5235	20	24	.	.	PUNCT
cana-5235	21	1	in	in	ADP
cana-5235	21	2	recent	recent	ADJ
cana-5235	21	3	decades	decade	NOUN
cana-5235	21	4	,	,	PUNCT
cana-5235	21	5	numerous	numerous	ADJ
cana-5235	21	6	studies	study	NOUN
cana-5235	21	7	have	have	AUX
cana-5235	21	8	been	be	AUX
cana-5235	21	9	carried	carry	VERB
cana-5235	21	10	out	out	ADP
cana-5235	21	11	to	to	PART
cana-5235	21	12	reveal	reveal	VERB
cana-5235	21	13	the	the	DET
cana-5235	21	14	underlying	underlying	ADJ
cana-5235	21	15	physical	physical	ADJ
cana-5235	21	16	mechanisms	mechanism	NOUN
cana-5235	21	17	of	of	ADP
cana-5235	21	18	these	these	DET
cana-5235	21	19	instabilities	instability	NOUN
cana-5235	21	20	and	and	CCONJ
cana-5235	21	21	to	to	PART
cana-5235	21	22	offer	offer	VERB
cana-5235	21	23	various	various	ADJ
cana-5235	21	24	explicit	explicit	ADJ
cana-5235	21	25	and	and	CCONJ
cana-5235	21	26	implicit	implicit	ADJ
cana-5235	21	27	management	management	NOUN
cana-5235	21	28	strategies	strategy	NOUN
cana-5235	21	29	to	to	PART
cana-5235	21	30	either	either	CCONJ
cana-5235	21	31	enhance	enhance	VERB
cana-5235	21	32	or	or	CCONJ
cana-5235	21	33	mitigate	mitigate	VERB
cana-5235	21	34	singleor	singleor	NOUN
cana-5235	21	35	double	double	ADJ
cana-5235	21	36	-	-	PUNCT
cana-5235	21	37	layer	layer	NOUN
cana-5235	21	38	free	free	ADJ
cana-5235	21	39	surface	surface	NOUN
cana-5235	21	40	flow	flow	NOUN
cana-5235	21	41	instabilities	instability	NOUN
cana-5235	21	42	,	,	PUNCT
cana-5235	21	43	depending	depend	VERB
cana-5235	21	44	on	on	ADP
cana-5235	21	45	the	the	DET
cana-5235	21	46	applications	application	NOUN
cana-5235	21	47	[	[	X
cana-5235	21	48	24	24	NUM
cana-5235	21	49	,	,	PUNCT
cana-5235	21	50	25	25	NUM
cana-5235	21	51	]	]	PUNCT
cana-5235	21	52	.	.	PUNCT
cana-5235	22	1	controlling	control	VERB
cana-5235	22	2	the	the	DET
cana-5235	22	3	surface	surface	NOUN
cana-5235	22	4	wave	wave	NOUN
cana-5235	22	5	instability	instability	NOUN
cana-5235	22	6	of	of	ADP
cana-5235	22	7	fluid	fluid	ADJ
cana-5235	22	8	flows	flow	NOUN
cana-5235	22	9	is	be	AUX
cana-5235	22	10	required	require	VERB
cana-5235	22	11	in	in	ADP
cana-5235	22	12	a	a	DET
cana-5235	22	13	number	number	NOUN
cana-5235	22	14	of	of	ADP
cana-5235	22	15	real	real	ADJ
cana-5235	22	16	-	-	PUNCT
cana-5235	22	17	world	world	NOUN
cana-5235	22	18	situations	situation	NOUN
cana-5235	22	19	.	.	PUNCT
cana-5235	23	1	controlling	control	VERB
cana-5235	23	2	the	the	DET
cana-5235	23	3	surface	surface	NOUN
cana-5235	23	4	wave	wave	NOUN
cana-5235	23	5	communications	communication	NOUN
cana-5235	23	6	on	on	ADP
cana-5235	23	7	applied	apply	VERB
cana-5235	23	8	nonlinear	nonlinear	ADJ
cana-5235	23	9	analysis	analysis	NOUN
cana-5235	23	10	issn	issn	NOUN
cana-5235	23	11	:	:	PUNCT
cana-5235	23	12	1074	1074	NUM
cana-5235	23	13	-	-	PUNCT
cana-5235	23	14	133x	133x	NUM
cana-5235	23	15	vol	vol	VERB
cana-5235	23	16	32	32	NUM
cana-5235	23	17	no	no	NOUN
cana-5235	23	18	.	.	PUNCT
cana-5235	24	1	10s	10	NOUN
cana-5235	24	2	(	(	PUNCT
cana-5235	24	3	2025	2025	NUM
cana-5235	24	4	)	)	PUNCT
cana-5235	24	5	1324	1324	NUM
cana-5235	24	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5235	24	7	instability	instability	NOUN
cana-5235	24	8	of	of	ADP
cana-5235	24	9	fluid	fluid	ADJ
cana-5235	24	10	flows	flow	NOUN
cana-5235	24	11	is	be	AUX
cana-5235	24	12	required	require	VERB
cana-5235	24	13	in	in	ADP
cana-5235	24	14	a	a	DET
cana-5235	24	15	number	number	NOUN
cana-5235	24	16	of	of	ADP
cana-5235	24	17	real	real	ADJ
cana-5235	24	18	-	-	PUNCT
cana-5235	24	19	world	world	NOUN
cana-5235	24	20	situations	situation	NOUN
cana-5235	24	21	.	.	PUNCT
cana-5235	25	1	these	these	DET
cana-5235	25	2	situations	situation	NOUN
cana-5235	25	3	can	can	AUX
cana-5235	25	4	be	be	AUX
cana-5235	25	5	addressed	address	VERB
cana-5235	25	6	either	either	CCONJ
cana-5235	25	7	by	by	ADP
cana-5235	25	8	surface	surface	NOUN
cana-5235	25	9	-	-	PUNCT
cana-5235	25	10	active	active	ADJ
cana-5235	25	11	or	or	CCONJ
cana-5235	25	12	surface	surface	NOUN
cana-5235	25	13	-	-	PUNCT
cana-5235	25	14	inactive	inactive	ADJ
cana-5235	25	15	agents	agent	NOUN
cana-5235	25	16	depending	depend	VERB
cana-5235	25	17	on	on	ADP
cana-5235	25	18	the	the	DET
cana-5235	25	19	use	use	NOUN
cana-5235	25	20	[	[	X
cana-5235	25	21	1	1	NUM
cana-5235	25	22	,	,	PUNCT
cana-5235	25	23	4	4	NUM
cana-5235	25	24	,	,	PUNCT
cana-5235	25	25	17	17	NUM
cana-5235	25	26	]	]	PUNCT
cana-5235	25	27	.	.	PUNCT
cana-5235	26	1	for	for	ADP
cana-5235	26	2	instance	instance	NOUN
cana-5235	26	3	,	,	PUNCT
cana-5235	26	4	consistent	consistent	ADJ
cana-5235	26	5	film	film	NOUN
cana-5235	26	6	flows	flow	VERB
cana-5235	26	7	with	with	ADP
cana-5235	26	8	superposed	superpose	VERB
cana-5235	26	9	layers	layer	NOUN
cana-5235	26	10	are	be	AUX
cana-5235	26	11	essential	essential	ADJ
cana-5235	26	12	in	in	ADP
cana-5235	26	13	coating	coat	VERB
cana-5235	26	14	technology	technology	NOUN
cana-5235	26	15	to	to	PART
cana-5235	26	16	guarantee	guarantee	VERB
cana-5235	26	17	the	the	DET
cana-5235	26	18	quality	quality	NOUN
cana-5235	26	19	of	of	ADP
cana-5235	26	20	photographic	photographic	ADJ
cana-5235	26	21	films	film	NOUN
cana-5235	26	22	[	[	X
cana-5235	26	23	26	26	NUM
cana-5235	26	24	]	]	PUNCT
cana-5235	26	25	.	.	PUNCT
cana-5235	27	1	the	the	DET
cana-5235	27	2	literature	literature	NOUN
cana-5235	27	3	contains	contain	VERB
cana-5235	27	4	a	a	DET
cana-5235	27	5	vast	vast	ADJ
cana-5235	27	6	number	number	NOUN
cana-5235	27	7	of	of	ADP
cana-5235	27	8	studies	study	NOUN
cana-5235	27	9	offering	offer	VERB
cana-5235	27	10	different	different	ADJ
cana-5235	27	11	control	control	NOUN
cana-5235	27	12	tactics	tactic	NOUN
cana-5235	27	13	for	for	ADP
cana-5235	27	14	surface	surface	NOUN
cana-5235	27	15	wave	wave	NOUN
cana-5235	27	16	instability	instability	NOUN
cana-5235	27	17	of	of	ADP
cana-5235	27	18	singleor	singleor	PROPN
cana-5235	27	19	multi	multi	ADJ
cana-5235	27	20	-	-	ADJ
cana-5235	27	21	layer	layer	ADJ
cana-5235	27	22	laminar	laminar	NOUN
cana-5235	27	23	,	,	PUNCT
cana-5235	27	24	newtonian	newtonian	NOUN
cana-5235	27	25	,	,	PUNCT
cana-5235	27	26	or	or	CCONJ
cana-5235	27	27	non	non	ADJ
cana-5235	27	28	-	-	ADJ
cana-5235	27	29	newtonian	newtonian	ADJ
cana-5235	27	30	fluid	fluid	NOUN
cana-5235	27	31	flows	flow	NOUN
cana-5235	27	32	over	over	ADP
cana-5235	27	33	an	an	DET
cana-5235	27	34	inclined	inclined	ADJ
cana-5235	27	35	bed	bed	NOUN
cana-5235	27	36	[	[	X
cana-5235	27	37	20	20	NUM
cana-5235	27	38	,	,	PUNCT
cana-5235	27	39	28	28	NUM
cana-5235	27	40	]	]	PUNCT
cana-5235	27	41	.	.	PUNCT
cana-5235	28	1	adding	add	VERB
cana-5235	28	2	an	an	DET
cana-5235	28	3	insoluble	insoluble	ADJ
cana-5235	28	4	surfactant	surfactant	NOUN
cana-5235	28	5	to	to	ADP
cana-5235	28	6	the	the	DET
cana-5235	28	7	fluid	fluid	ADJ
cana-5235	28	8	surface	surface	NOUN
cana-5235	28	9	as	as	ADP
cana-5235	28	10	a	a	DET
cana-5235	28	11	surface	surface	NOUN
cana-5235	28	12	-	-	PUNCT
cana-5235	28	13	active	active	ADJ
cana-5235	28	14	agent	agent	NOUN
cana-5235	28	15	is	be	AUX
cana-5235	28	16	one	one	NUM
cana-5235	28	17	method	method	NOUN
cana-5235	28	18	of	of	ADP
cana-5235	28	19	managing	manage	VERB
cana-5235	28	20	the	the	DET
cana-5235	28	21	instability	instability	NOUN
cana-5235	28	22	[	[	X
cana-5235	28	23	1	1	NUM
cana-5235	28	24	]	]	PUNCT
cana-5235	28	25	.	.	PUNCT
cana-5235	29	1	by	by	ADP
cana-5235	29	2	resolving	resolve	VERB
cana-5235	29	3	the	the	DET
cana-5235	29	4	associated	associated	ADJ
cana-5235	29	5	orr	orr	PROPN
cana-5235	29	6	-	-	PUNCT
cana-5235	29	7	sommerfeld	sommerfeld	ADJ
cana-5235	29	8	boundary	boundary	ADJ
cana-5235	29	9	value	value	NOUN
cana-5235	29	10	problem	problem	NOUN
cana-5235	29	11	,	,	PUNCT
cana-5235	29	12	blyth	blyth	PROPN
cana-5235	29	13	and	and	CCONJ
cana-5235	29	14	pozrikidis	pozrikidi	NOUN
cana-5235	30	1	[	[	X
cana-5235	30	2	4	4	NUM
cana-5235	30	3	]	]	PUNCT
cana-5235	30	4	discovered	discover	VERB
cana-5235	30	5	that	that	SCONJ
cana-5235	30	6	the	the	DET
cana-5235	30	7	local	local	ADJ
cana-5235	30	8	variation	variation	NOUN
cana-5235	30	9	in	in	ADP
cana-5235	30	10	surface	surface	NOUN
cana-5235	30	11	tension	tension	NOUN
cana-5235	30	12	caused	cause	VERB
cana-5235	30	13	by	by	ADP
cana-5235	30	14	the	the	DET
cana-5235	30	15	surfactant	surfactant	ADJ
cana-5235	30	16	agent	agent	NOUN
cana-5235	30	17	is	be	AUX
cana-5235	30	18	the	the	DET
cana-5235	30	19	source	source	NOUN
cana-5235	30	20	of	of	ADP
cana-5235	30	21	the	the	DET
cana-5235	30	22	surfactant	surfactant	ADJ
cana-5235	30	23	mode	mode	NOUN
cana-5235	30	24	,	,	PUNCT
cana-5235	30	25	also	also	ADV
cana-5235	30	26	known	know	VERB
cana-5235	30	27	as	as	ADP
cana-5235	30	28	the	the	DET
cana-5235	30	29	marangoni	marangoni	NOUN
cana-5235	30	30	mode	mode	NOUN
cana-5235	30	31	,	,	PUNCT
cana-5235	30	32	connected	connect	VERB
cana-5235	30	33	with	with	ADP
cana-5235	30	34	the	the	DET
cana-5235	30	35	surfactant	surfactant	NOUN
cana-5235	30	36	.	.	PUNCT
cana-5235	31	1	faruq	faruq	PROPN
cana-5235	31	2	ahmad	ahmad	PROPN
cana-5235	31	3	bhat	bhat	PROPN
cana-5235	31	4	et	et	PROPN
cana-5235	31	5	al	al	PROPN
cana-5235	31	6	.	.	PUNCT
cana-5235	32	1	[	[	X
cana-5235	32	2	2	2	NUM
cana-5235	32	3	]	]	PUNCT
cana-5235	32	4	demonstrated	demonstrate	VERB
cana-5235	32	5	the	the	DET
cana-5235	32	6	influence	influence	NOUN
cana-5235	32	7	of	of	ADP
cana-5235	32	8	surfactants	surfactant	NOUN
cana-5235	32	9	on	on	ADP
cana-5235	32	10	the	the	DET
cana-5235	32	11	stability	stability	NOUN
cana-5235	32	12	of	of	ADP
cana-5235	32	13	the	the	DET
cana-5235	32	14	yih	yih	NOUN
cana-5235	32	15	mode	mode	NOUN
cana-5235	32	16	using	use	VERB
cana-5235	32	17	an	an	DET
cana-5235	32	18	insoluble	insoluble	ADJ
cana-5235	32	19	surfactant	surfactant	NOUN
cana-5235	32	20	at	at	ADP
cana-5235	32	21	the	the	DET
cana-5235	32	22	single	single	ADJ
cana-5235	32	23	-	-	PUNCT
cana-5235	32	24	layer	layer	NOUN
cana-5235	32	25	fluid	fluid	ADJ
cana-5235	32	26	surface	surface	NOUN
cana-5235	32	27	.	.	PUNCT
cana-5235	33	1	for	for	ADP
cana-5235	33	2	a	a	DET
cana-5235	33	3	number	number	NOUN
cana-5235	33	4	of	of	ADP
cana-5235	33	5	applications	application	NOUN
cana-5235	33	6	,	,	PUNCT
cana-5235	33	7	this	this	PRON
cana-5235	33	8	is	be	AUX
cana-5235	33	9	highly	highly	ADV
cana-5235	33	10	significant	significant	ADJ
cana-5235	33	11	in	in	ADP
cana-5235	33	12	the	the	DET
cana-5235	33	13	scientific	scientific	ADJ
cana-5235	33	14	community	community	NOUN
cana-5235	33	15	[	[	X
cana-5235	33	16	8	8	NUM
cana-5235	33	17	]	]	PUNCT
cana-5235	33	18	.	.	PUNCT
cana-5235	34	1	in	in	ADP
cana-5235	34	2	addition	addition	NOUN
cana-5235	34	3	to	to	ADP
cana-5235	34	4	the	the	DET
cana-5235	34	5	instability	instability	NOUN
cana-5235	34	6	management	management	NOUN
cana-5235	34	7	method	method	NOUN
cana-5235	34	8	mentioned	mention	VERB
cana-5235	34	9	above	above	ADV
cana-5235	34	10	,	,	PUNCT
cana-5235	34	11	another	another	DET
cana-5235	34	12	control	control	NOUN
cana-5235	34	13	technique	technique	NOUN
cana-5235	34	14	to	to	PART
cana-5235	34	15	stabilize	stabilize	VERB
cana-5235	34	16	the	the	DET
cana-5235	34	17	most	most	ADV
cana-5235	34	18	unstable	unstable	ADJ
cana-5235	34	19	modes	mode	NOUN
cana-5235	34	20	is	be	AUX
cana-5235	34	21	to	to	PART
cana-5235	34	22	insert	insert	VERB
cana-5235	34	23	a	a	DET
cana-5235	34	24	floating	float	VERB
cana-5235	34	25	flexible	flexible	ADJ
cana-5235	34	26	membrane	membrane	NOUN
cana-5235	34	27	or	or	CCONJ
cana-5235	34	28	plate	plate	NOUN
cana-5235	34	29	at	at	ADP
cana-5235	34	30	the	the	DET
cana-5235	34	31	top	top	ADJ
cana-5235	34	32	surface	surface	NOUN
cana-5235	34	33	.	.	PUNCT
cana-5235	35	1	in	in	ADP
cana-5235	35	2	accordance	accordance	NOUN
cana-5235	35	3	with	with	ADP
cana-5235	35	4	the	the	DET
cana-5235	35	5	aforementioned	aforementioned	ADJ
cana-5235	35	6	concepts	concept	NOUN
cana-5235	35	7	,	,	PUNCT
cana-5235	35	8	selvan	selvan	NOUN
cana-5235	35	9	et	et	PROPN
cana-5235	35	10	al	al	PROPN
cana-5235	35	11	.	.	PUNCT
cana-5235	36	1	[	[	X
cana-5235	36	2	28	28	NUM
cana-5235	36	3	]	]	PUNCT
cana-5235	36	4	examined	examine	VERB
cana-5235	36	5	the	the	DET
cana-5235	36	6	use	use	NOUN
cana-5235	36	7	of	of	ADP
cana-5235	36	8	a	a	DET
cana-5235	36	9	floating	float	VERB
cana-5235	36	10	,	,	PUNCT
cana-5235	36	11	flexible	flexible	ADJ
cana-5235	36	12	plate	plate	NOUN
cana-5235	36	13	to	to	PART
cana-5235	36	14	control	control	VERB
cana-5235	36	15	hydrodynamic	hydrodynamic	ADJ
cana-5235	36	16	instability	instability	NOUN
cana-5235	36	17	in	in	ADP
cana-5235	36	18	both	both	CCONJ
cana-5235	36	19	linear	linear	ADJ
cana-5235	36	20	and	and	CCONJ
cana-5235	36	21	nonlinear	nonlinear	ADJ
cana-5235	36	22	regimes	regime	NOUN
cana-5235	36	23	at	at	ADP
cana-5235	36	24	the	the	DET
cana-5235	36	25	surface	surface	NOUN
cana-5235	36	26	of	of	ADP
cana-5235	36	27	a	a	DET
cana-5235	36	28	gravity	gravity	NOUN
cana-5235	36	29	-	-	PUNCT
cana-5235	36	30	viscous	viscous	ADJ
cana-5235	36	31	liquid	liquid	ADJ
cana-5235	36	32	film	film	NOUN
cana-5235	36	33	over	over	ADP
cana-5235	36	34	a	a	DET
cana-5235	36	35	rigid	rigid	ADJ
cana-5235	36	36	substrate	substrate	NOUN
cana-5235	36	37	.	.	PUNCT
cana-5235	37	1	the	the	DET
cana-5235	37	2	authors	author	NOUN
cana-5235	37	3	observed	observe	VERB
cana-5235	37	4	that	that	SCONJ
cana-5235	37	5	the	the	DET
cana-5235	37	6	instability	instability	NOUN
cana-5235	37	7	mechanism	mechanism	NOUN
cana-5235	37	8	of	of	ADP
cana-5235	37	9	the	the	DET
cana-5235	37	10	floating	float	VERB
cana-5235	37	11	elastic	elastic	ADJ
cana-5235	37	12	membrane	membrane	NOUN
cana-5235	37	13	is	be	AUX
cana-5235	37	14	the	the	DET
cana-5235	37	15	same	same	ADJ
cana-5235	37	16	as	as	ADP
cana-5235	37	17	the	the	DET
cana-5235	37	18	marangoni	marangoni	NOUN
cana-5235	37	19	mechanism	mechanism	NOUN
cana-5235	37	20	of	of	ADP
cana-5235	37	21	a	a	DET
cana-5235	37	22	single	single	ADJ
cana-5235	37	23	-	-	PUNCT
cana-5235	37	24	layer	layer	NOUN
cana-5235	37	25	falling	fall	VERB
cana-5235	37	26	liquid	liquid	ADJ
cana-5235	37	27	film	film	NOUN
cana-5235	37	28	polluted	pollute	VERB
cana-5235	37	29	by	by	ADP
cana-5235	37	30	surfactants	surfactant	NOUN
cana-5235	37	31	.	.	PUNCT
cana-5235	38	1	their	their	PRON
cana-5235	38	2	research	research	NOUN
cana-5235	38	3	verified	verify	VERB
cana-5235	38	4	that	that	SCONJ
cana-5235	38	5	,	,	PUNCT
cana-5235	38	6	in	in	ADP
cana-5235	38	7	situations	situation	NOUN
cana-5235	38	8	where	where	SCONJ
cana-5235	38	9	the	the	DET
cana-5235	38	10	compressive	compressive	ADJ
cana-5235	38	11	force	force	NOUN
cana-5235	38	12	is	be	AUX
cana-5235	38	13	either	either	CCONJ
cana-5235	38	14	absent	absent	ADJ
cana-5235	38	15	or	or	CCONJ
cana-5235	38	16	present	present	ADJ
cana-5235	38	17	,	,	PUNCT
cana-5235	38	18	the	the	DET
cana-5235	38	19	flexible	flexible	ADJ
cana-5235	38	20	plate	plate	NOUN
cana-5235	38	21	on	on	ADP
cana-5235	38	22	a	a	DET
cana-5235	38	23	falling	fall	VERB
cana-5235	38	24	fluid	fluid	ADJ
cana-5235	38	25	surface	surface	NOUN
cana-5235	38	26	might	might	AUX
cana-5235	38	27	be	be	AUX
cana-5235	38	28	employed	employ	VERB
cana-5235	38	29	as	as	ADP
cana-5235	38	30	a	a	DET
cana-5235	38	31	substitute	substitute	NOUN
cana-5235	38	32	for	for	ADP
cana-5235	38	33	passive	passive	ADJ
cana-5235	38	34	or	or	CCONJ
cana-5235	38	35	active	active	ADJ
cana-5235	38	36	control	control	NOUN
cana-5235	38	37	.	.	PUNCT
cana-5235	39	1	the	the	DET
cana-5235	39	2	orr	orr	PROPN
cana-5235	39	3	-	-	PUNCT
cana-5235	39	4	sommerfeld	sommerfeld	VERB
cana-5235	39	5	eigenvalue	eigenvalue	NOUN
cana-5235	39	6	problem	problem	NOUN
cana-5235	39	7	obtained	obtain	VERB
cana-5235	39	8	by	by	ADP
cana-5235	39	9	the	the	DET
cana-5235	39	10	authors	author	NOUN
cana-5235	39	11	was	be	AUX
cana-5235	39	12	solved	solve	VERB
cana-5235	39	13	numerically	numerically	ADV
cana-5235	39	14	using	use	VERB
cana-5235	39	15	the	the	DET
cana-5235	39	16	chebyshev	chebyshev	NOUN
cana-5235	39	17	collocation	collocation	NOUN
cana-5235	39	18	method	method	NOUN
cana-5235	39	19	,	,	PUNCT
cana-5235	39	20	and	and	CCONJ
cana-5235	39	21	it	it	PRON
cana-5235	39	22	was	be	AUX
cana-5235	39	23	established	establish	VERB
cana-5235	39	24	that	that	SCONJ
cana-5235	39	25	the	the	DET
cana-5235	39	26	floating	float	VERB
cana-5235	39	27	elastic	elastic	ADJ
cana-5235	39	28	plate	plate	NOUN
cana-5235	39	29	suppresses	suppress	VERB
cana-5235	39	30	the	the	DET
cana-5235	39	31	unstable	unstable	ADJ
cana-5235	39	32	yih	yih	NOUN
cana-5235	39	33	mode	mode	NOUN
cana-5235	40	1	[	[	X
cana-5235	40	2	32	32	NUM
cana-5235	40	3	]	]	PUNCT
cana-5235	40	4	,	,	PUNCT
cana-5235	40	5	which	which	PRON
cana-5235	40	6	is	be	AUX
cana-5235	40	7	connected	connect	VERB
cana-5235	40	8	to	to	ADP
cana-5235	40	9	the	the	DET
cana-5235	40	10	disturbance	disturbance	NOUN
cana-5235	40	11	wave	wave	NOUN
cana-5235	40	12	superimposed	superimpose	VERB
cana-5235	40	13	on	on	ADP
cana-5235	40	14	the	the	DET
cana-5235	40	15	liquid	liquid	ADJ
cana-5235	40	16	surface	surface	NOUN
cana-5235	40	17	.	.	PUNCT
cana-5235	41	1	physically	physically	ADV
cana-5235	41	2	,	,	PUNCT
cana-5235	41	3	by	by	ADP
cana-5235	41	4	decreasing	decrease	VERB
cana-5235	41	5	the	the	DET
cana-5235	41	6	flow	flow	NOUN
cana-5235	41	7	velocity	velocity	NOUN
cana-5235	41	8	in	in	ADP
cana-5235	41	9	the	the	DET
cana-5235	41	10	boundary	boundary	ADJ
cana-5235	41	11	layer	layer	NOUN
cana-5235	41	12	beneath	beneath	ADP
cana-5235	41	13	the	the	DET
cana-5235	41	14	plate	plate	NOUN
cana-5235	41	15	,	,	PUNCT
cana-5235	41	16	the	the	DET
cana-5235	41	17	elastic	elastic	ADJ
cana-5235	41	18	membrane	membrane	NOUN
cana-5235	41	19	prevents	prevent	VERB
cana-5235	41	20	the	the	DET
cana-5235	41	21	laminar	laminar	ADJ
cana-5235	41	22	flow	flow	NOUN
cana-5235	41	23	from	from	ADP
cana-5235	41	24	transitioning	transition	VERB
cana-5235	41	25	to	to	ADP
cana-5235	41	26	turbulence	turbulence	NOUN
cana-5235	41	27	.	.	PUNCT
cana-5235	42	1	moreover	moreover	ADV
cana-5235	42	2	,	,	PUNCT
cana-5235	42	3	imposing	impose	VERB
cana-5235	42	4	an	an	DET
cana-5235	42	5	external	external	ADJ
cana-5235	42	6	shear	shear	NOUN
cana-5235	42	7	at	at	ADP
cana-5235	42	8	the	the	DET
cana-5235	42	9	free	free	ADJ
cana-5235	42	10	surface	surface	NOUN
cana-5235	42	11	is	be	AUX
cana-5235	42	12	another	another	DET
cana-5235	42	13	method	method	NOUN
cana-5235	42	14	for	for	ADP
cana-5235	42	15	managing	manage	VERB
cana-5235	42	16	the	the	DET
cana-5235	42	17	energy	energy	NOUN
cana-5235	42	18	of	of	ADP
cana-5235	42	19	surface	surface	NOUN
cana-5235	42	20	waves	wave	NOUN
cana-5235	42	21	[	[	X
cana-5235	42	22	20	20	NUM
cana-5235	42	23	]	]	PUNCT
cana-5235	42	24	.	.	PUNCT
cana-5235	43	1	physically	physically	ADV
cana-5235	43	2	,	,	PUNCT
cana-5235	43	3	this	this	DET
cana-5235	43	4	procedure	procedure	NOUN
cana-5235	43	5	can	can	AUX
cana-5235	43	6	be	be	AUX
cana-5235	43	7	used	use	VERB
cana-5235	43	8	in	in	ADP
cana-5235	43	9	the	the	DET
cana-5235	43	10	airway	airway	NOUN
cana-5235	43	11	occlusion	occlusion	NOUN
cana-5235	43	12	process	process	NOUN
cana-5235	43	13	[	[	X
cana-5235	43	14	16	16	NUM
cana-5235	43	15	]	]	PUNCT
cana-5235	43	16	.	.	PUNCT
cana-5235	44	1	another	another	DET
cana-5235	44	2	active	active	ADJ
cana-5235	44	3	mechanism	mechanism	NOUN
cana-5235	44	4	for	for	ADP
cana-5235	44	5	controlling	control	VERB
cana-5235	44	6	the	the	DET
cana-5235	44	7	yih	yih	NOUN
cana-5235	44	8	mode	mode	NOUN
cana-5235	44	9	different	different	ADV
cana-5235	44	10	from	from	ADP
cana-5235	44	11	the	the	DET
cana-5235	44	12	ones	one	NOUN
cana-5235	44	13	mentioned	mention	VERB
cana-5235	44	14	above	above	ADV
cana-5235	44	15	is	be	AUX
cana-5235	44	16	by	by	ADP
cana-5235	44	17	imposing	impose	VERB
cana-5235	44	18	shear	shear	NOUN
cana-5235	44	19	at	at	ADP
cana-5235	44	20	the	the	DET
cana-5235	44	21	free	free	ADJ
cana-5235	44	22	surface	surface	NOUN
cana-5235	44	23	,	,	PUNCT
cana-5235	44	24	the	the	DET
cana-5235	44	25	influence	influence	NOUN
cana-5235	44	26	of	of	ADP
cana-5235	44	27	the	the	DET
cana-5235	44	28	shear	shear	NOUN
cana-5235	44	29	helps	help	VERB
cana-5235	44	30	in	in	ADP
cana-5235	44	31	the	the	DET
cana-5235	44	32	dissipation	dissipation	NOUN
cana-5235	44	33	of	of	ADP
cana-5235	44	34	energy	energy	NOUN
cana-5235	44	35	at	at	ADP
cana-5235	44	36	the	the	DET
cana-5235	44	37	free	free	ADJ
cana-5235	44	38	surface	surface	NOUN
cana-5235	44	39	.	.	PUNCT
cana-5235	45	1	because	because	SCONJ
cana-5235	45	2	of	of	ADP
cana-5235	45	3	this	this	PRON
cana-5235	45	4	,	,	PUNCT
cana-5235	45	5	samanta	samanta	PROPN
cana-5235	45	6	[	[	X
cana-5235	45	7	21	21	NUM
cana-5235	45	8	]	]	PUNCT
cana-5235	45	9	investigated	investigate	VERB
cana-5235	45	10	how	how	SCONJ
cana-5235	45	11	external	external	ADJ
cana-5235	45	12	shear	shear	NOUN
cana-5235	45	13	affected	affect	VERB
cana-5235	45	14	the	the	DET
cana-5235	45	15	falling	fall	VERB
cana-5235	45	16	film	film	NOUN
cana-5235	45	17	caused	cause	VERB
cana-5235	45	18	by	by	ADP
cana-5235	45	19	gravity	gravity	NOUN
cana-5235	45	20	down	down	ADP
cana-5235	45	21	a	a	DET
cana-5235	45	22	sharp	sharp	ADJ
cana-5235	45	23	slope	slope	NOUN
cana-5235	45	24	and	and	CCONJ
cana-5235	45	25	flow	flow	NOUN
cana-5235	45	26	-	-	PUNCT
cana-5235	45	27	directed	direct	VERB
cana-5235	45	28	external	external	ADJ
cana-5235	45	29	force	force	NOUN
cana-5235	45	30	which	which	PRON
cana-5235	45	31	lowers	lower	VERB
cana-5235	45	32	the	the	DET
cana-5235	45	33	essential	essential	ADJ
cana-5235	45	34	reynolds	reynold	NOUN
cana-5235	45	35	number	number	NOUN
cana-5235	45	36	in	in	ADP
cana-5235	45	37	order	order	NOUN
cana-5235	45	38	to	to	PART
cana-5235	45	39	encourage	encourage	VERB
cana-5235	45	40	long	long	ADJ
cana-5235	45	41	wave	wave	NOUN
cana-5235	45	42	instability	instability	NOUN
cana-5235	45	43	.	.	PUNCT
cana-5235	46	1	subsequently	subsequently	ADV
cana-5235	46	2	,	,	PUNCT
cana-5235	46	3	an	an	DET
cana-5235	46	4	external	external	ADJ
cana-5235	46	5	force	force	NOUN
cana-5235	46	6	was	be	AUX
cana-5235	46	7	applied	apply	VERB
cana-5235	46	8	to	to	ADP
cana-5235	46	9	the	the	DET
cana-5235	46	10	top	top	ADJ
cana-5235	46	11	surface	surface	NOUN
cana-5235	46	12	of	of	ADP
cana-5235	46	13	a	a	DET
cana-5235	46	14	surfactant	surfactant	NOUN
cana-5235	46	15	-	-	PUNCT
cana-5235	46	16	laden	laden	ADJ
cana-5235	46	17	single	single	ADJ
cana-5235	46	18	-	-	PUNCT
cana-5235	46	19	layer	layer	NOUN
cana-5235	46	20	fluid	fluid	ADJ
cana-5235	46	21	film	film	NOUN
cana-5235	46	22	flowing	flow	VERB
cana-5235	46	23	down	down	ADP
cana-5235	46	24	a	a	DET
cana-5235	46	25	rigid	rigid	ADJ
cana-5235	46	26	bed	bed	NOUN
cana-5235	46	27	,	,	PUNCT
cana-5235	46	28	as	as	SCONJ
cana-5235	46	29	studied	study	VERB
cana-5235	46	30	by	by	ADP
cana-5235	46	31	samanta	samanta	PROPN
cana-5235	46	32	[	[	X
cana-5235	46	33	20	20	NUM
cana-5235	46	34	]	]	PUNCT
cana-5235	46	35	.	.	PUNCT
cana-5235	47	1	the	the	DET
cana-5235	47	2	authors	author	NOUN
cana-5235	47	3	examined	examine	VERB
cana-5235	47	4	how	how	SCONJ
cana-5235	47	5	wave	wave	NOUN
cana-5235	47	6	energy	energy	NOUN
cana-5235	47	7	created	create	VERB
cana-5235	47	8	by	by	ADP
cana-5235	47	9	external	external	ADJ
cana-5235	47	10	shear	shear	NOUN
cana-5235	47	11	was	be	AUX
cana-5235	47	12	attenuated	attenuate	VERB
cana-5235	47	13	using	use	VERB
cana-5235	47	14	an	an	DET
cana-5235	47	15	insoluble	insoluble	ADJ
cana-5235	47	16	surfactant	surfactant	NOUN
cana-5235	47	17	at	at	ADP
cana-5235	47	18	the	the	DET
cana-5235	47	19	fluid	fluid	ADJ
cana-5235	47	20	surface	surface	NOUN
cana-5235	47	21	.	.	PUNCT
cana-5235	48	1	in	in	ADP
cana-5235	48	2	addition	addition	NOUN
cana-5235	48	3	to	to	ADP
cana-5235	48	4	the	the	DET
cana-5235	48	5	surface	surface	NOUN
cana-5235	48	6	and	and	CCONJ
cana-5235	48	7	surfactant	surfactant	NOUN
cana-5235	48	8	modes	mode	NOUN
cana-5235	48	9	,	,	PUNCT
cana-5235	48	10	they	they	PRON
cana-5235	48	11	discovered	discover	VERB
cana-5235	48	12	the	the	DET
cana-5235	48	13	existence	existence	NOUN
cana-5235	48	14	of	of	ADP
cana-5235	48	15	a	a	DET
cana-5235	48	16	third	third	ADJ
cana-5235	48	17	mode	mode	NOUN
cana-5235	48	18	,	,	PUNCT
cana-5235	48	19	called	call	VERB
cana-5235	48	20	the	the	DET
cana-5235	48	21	shear	shear	NOUN
cana-5235	48	22	mode	mode	NOUN
cana-5235	48	23	.	.	PUNCT
cana-5235	49	1	the	the	DET
cana-5235	49	2	onset	onset	NOUN
cana-5235	49	3	of	of	ADP
cana-5235	49	4	the	the	DET
cana-5235	49	5	shear	shear	NOUN
cana-5235	49	6	mode	mode	NOUN
cana-5235	49	7	is	be	AUX
cana-5235	49	8	primarily	primarily	ADV
cana-5235	49	9	caused	cause	VERB
cana-5235	49	10	by	by	ADP
cana-5235	49	11	the	the	DET
cana-5235	49	12	inclination	inclination	NOUN
cana-5235	49	13	angle	angle	NOUN
cana-5235	49	14	and	and	CCONJ
cana-5235	49	15	large	large	ADJ
cana-5235	49	16	inertia	inertia	NOUN
cana-5235	49	17	force	force	NOUN
cana-5235	49	18	.	.	PUNCT
cana-5235	50	1	it	it	PRON
cana-5235	50	2	was	be	AUX
cana-5235	50	3	determined	determine	VERB
cana-5235	50	4	that	that	SCONJ
cana-5235	50	5	strong	strong	ADJ
cana-5235	50	6	stabilization	stabilization	NOUN
cana-5235	50	7	of	of	ADP
cana-5235	50	8	the	the	DET
cana-5235	50	9	surface	surface	NOUN
cana-5235	50	10	mode	mode	NOUN
cana-5235	50	11	is	be	AUX
cana-5235	50	12	possible	possible	ADJ
cana-5235	50	13	if	if	SCONJ
cana-5235	50	14	the	the	DET
cana-5235	50	15	applied	apply	VERB
cana-5235	50	16	force	force	NOUN
cana-5235	50	17	acts	act	VERB
cana-5235	50	18	in	in	ADP
cana-5235	50	19	the	the	DET
cana-5235	50	20	reverse	reverse	ADJ
cana-5235	50	21	flow	flow	NOUN
cana-5235	50	22	direction	direction	NOUN
cana-5235	50	23	with	with	ADP
cana-5235	50	24	a	a	DET
cana-5235	50	25	stronger	strong	ADJ
cana-5235	50	26	marangoni	marangoni	NOUN
cana-5235	50	27	force	force	NOUN
cana-5235	50	28	[	[	X
cana-5235	50	29	18	18	NUM
cana-5235	50	30	]	]	PUNCT
cana-5235	50	31	.	.	PUNCT
cana-5235	51	1	recently	recently	ADV
cana-5235	51	2	,	,	PUNCT
cana-5235	51	3	researchers	researcher	NOUN
cana-5235	51	4	have	have	AUX
cana-5235	51	5	shown	show	VERB
cana-5235	51	6	increasing	increase	VERB
cana-5235	51	7	interest	interest	NOUN
cana-5235	51	8	in	in	ADP
cana-5235	51	9	studying	study	VERB
cana-5235	51	10	interfacial	interfacial	ADJ
cana-5235	51	11	instability	instability	NOUN
cana-5235	51	12	in	in	ADP
cana-5235	51	13	doubleor	doubleor	ADJ
cana-5235	51	14	multi	multi	ADJ
cana-5235	51	15	-	-	ADJ
cana-5235	51	16	layer	layer	ADJ
cana-5235	51	17	liquid	liquid	NOUN
cana-5235	51	18	films	film	NOUN
cana-5235	51	19	influenced	influence	VERB
cana-5235	51	20	by	by	ADP
cana-5235	51	21	kinetic	kinetic	ADJ
cana-5235	51	22	factors	factor	NOUN
cana-5235	51	23	.	.	PUNCT
cana-5235	52	1	in	in	ADP
cana-5235	52	2	a	a	DET
cana-5235	52	3	single	single	ADJ
cana-5235	52	4	-	-	PUNCT
cana-5235	52	5	layer	layer	NOUN
cana-5235	52	6	falling	fall	VERB
cana-5235	52	7	film	film	NOUN
cana-5235	52	8	over	over	ADP
cana-5235	52	9	an	an	DET
cana-5235	52	10	inclined	inclined	ADJ
cana-5235	52	11	wall	wall	NOUN
cana-5235	52	12	,	,	PUNCT
cana-5235	52	13	instability	instability	NOUN
cana-5235	52	14	mainly	mainly	ADV
cana-5235	52	15	arises	arise	VERB
cana-5235	52	16	due	due	ADJ
cana-5235	52	17	to	to	ADP
cana-5235	52	18	inertial	inertial	ADJ
cana-5235	52	19	effects	effect	NOUN
cana-5235	52	20	,	,	PUNCT
cana-5235	52	21	leading	lead	VERB
cana-5235	52	22	to	to	ADP
cana-5235	52	23	surface	surface	NOUN
cana-5235	52	24	wave	wave	NOUN
cana-5235	52	25	formation	formation	NOUN
cana-5235	52	26	.	.	PUNCT
cana-5235	53	1	in	in	ADP
cana-5235	53	2	multi	multi	ADJ
cana-5235	53	3	-	-	ADJ
cana-5235	53	4	layer	layer	ADJ
cana-5235	53	5	films	film	NOUN
cana-5235	53	6	,	,	PUNCT
cana-5235	53	7	additional	additional	ADJ
cana-5235	53	8	factors	factor	NOUN
cana-5235	53	9	such	such	ADJ
cana-5235	53	10	as	as	ADP
cana-5235	53	11	viscosity	viscosity	NOUN
cana-5235	53	12	contrast	contrast	NOUN
cana-5235	53	13	,	,	PUNCT
cana-5235	53	14	density	density	NOUN
cana-5235	53	15	differences	difference	NOUN
cana-5235	53	16	,	,	PUNCT
cana-5235	53	17	and	and	CCONJ
cana-5235	53	18	interfacial	interfacial	ADJ
cana-5235	53	19	tension	tension	NOUN
cana-5235	53	20	play	play	VERB
cana-5235	53	21	a	a	DET
cana-5235	53	22	significant	significant	ADJ
cana-5235	53	23	role	role	NOUN
cana-5235	53	24	.	.	PUNCT
cana-5235	54	1	these	these	DET
cana-5235	54	2	complexities	complexity	NOUN
cana-5235	54	3	can	can	AUX
cana-5235	54	4	either	either	CCONJ
cana-5235	54	5	amplify	amplify	VERB
cana-5235	54	6	or	or	CCONJ
cana-5235	54	7	suppress	suppress	ADJ
cana-5235	54	8	disturbances	disturbance	NOUN
cana-5235	54	9	,	,	PUNCT
cana-5235	54	10	depending	depend	VERB
cana-5235	54	11	on	on	ADP
cana-5235	54	12	the	the	DET
cana-5235	54	13	flow	flow	NOUN
cana-5235	54	14	conditions	condition	NOUN
cana-5235	54	15	.	.	PUNCT
cana-5235	55	1	understanding	understand	VERB
cana-5235	55	2	these	these	DET
cana-5235	55	3	instabilities	instability	NOUN
cana-5235	55	4	is	be	AUX
cana-5235	55	5	crucial	crucial	ADJ
cana-5235	55	6	for	for	ADP
cana-5235	55	7	applications	application	NOUN
cana-5235	55	8	in	in	ADP
cana-5235	55	9	coating	coating	NOUN
cana-5235	55	10	technologies	technology	NOUN
cana-5235	55	11	,	,	PUNCT
cana-5235	55	12	microfluidics	microfluidic	NOUN
cana-5235	55	13	,	,	PUNCT
cana-5235	55	14	and	and	CCONJ
cana-5235	55	15	industrial	industrial	ADJ
cana-5235	55	16	fluid	fluid	NOUN
cana-5235	55	17	processes	process	NOUN
cana-5235	55	18	[	[	X
cana-5235	55	19	11	11	NUM
cana-5235	55	20	,	,	PUNCT
cana-5235	55	21	12	12	NUM
cana-5235	55	22	]	]	PUNCT
cana-5235	55	23	.	.	PUNCT
cana-5235	56	1	concurrently	concurrently	ADV
cana-5235	56	2	,	,	PUNCT
cana-5235	56	3	due	due	ADP
cana-5235	56	4	to	to	ADP
cana-5235	56	5	its	its	PRON
cana-5235	56	6	widespread	widespread	ADJ
cana-5235	56	7	applications	application	NOUN
cana-5235	56	8	in	in	ADP
cana-5235	56	9	various	various	ADJ
cana-5235	56	10	technical	technical	ADJ
cana-5235	56	11	and	and	CCONJ
cana-5235	56	12	chemical	chemical	NOUN
cana-5235	56	13	processes	process	NOUN
cana-5235	56	14	,	,	PUNCT
cana-5235	56	15	such	such	ADJ
cana-5235	56	16	as	as	ADP
cana-5235	56	17	liquid	liquid	NOUN
cana-5235	56	18	-	-	PUNCT
cana-5235	56	19	liquid	liquid	NOUN
cana-5235	56	20	extraction	extraction	NOUN
cana-5235	56	21	,	,	PUNCT
cana-5235	56	22	food	food	NOUN
cana-5235	56	23	manufacturing	manufacturing	NOUN
cana-5235	56	24	,	,	PUNCT
cana-5235	56	25	and	and	CCONJ
cana-5235	56	26	liquid	liquid	ADJ
cana-5235	56	27	coating	coating	NOUN
cana-5235	56	28	,	,	PUNCT
cana-5235	56	29	several	several	ADJ
cana-5235	56	30	researchers	researcher	NOUN
cana-5235	56	31	have	have	AUX
cana-5235	56	32	shown	show	VERB
cana-5235	56	33	interest	interest	NOUN
cana-5235	56	34	in	in	ADP
cana-5235	56	35	studying	study	VERB
cana-5235	56	36	instability	instability	NOUN
cana-5235	56	37	control	control	NOUN
cana-5235	56	38	mechanisms	mechanism	NOUN
cana-5235	56	39	in	in	ADP
cana-5235	56	40	double	double	ADJ
cana-5235	56	41	-	-	PUNCT
cana-5235	56	42	layer	layer	NOUN
cana-5235	56	43	fluid	fluid	NOUN
cana-5235	56	44	flow	flow	NOUN
cana-5235	56	45	systems	system	NOUN
cana-5235	56	46	[	[	X
cana-5235	56	47	10	10	NUM
cana-5235	56	48	,	,	PUNCT
cana-5235	56	49	29	29	NUM
cana-5235	56	50	,	,	PUNCT
cana-5235	56	51	30	30	NUM
cana-5235	56	52	]	]	PUNCT
cana-5235	56	53	.	.	PUNCT
cana-5235	57	1	in	in	ADP
cana-5235	57	2	communications	communication	NOUN
cana-5235	57	3	on	on	ADP
cana-5235	57	4	applied	apply	VERB
cana-5235	57	5	nonlinear	nonlinear	ADJ
cana-5235	57	6	analysis	analysis	NOUN
cana-5235	57	7	issn	issn	NOUN
cana-5235	57	8	:	:	PUNCT
cana-5235	57	9	1074	1074	NUM
cana-5235	57	10	-	-	PUNCT
cana-5235	57	11	133x	133x	NUM
cana-5235	57	12	vol	vol	VERB
cana-5235	57	13	32	32	NUM
cana-5235	57	14	no	no	NOUN
cana-5235	57	15	.	.	PUNCT
cana-5235	58	1	10s	10	NOUN
cana-5235	58	2	(	(	PUNCT
cana-5235	58	3	2025	2025	NUM
cana-5235	58	4	)	)	PUNCT
cana-5235	58	5	1325	1325	NUM
cana-5235	58	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5235	58	7	coating	coating	NOUN
cana-5235	58	8	processes	process	NOUN
cana-5235	58	9	and	and	CCONJ
cana-5235	58	10	related	related	ADJ
cana-5235	58	11	applications	application	NOUN
cana-5235	58	12	,	,	PUNCT
cana-5235	58	13	interfacial	interfacial	ADJ
cana-5235	58	14	and	and	CCONJ
cana-5235	58	15	free	free	ADJ
cana-5235	58	16	surface	surface	NOUN
cana-5235	58	17	instabilities	instability	NOUN
cana-5235	58	18	can	can	AUX
cana-5235	58	19	arise	arise	VERB
cana-5235	58	20	under	under	ADP
cana-5235	58	21	specific	specific	ADJ
cana-5235	58	22	flow	flow	NOUN
cana-5235	58	23	conditions	condition	NOUN
cana-5235	58	24	,	,	PUNCT
cana-5235	58	25	potentially	potentially	ADV
cana-5235	58	26	compromising	compromise	VERB
cana-5235	58	27	the	the	DET
cana-5235	58	28	quality	quality	NOUN
cana-5235	58	29	of	of	ADP
cana-5235	58	30	the	the	DET
cana-5235	58	31	final	final	ADJ
cana-5235	58	32	product	product	NOUN
cana-5235	58	33	.	.	PUNCT
cana-5235	59	1	effective	effective	ADJ
cana-5235	59	2	control	control	NOUN
cana-5235	59	3	of	of	ADP
cana-5235	59	4	these	these	DET
cana-5235	59	5	instabilities	instability	NOUN
cana-5235	59	6	is	be	AUX
cana-5235	59	7	therefore	therefore	ADV
cana-5235	59	8	crucial	crucial	ADJ
cana-5235	59	9	for	for	ADP
cana-5235	59	10	ensuring	ensure	VERB
cana-5235	59	11	consistency	consistency	NOUN
cana-5235	59	12	,	,	PUNCT
cana-5235	59	13	precision	precision	NOUN
cana-5235	59	14	,	,	PUNCT
cana-5235	59	15	and	and	CCONJ
cana-5235	59	16	overall	overall	ADJ
cana-5235	59	17	product	product	NOUN
cana-5235	59	18	reliability	reliability	NOUN
cana-5235	59	19	.	.	PUNCT
cana-5235	60	1	gao	gao	PROPN
cana-5235	60	2	and	and	CCONJ
cana-5235	60	3	lu	lu	PROPN
cana-5235	61	1	[	[	X
cana-5235	61	2	14	14	NUM
cana-5235	61	3	]	]	PUNCT
cana-5235	61	4	examined	examine	VERB
cana-5235	61	5	the	the	DET
cana-5235	61	6	effect	effect	NOUN
cana-5235	61	7	of	of	ADP
cana-5235	61	8	an	an	DET
cana-5235	61	9	insoluble	insoluble	ADJ
cana-5235	61	10	surfactant	surfactant	NOUN
cana-5235	61	11	on	on	ADP
cana-5235	61	12	the	the	DET
cana-5235	61	13	free	free	ADJ
cana-5235	61	14	surface	surface	NOUN
cana-5235	61	15	and	and	CCONJ
cana-5235	61	16	interface	interface	NOUN
cana-5235	61	17	in	in	ADP
cana-5235	61	18	the	the	DET
cana-5235	61	19	inertialess	inertialess	NOUN
cana-5235	61	20	limit	limit	NOUN
cana-5235	61	21	while	while	SCONJ
cana-5235	61	22	studying	study	VERB
cana-5235	61	23	a	a	DET
cana-5235	61	24	two	two	NUM
cana-5235	61	25	-	-	PUNCT
cana-5235	61	26	layer	layer	NOUN
cana-5235	61	27	system	system	NOUN
cana-5235	61	28	.	.	PUNCT
cana-5235	62	1	they	they	PRON
cana-5235	62	2	identified	identify	VERB
cana-5235	62	3	four	four	NUM
cana-5235	62	4	modes	mode	NOUN
cana-5235	62	5	but	but	CCONJ
cana-5235	62	6	primarily	primarily	ADV
cana-5235	62	7	focused	focus	VERB
cana-5235	62	8	on	on	ADP
cana-5235	62	9	the	the	DET
cana-5235	62	10	surface	surface	NOUN
cana-5235	62	11	and	and	CCONJ
cana-5235	62	12	interface	interface	NOUN
cana-5235	62	13	modes	mode	NOUN
cana-5235	62	14	.	.	PUNCT
cana-5235	63	1	their	their	PRON
cana-5235	63	2	study	study	NOUN
cana-5235	63	3	revealed	reveal	VERB
cana-5235	63	4	that	that	SCONJ
cana-5235	63	5	longwave	longwave	NOUN
cana-5235	63	6	region	region	NOUN
cana-5235	63	7	inertialess	inertialess	NOUN
cana-5235	63	8	instability	instability	NOUN
cana-5235	63	9	could	could	AUX
cana-5235	63	10	be	be	AUX
cana-5235	63	11	either	either	CCONJ
cana-5235	63	12	suppressed	suppress	VERB
cana-5235	63	13	or	or	CCONJ
cana-5235	63	14	amplified	amplify	VERB
cana-5235	63	15	by	by	ADP
cana-5235	63	16	surface	surface	NOUN
cana-5235	63	17	or	or	CCONJ
cana-5235	63	18	interfacial	interfacial	ADJ
cana-5235	63	19	surfactants	surfactant	NOUN
cana-5235	63	20	.	.	PUNCT
cana-5235	64	1	furthermore	furthermore	ADV
cana-5235	64	2	,	,	PUNCT
cana-5235	64	3	two	two	NUM
cana-5235	64	4	-	-	PUNCT
cana-5235	64	5	layer	layer	NOUN
cana-5235	64	6	flows	flow	NOUN
cana-5235	64	7	are	be	AUX
cana-5235	64	8	widely	widely	ADV
cana-5235	64	9	relevant	relevant	ADJ
cana-5235	64	10	as	as	SCONJ
cana-5235	64	11	they	they	PRON
cana-5235	64	12	occur	occur	VERB
cana-5235	64	13	in	in	ADP
cana-5235	64	14	various	various	ADJ
cana-5235	64	15	natural	natural	ADJ
cana-5235	64	16	settings	setting	NOUN
cana-5235	64	17	and	and	CCONJ
cana-5235	64	18	play	play	VERB
cana-5235	64	19	a	a	DET
cana-5235	64	20	crucial	crucial	ADJ
cana-5235	64	21	role	role	NOUN
cana-5235	64	22	in	in	ADP
cana-5235	64	23	biological	biological	ADJ
cana-5235	64	24	and	and	CCONJ
cana-5235	64	25	technical	technical	ADJ
cana-5235	64	26	systems	system	NOUN
cana-5235	64	27	,	,	PUNCT
cana-5235	64	28	including	include	VERB
cana-5235	64	29	the	the	DET
cana-5235	64	30	plastics	plastic	NOUN
cana-5235	64	31	and	and	CCONJ
cana-5235	64	32	petroleum	petroleum	NOUN
cana-5235	64	33	industries	industry	NOUN
cana-5235	64	34	[	[	X
cana-5235	64	35	7	7	NUM
cana-5235	64	36	,	,	PUNCT
cana-5235	64	37	13	13	NUM
cana-5235	64	38	,	,	PUNCT
cana-5235	64	39	15	15	NUM
cana-5235	64	40	]	]	PUNCT
cana-5235	64	41	.	.	PUNCT
cana-5235	65	1	by	by	ADP
cana-5235	65	2	analyzing	analyze	VERB
cana-5235	65	3	the	the	DET
cana-5235	65	4	effects	effect	NOUN
cana-5235	65	5	of	of	ADP
cana-5235	65	6	depth	depth	NOUN
cana-5235	65	7	ratio	ratio	NOUN
cana-5235	65	8	,	,	PUNCT
cana-5235	65	9	viscosity	viscosity	NOUN
cana-5235	65	10	ratio	ratio	NOUN
cana-5235	65	11	,	,	PUNCT
cana-5235	65	12	and	and	CCONJ
cana-5235	65	13	density	density	NOUN
cana-5235	65	14	ratio	ratio	NOUN
cana-5235	65	15	on	on	ADP
cana-5235	65	16	the	the	DET
cana-5235	65	17	fundamental	fundamental	ADJ
cana-5235	65	18	instability	instability	NOUN
cana-5235	65	19	produced	produce	VERB
cana-5235	65	20	by	by	ADP
cana-5235	65	21	surface	surface	NOUN
cana-5235	65	22	and	and	CCONJ
cana-5235	65	23	interface	interface	NOUN
cana-5235	65	24	modes	mode	NOUN
cana-5235	65	25	,	,	PUNCT
cana-5235	65	26	kao	kao	PROPN
cana-5235	66	1	[	[	X
cana-5235	66	2	13	13	NUM
cana-5235	66	3	]	]	PUNCT
cana-5235	66	4	,	,	PUNCT
cana-5235	66	5	first	first	ADV
cana-5235	66	6	introduced	introduce	VERB
cana-5235	66	7	the	the	DET
cana-5235	66	8	concept	concept	NOUN
cana-5235	66	9	of	of	ADP
cana-5235	66	10	doublelayered	doublelayered	ADJ
cana-5235	66	11	fluid	fluid	ADJ
cana-5235	66	12	flow	flow	NOUN
cana-5235	66	13	.	.	PUNCT
cana-5235	67	1	subsequently	subsequently	ADV
cana-5235	67	2	,	,	PUNCT
cana-5235	67	3	chen	chen	PROPN
cana-5235	68	1	[	[	X
cana-5235	68	2	5	5	NUM
cana-5235	68	3	]	]	PUNCT
cana-5235	68	4	investigated	investigate	VERB
cana-5235	68	5	the	the	DET
cana-5235	68	6	linear	linear	ADJ
cana-5235	68	7	stability	stability	NOUN
cana-5235	68	8	of	of	ADP
cana-5235	68	9	a	a	DET
cana-5235	68	10	double	double	ADJ
cana-5235	68	11	-	-	PUNCT
cana-5235	68	12	layered	layered	ADJ
cana-5235	68	13	falling	fall	VERB
cana-5235	68	14	film	film	NOUN
cana-5235	68	15	at	at	ADP
cana-5235	68	16	low	low	ADJ
cana-5235	68	17	reynolds	reynolds	PROPN
cana-5235	68	18	numbers	number	NOUN
cana-5235	68	19	.	.	PUNCT
cana-5235	69	1	the	the	DET
cana-5235	69	2	author	author	NOUN
cana-5235	69	3	observed	observe	VERB
cana-5235	69	4	that	that	SCONJ
cana-5235	69	5	viscosity	viscosity	NOUN
cana-5235	69	6	stratification	stratification	NOUN
cana-5235	69	7	plays	play	VERB
cana-5235	69	8	a	a	DET
cana-5235	69	9	crucial	crucial	ADJ
cana-5235	69	10	role	role	NOUN
cana-5235	69	11	in	in	ADP
cana-5235	69	12	the	the	DET
cana-5235	69	13	interface	interface	NOUN
cana-5235	69	14	mode	mode	NOUN
cana-5235	69	15	and	and	CCONJ
cana-5235	69	16	confirmed	confirm	VERB
cana-5235	69	17	that	that	SCONJ
cana-5235	69	18	instability	instability	NOUN
cana-5235	69	19	occurs	occur	VERB
cana-5235	69	20	when	when	SCONJ
cana-5235	69	21	the	the	DET
cana-5235	69	22	viscosity	viscosity	NOUN
cana-5235	69	23	of	of	ADP
cana-5235	69	24	the	the	DET
cana-5235	69	25	lower	low	ADJ
cana-5235	69	26	layer	layer	NOUN
cana-5235	69	27	is	be	AUX
cana-5235	69	28	greater	great	ADJ
cana-5235	69	29	than	than	ADP
cana-5235	69	30	that	that	PRON
cana-5235	69	31	of	of	ADP
cana-5235	69	32	the	the	DET
cana-5235	69	33	overlying	overlying	ADJ
cana-5235	69	34	layer	layer	NOUN
cana-5235	69	35	.	.	PUNCT
cana-5235	70	1	samanta	samanta	PROPN
cana-5235	71	1	[	[	X
cana-5235	71	2	19	19	NUM
cana-5235	71	3	]	]	X
cana-5235	71	4	added	add	VERB
cana-5235	71	5	inertia	inertia	NOUN
cana-5235	71	6	force	force	NOUN
cana-5235	71	7	up	up	ADP
cana-5235	71	8	to	to	ADP
cana-5235	71	9	moderate	moderate	ADJ
cana-5235	71	10	reynolds	reynold	NOUN
cana-5235	71	11	number	number	NOUN
cana-5235	71	12	values	value	NOUN
cana-5235	71	13	,	,	PUNCT
cana-5235	71	14	extending	extend	VERB
cana-5235	71	15	the	the	DET
cana-5235	71	16	work	work	NOUN
cana-5235	71	17	of	of	ADP
cana-5235	71	18	gao	gao	PROPN
cana-5235	71	19	and	and	CCONJ
cana-5235	71	20	lu	lu	PROPN
cana-5235	72	1	[	[	X
cana-5235	72	2	14	14	NUM
cana-5235	72	3	]	]	PUNCT
cana-5235	72	4	even	even	ADV
cana-5235	72	5	further	far	ADV
cana-5235	72	6	,	,	PUNCT
cana-5235	72	7	investigated	investigate	VERB
cana-5235	72	8	how	how	SCONJ
cana-5235	72	9	the	the	DET
cana-5235	72	10	free	free	ADJ
cana-5235	72	11	surface	surface	NOUN
cana-5235	72	12	and	and	CCONJ
cana-5235	72	13	interface	interface	NOUN
cana-5235	72	14	mode	mode	NOUN
cana-5235	72	15	-	-	PUNCT
cana-5235	72	16	induced	induce	VERB
cana-5235	72	17	primary	primary	ADJ
cana-5235	72	18	instability	instability	NOUN
cana-5235	72	19	was	be	AUX
cana-5235	72	20	affected	affect	VERB
cana-5235	72	21	by	by	ADP
cana-5235	72	22	insoluble	insoluble	ADJ
cana-5235	72	23	surfactant	surfactant	NOUN
cana-5235	72	24	.	.	PUNCT
cana-5235	73	1	it	it	PRON
cana-5235	73	2	was	be	AUX
cana-5235	73	3	demonstrated	demonstrate	VERB
cana-5235	73	4	that	that	SCONJ
cana-5235	73	5	when	when	SCONJ
cana-5235	73	6	the	the	DET
cana-5235	73	7	top	top	ADJ
cana-5235	73	8	layer	layer	NOUN
cana-5235	73	9	is	be	AUX
cana-5235	73	10	less	less	ADV
cana-5235	73	11	viscous	viscous	ADJ
cana-5235	73	12	than	than	ADP
cana-5235	73	13	the	the	DET
cana-5235	73	14	bottom	bottom	ADJ
cana-5235	73	15	layer	layer	NOUN
cana-5235	73	16	,	,	PUNCT
cana-5235	73	17	the	the	DET
cana-5235	73	18	interfacial	interfacial	ADJ
cana-5235	73	19	instability	instability	NOUN
cana-5235	73	20	weakens	weaken	VERB
cana-5235	73	21	due	due	ADP
cana-5235	73	22	to	to	ADP
cana-5235	73	23	the	the	DET
cana-5235	73	24	presence	presence	NOUN
cana-5235	73	25	of	of	ADP
cana-5235	73	26	the	the	DET
cana-5235	73	27	interfacial	interfacial	ADJ
cana-5235	73	28	surfactant	surfactant	NOUN
cana-5235	73	29	.	.	PUNCT
cana-5235	74	1	bhat	bhat	PROPN
cana-5235	74	2	and	and	CCONJ
cana-5235	74	3	samanta[3	samanta[3	PROPN
cana-5235	74	4	]	]	X
cana-5235	74	5	further	far	ADV
cana-5235	74	6	examined	examine	VERB
cana-5235	74	7	the	the	DET
cana-5235	74	8	effects	effect	NOUN
cana-5235	74	9	of	of	ADP
cana-5235	74	10	surfactants	surfactant	NOUN
cana-5235	74	11	on	on	ADP
cana-5235	74	12	two	two	NUM
cana-5235	74	13	-	-	PUNCT
cana-5235	74	14	layer	layer	NOUN
cana-5235	74	15	falling	fall	VERB
cana-5235	74	16	films	film	NOUN
cana-5235	74	17	over	over	ADP
cana-5235	74	18	a	a	DET
cana-5235	74	19	slippery	slippery	ADJ
cana-5235	74	20	incline	incline	NOUN
cana-5235	74	21	,	,	PUNCT
cana-5235	74	22	highlighting	highlight	VERB
cana-5235	74	23	the	the	DET
cana-5235	74	24	dual	dual	ADJ
cana-5235	74	25	role	role	NOUN
cana-5235	74	26	of	of	ADP
cana-5235	74	27	the	the	DET
cana-5235	74	28	viscosity	viscosity	NOUN
cana-5235	74	29	ratio	ratio	NOUN
cana-5235	74	30	in	in	ADP
cana-5235	74	31	surface	surface	NOUN
cana-5235	74	32	mode	mode	NOUN
cana-5235	74	33	instability	instability	NOUN
cana-5235	74	34	.	.	PUNCT
cana-5235	75	1	additionally	additionally	ADV
cana-5235	75	2	,	,	PUNCT
cana-5235	75	3	studies	study	NOUN
cana-5235	75	4	with	with	ADP
cana-5235	75	5	various	various	ADJ
cana-5235	75	6	flow	flow	NOUN
cana-5235	75	7	configurations	configuration	NOUN
cana-5235	75	8	have	have	AUX
cana-5235	75	9	explored	explore	VERB
cana-5235	75	10	the	the	DET
cana-5235	75	11	use	use	NOUN
cana-5235	75	12	of	of	ADP
cana-5235	75	13	external	external	ADJ
cana-5235	75	14	shear	shear	NOUN
cana-5235	75	15	as	as	ADP
cana-5235	75	16	a	a	DET
cana-5235	75	17	surface	surface	NOUN
cana-5235	75	18	-	-	PUNCT
cana-5235	75	19	active	active	ADJ
cana-5235	75	20	agent	agent	NOUN
cana-5235	75	21	to	to	PART
cana-5235	75	22	control	control	VERB
cana-5235	75	23	instabilities	instability	NOUN
cana-5235	75	24	caused	cause	VERB
cana-5235	75	25	by	by	ADP
cana-5235	75	26	free	free	ADJ
cana-5235	75	27	surface	surface	NOUN
cana-5235	75	28	waves	wave	NOUN
cana-5235	75	29	[	[	X
cana-5235	75	30	9	9	NUM
cana-5235	75	31	,	,	PUNCT
cana-5235	75	32	22	22	NUM
cana-5235	75	33	,	,	PUNCT
cana-5235	75	34	23	23	NUM
cana-5235	75	35	]	]	PUNCT
cana-5235	75	36	.	.	PUNCT
cana-5235	76	1	it	it	PRON
cana-5235	76	2	is	be	AUX
cana-5235	76	3	worth	worth	ADJ
cana-5235	76	4	noting	note	VERB
cana-5235	76	5	that	that	SCONJ
cana-5235	76	6	several	several	ADJ
cana-5235	76	7	applications	application	NOUN
cana-5235	76	8	of	of	ADP
cana-5235	76	9	heterogeneous	heterogeneous	ADJ
cana-5235	76	10	fluid	fluid	NOUN
cana-5235	76	11	mostly	mostly	ADV
cana-5235	76	12	deal	deal	VERB
cana-5235	76	13	with	with	ADP
cana-5235	76	14	liquidliquid	liquidliquid	ADJ
cana-5235	76	15	extraction	extraction	NOUN
cana-5235	76	16	.	.	PUNCT
cana-5235	77	1	however	however	ADV
cana-5235	77	2	,	,	PUNCT
cana-5235	77	3	there	there	PRON
cana-5235	77	4	are	be	VERB
cana-5235	77	5	few	few	ADJ
cana-5235	77	6	applications	application	NOUN
cana-5235	77	7	related	relate	VERB
cana-5235	77	8	to	to	ADP
cana-5235	77	9	large	large	ADJ
cana-5235	77	10	airways	airway	NOUN
cana-5235	77	11	and	and	CCONJ
cana-5235	77	12	bolus	bolus	NOUN
cana-5235	77	13	-	-	PUNCT
cana-5235	77	14	dispersal	dispersal	NOUN
cana-5235	77	15	surfactant	surfactant	ADJ
cana-5235	77	16	replacement	replacement	NOUN
cana-5235	77	17	therapy	therapy	NOUN
cana-5235	77	18	.	.	PUNCT
cana-5235	78	1	in	in	ADP
cana-5235	78	2	viewing	view	VERB
cana-5235	78	3	the	the	DET
cana-5235	78	4	respiratory	respiratory	ADJ
cana-5235	78	5	tract	tract	NOUN
cana-5235	78	6	at	at	ADP
cana-5235	78	7	the	the	DET
cana-5235	78	8	microscopic	microscopic	ADJ
cana-5235	78	9	level	level	NOUN
cana-5235	78	10	,	,	PUNCT
cana-5235	78	11	there	there	PRON
cana-5235	78	12	is	be	VERB
cana-5235	78	13	a	a	DET
cana-5235	78	14	thin	thin	ADJ
cana-5235	78	15	layer	layer	NOUN
cana-5235	78	16	of	of	ADP
cana-5235	78	17	membrane	membrane	NOUN
cana-5235	78	18	that	that	PRON
cana-5235	78	19	lies	lie	VERB
cana-5235	78	20	between	between	ADP
cana-5235	78	21	the	the	DET
cana-5235	78	22	loosely	loosely	ADV
cana-5235	78	23	bound	bind	VERB
cana-5235	78	24	connective	connective	ADJ
cana-5235	78	25	tissue	tissue	NOUN
cana-5235	78	26	and	and	CCONJ
cana-5235	78	27	mucus	mucus	NOUN
cana-5235	78	28	layer	layer	NOUN
cana-5235	78	29	,	,	PUNCT
cana-5235	78	30	which	which	PRON
cana-5235	78	31	behaves	behave	VERB
cana-5235	78	32	like	like	ADP
cana-5235	78	33	a	a	DET
cana-5235	78	34	two	two	NUM
cana-5235	78	35	-	-	PUNCT
cana-5235	78	36	layer	layer	NOUN
cana-5235	78	37	fluid	fluid	NOUN
cana-5235	78	38	in	in	ADP
cana-5235	78	39	the	the	DET
cana-5235	78	40	presence	presence	NOUN
cana-5235	78	41	of	of	ADP
cana-5235	78	42	insoluble	insoluble	ADJ
cana-5235	78	43	surfactant	surfactant	NOUN
cana-5235	78	44	.	.	PUNCT
cana-5235	79	1	in	in	ADP
cana-5235	79	2	the	the	DET
cana-5235	79	3	present	present	ADJ
cana-5235	79	4	study	study	NOUN
cana-5235	79	5	,	,	PUNCT
cana-5235	79	6	the	the	DET
cana-5235	79	7	instability	instability	NOUN
cana-5235	79	8	control	control	NOUN
cana-5235	79	9	mechanism	mechanism	NOUN
cana-5235	79	10	by	by	ADP
cana-5235	79	11	insoluble	insoluble	ADJ
cana-5235	79	12	surfactant	surfactant	NOUN
cana-5235	79	13	on	on	ADP
cana-5235	79	14	the	the	DET
cana-5235	79	15	two	two	NUM
cana-5235	79	16	-	-	PUNCT
cana-5235	79	17	layer	layer	NOUN
cana-5235	79	18	fluid	fluid	NOUN
cana-5235	79	19	due	due	ADP
cana-5235	79	20	to	to	ADP
cana-5235	79	21	the	the	DET
cana-5235	79	22	imposed	impose	VERB
cana-5235	79	23	shear	shear	NOUN
cana-5235	79	24	on	on	ADP
cana-5235	79	25	the	the	DET
cana-5235	79	26	airway	airway	NOUN
cana-5235	79	27	track	track	NOUN
cana-5235	79	28	is	be	AUX
cana-5235	79	29	analyzed	analyze	VERB
cana-5235	79	30	.	.	PUNCT
cana-5235	80	1	the	the	DET
cana-5235	80	2	orr	orr	PROPN
cana-5235	80	3	-	-	PUNCT
cana-5235	80	4	sommerfeld	sommerfeld	ADJ
cana-5235	80	5	system	system	NOUN
cana-5235	80	6	obtained	obtain	VERB
cana-5235	80	7	for	for	ADP
cana-5235	80	8	the	the	DET
cana-5235	80	9	governing	govern	VERB
cana-5235	80	10	equations	equation	NOUN
cana-5235	80	11	and	and	CCONJ
cana-5235	80	12	boundary	boundary	ADJ
cana-5235	80	13	conditions	condition	NOUN
cana-5235	80	14	is	be	AUX
cana-5235	80	15	solved	solve	VERB
cana-5235	80	16	numerically	numerically	ADV
cana-5235	80	17	using	use	VERB
cana-5235	80	18	the	the	DET
cana-5235	80	19	spectral	spectral	ADJ
cana-5235	80	20	collocation	collocation	NOUN
cana-5235	80	21	method	method	NOUN
cana-5235	80	22	.	.	PUNCT
cana-5235	81	1	the	the	DET
cana-5235	81	2	numerical	numerical	ADJ
cana-5235	81	3	results	result	NOUN
cana-5235	81	4	such	such	ADJ
cana-5235	81	5	as	as	ADP
cana-5235	81	6	dispersion	dispersion	NOUN
cana-5235	81	7	and	and	CCONJ
cana-5235	81	8	neutral	neutral	ADJ
cana-5235	81	9	stability	stability	NOUN
cana-5235	81	10	curves	curve	NOUN
cana-5235	81	11	are	be	AUX
cana-5235	81	12	analyzed	analyze	VERB
cana-5235	81	13	extensively	extensively	ADV
cana-5235	81	14	for	for	ADP
cana-5235	81	15	different	different	ADJ
cana-5235	81	16	surfactant	surfactant	ADJ
cana-5235	81	17	concentration	concentration	NOUN
cana-5235	81	18	,	,	PUNCT
cana-5235	81	19	shear	shear	NOUN
cana-5235	81	20	,	,	PUNCT
cana-5235	81	21	and	and	CCONJ
cana-5235	81	22	slip	slip	VERB
cana-5235	81	23	parameters	parameter	NOUN
cana-5235	81	24	for	for	ADP
cana-5235	81	25	smaller	small	ADJ
cana-5235	81	26	reynolds	reynold	NOUN
cana-5235	81	27	numbers	number	NOUN
cana-5235	81	28	.	.	PUNCT
cana-5235	82	1	the	the	DET
cana-5235	82	2	paper	paper	NOUN
cana-5235	82	3	is	be	AUX
cana-5235	82	4	organized	organize	VERB
cana-5235	82	5	as	as	SCONJ
cana-5235	82	6	follows	follow	VERB
cana-5235	82	7	:	:	PUNCT
cana-5235	82	8	the	the	DET
cana-5235	82	9	mathematical	mathematical	ADJ
cana-5235	82	10	formulation	formulation	NOUN
cana-5235	82	11	along	along	ADP
cana-5235	82	12	with	with	ADP
cana-5235	82	13	the	the	DET
cana-5235	82	14	solution	solution	NOUN
cana-5235	82	15	of	of	ADP
cana-5235	82	16	the	the	DET
cana-5235	82	17	physical	physical	ADJ
cana-5235	82	18	problem	problem	NOUN
cana-5235	82	19	is	be	AUX
cana-5235	82	20	discussed	discuss	VERB
cana-5235	82	21	in	in	ADP
cana-5235	82	22	section	section	NOUN
cana-5235	82	23	2	2	NUM
cana-5235	82	24	,	,	PUNCT
cana-5235	82	25	the	the	DET
cana-5235	82	26	numerical	numerical	ADJ
cana-5235	82	27	results	result	NOUN
cana-5235	82	28	are	be	AUX
cana-5235	82	29	analyzed	analyze	VERB
cana-5235	82	30	in	in	ADP
cana-5235	82	31	section	section	NOUN
cana-5235	82	32	3	3	NUM
cana-5235	82	33	,	,	PUNCT
cana-5235	82	34	and	and	CCONJ
cana-5235	82	35	the	the	DET
cana-5235	82	36	concluding	conclude	VERB
cana-5235	82	37	remark	remark	NOUN
cana-5235	82	38	is	be	AUX
cana-5235	82	39	highlighted	highlight	VERB
cana-5235	82	40	in	in	ADP
cana-5235	82	41	section	section	NOUN
cana-5235	82	42	4	4	NUM
cana-5235	82	43	2	2	NUM
cana-5235	82	44	.	.	PUNCT
cana-5235	82	45	mathematical	mathematical	ADJ
cana-5235	82	46	formulation	formulation	NOUN
cana-5235	82	47	a	a	DET
cana-5235	82	48	two	two	NUM
cana-5235	82	49	-	-	PUNCT
cana-5235	82	50	dimensional	dimensional	ADJ
cana-5235	82	51	shear	shear	NOUN
cana-5235	82	52	-	-	PUNCT
cana-5235	82	53	imposed	impose	VERB
cana-5235	82	54	flow	flow	NOUN
cana-5235	82	55	of	of	ADP
cana-5235	82	56	immiscible	immiscible	ADJ
cana-5235	82	57	,	,	PUNCT
cana-5235	82	58	incompressible	incompressible	ADJ
cana-5235	82	59	and	and	CCONJ
cana-5235	82	60	newtonian	newtonian	ADJ
cana-5235	82	61	fluids	fluid	NOUN
cana-5235	82	62	having	have	VERB
cana-5235	82	63	different	different	ADJ
cana-5235	82	64	density	density	NOUN
cana-5235	82	65	and	and	CCONJ
cana-5235	82	66	viscosity	viscosity	NOUN
cana-5235	82	67	in	in	ADP
cana-5235	82	68	an	an	DET
cana-5235	82	69	inclined	inclined	ADJ
cana-5235	82	70	slippery	slippery	ADJ
cana-5235	82	71	plane	plane	NOUN
cana-5235	82	72	is	be	AUX
cana-5235	82	73	considered	consider	VERB
cana-5235	82	74	as	as	ADP
cana-5235	82	75	in	in	ADP
cana-5235	82	76	fig	fig	NOUN
cana-5235	82	77	.	.	PUNCT
cana-5235	83	1	1	1	X
cana-5235	83	2	.	.	X
cana-5235	83	3	the	the	DET
cana-5235	83	4	upper	upper	ADJ
cana-5235	83	5	layer	layer	NOUN
cana-5235	83	6	is	be	AUX
cana-5235	83	7	denoted	denote	VERB
cana-5235	83	8	as	as	ADP
cana-5235	83	9	fluid-1	fluid-1	NUM
cana-5235	83	10	with	with	ADP
cana-5235	83	11	density	density	NOUN
cana-5235	83	12	𝜌1	𝜌1	NOUN
cana-5235	83	13	and	and	CCONJ
cana-5235	83	14	viscosity	viscosity	NOUN
cana-5235	83	15	𝜇1	𝜇1	NOUN
cana-5235	83	16	,	,	PUNCT
cana-5235	83	17	whereas	whereas	SCONJ
cana-5235	83	18	the	the	DET
cana-5235	83	19	lower	low	ADJ
cana-5235	83	20	layer	layer	NOUN
cana-5235	83	21	is	be	AUX
cana-5235	83	22	denoted	denote	VERB
cana-5235	83	23	as	as	ADP
cana-5235	83	24	fluid-2	fluid-2	NUM
cana-5235	83	25	with	with	ADP
cana-5235	83	26	density	density	NOUN
cana-5235	83	27	𝜌2	𝜌2	ADJ
cana-5235	83	28	and	and	CCONJ
cana-5235	83	29	viscosity	viscosity	NOUN
cana-5235	83	30	𝜇2	𝜇2	NOUN
cana-5235	83	31	.	.	PUNCT
cana-5235	84	1	the	the	DET
cana-5235	84	2	distance	distance	NOUN
cana-5235	84	3	between	between	ADP
cana-5235	84	4	the	the	DET
cana-5235	84	5	slippery	slippery	ADJ
cana-5235	84	6	bottom	bottom	NOUN
cana-5235	84	7	and	and	CCONJ
cana-5235	84	8	mean	mean	VERB
cana-5235	84	9	free	free	ADJ
cana-5235	84	10	surface	surface	NOUN
cana-5235	84	11	is	be	AUX
cana-5235	84	12	𝐻	𝐻	PROPN
cana-5235	84	13	and	and	CCONJ
cana-5235	84	14	width	width	VERB
cana-5235	84	15	of	of	ADP
cana-5235	84	16	the	the	DET
cana-5235	84	17	upper	upper	ADJ
cana-5235	84	18	layer	layer	NOUN
cana-5235	84	19	fluid	fluid	NOUN
cana-5235	84	20	is	be	AUX
cana-5235	84	21	𝑑.	𝑑.	ADJ
cana-5235	84	22	the	the	DET
cana-5235	84	23	origin	origin	NOUN
cana-5235	84	24	is	be	AUX
cana-5235	84	25	assumed	assume	VERB
cana-5235	84	26	at	at	ADP
cana-5235	84	27	the	the	DET
cana-5235	84	28	mean	mean	ADJ
cana-5235	84	29	free	free	ADJ
cana-5235	84	30	surface	surface	NOUN
cana-5235	84	31	as	as	SCONJ
cana-5235	84	32	𝑂	𝑂	PROPN
cana-5235	84	33	and	and	CCONJ
cana-5235	84	34	the	the	DET
cana-5235	84	35	positive	positive	ADJ
cana-5235	84	36	𝑦-axis	𝑦-axis	NOUN
cana-5235	84	37	is	be	AUX
cana-5235	84	38	pointing	point	VERB
cana-5235	84	39	downward	downward	ADJ
cana-5235	84	40	perpendicular	perpendicular	NOUN
cana-5235	84	41	to	to	ADP
cana-5235	84	42	the	the	DET
cana-5235	84	43	flow	flow	NOUN
cana-5235	84	44	direction	direction	NOUN
cana-5235	84	45	.	.	PUNCT
cana-5235	85	1	𝜏	𝜏	PRON
cana-5235	85	2	represent	represent	VERB
cana-5235	85	3	the	the	DET
cana-5235	85	4	external	external	ADJ
cana-5235	85	5	share	share	NOUN
cana-5235	85	6	pointing	pointing	NOUN
cana-5235	85	7	in	in	ADP
cana-5235	85	8	the	the	DET
cana-5235	85	9	opposite	opposite	ADJ
cana-5235	85	10	direction	direction	NOUN
cana-5235	85	11	of	of	ADP
cana-5235	85	12	the	the	DET
cana-5235	85	13	fluid	fluid	ADJ
cana-5235	85	14	flow	flow	NOUN
cana-5235	85	15	.	.	PUNCT
cana-5235	86	1	moreover	moreover	ADV
cana-5235	86	2	,	,	PUNCT
cana-5235	86	3	ℎ1(𝑥	ℎ1(𝑥	NOUN
cana-5235	86	4	,	,	PUNCT
cana-5235	86	5	𝑡	𝑡	PROPN
cana-5235	86	6	)	)	PUNCT
cana-5235	86	7	and	and	CCONJ
cana-5235	86	8	ℎ2(𝑥	ℎ2(𝑥	PROPN
cana-5235	86	9	,	,	PUNCT
cana-5235	86	10	𝑡	𝑡	NOUN
cana-5235	86	11	)	)	PUNCT
cana-5235	86	12	are	be	AUX
cana-5235	86	13	denoted	denote	VERB
cana-5235	86	14	as	as	ADP
cana-5235	86	15	the	the	DET
cana-5235	86	16	elevation	elevation	NOUN
cana-5235	86	17	of	of	ADP
cana-5235	86	18	upper	upper	ADJ
cana-5235	86	19	and	and	CCONJ
cana-5235	86	20	lower	low	ADJ
cana-5235	86	21	layers	layer	NOUN
cana-5235	86	22	,	,	PUNCT
cana-5235	86	23	respectively	respectively	ADV
cana-5235	86	24	.	.	PUNCT
cana-5235	87	1	further	far	ADV
cana-5235	87	2	,	,	PUNCT
cana-5235	87	3	the	the	DET
cana-5235	87	4	angle	angle	NOUN
cana-5235	87	5	between	between	ADP
cana-5235	87	6	the	the	DET
cana-5235	87	7	flat	flat	ADJ
cana-5235	87	8	and	and	CCONJ
cana-5235	87	9	tilted	tilted	ADJ
cana-5235	87	10	bottom	bottom	NOUN
cana-5235	87	11	is	be	AUX
cana-5235	87	12	denoted	denote	VERB
cana-5235	87	13	as	as	ADP
cana-5235	87	14	𝜃.	𝜃.	ADP
cana-5235	87	15	the	the	DET
cana-5235	87	16	governing	govern	VERB
cana-5235	87	17	equations	equation	NOUN
cana-5235	87	18	of	of	ADP
cana-5235	87	19	fluid	fluid	ADJ
cana-5235	87	20	flow	flow	NOUN
cana-5235	87	21	in	in	ADP
cana-5235	87	22	both	both	DET
cana-5235	87	23	layers	layer	NOUN
cana-5235	87	24	are	be	AUX
cana-5235	87	25	given	give	VERB
cana-5235	87	26	by	by	ADP
cana-5235	87	27	the	the	DET
cana-5235	87	28	two	two	NUM
cana-5235	87	29	-	-	PUNCT
cana-5235	87	30	dimensional	dimensional	ADJ
cana-5235	87	31	navier	navier	NOUN
cana-5235	87	32	-	-	PUNCT
cana-5235	87	33	stokes	stoke	NOUN
cana-5235	87	34	equations	equation	NOUN
cana-5235	87	35	,	,	PUNCT
cana-5235	87	36	communications	communication	NOUN
cana-5235	87	37	on	on	ADP
cana-5235	87	38	applied	apply	VERB
cana-5235	87	39	nonlinear	nonlinear	ADJ
cana-5235	87	40	analysis	analysis	NOUN
cana-5235	87	41	issn	issn	NOUN
cana-5235	87	42	:	:	PUNCT
cana-5235	87	43	1074	1074	NUM
cana-5235	87	44	-	-	PUNCT
cana-5235	87	45	133x	133x	NUM
cana-5235	87	46	vol	vol	VERB
cana-5235	87	47	32	32	NUM
cana-5235	87	48	no	no	NOUN
cana-5235	87	49	.	.	PUNCT
cana-5235	88	1	10s	10	NOUN
cana-5235	88	2	(	(	PUNCT
cana-5235	88	3	2025	2025	NUM
cana-5235	88	4	)	)	PUNCT
cana-5235	88	5	1326	1326	NUM
cana-5235	88	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5235	88	7	𝜕𝑥𝑢𝑗	𝜕𝑥𝑢𝑗	PROPN
cana-5235	88	8	+	+	CCONJ
cana-5235	88	9	𝜕𝑦𝑣𝑗	𝜕𝑦𝑣𝑗	NUM
cana-5235	88	10	=	=	SYM
cana-5235	88	11	0	0	NUM
cana-5235	88	12	,	,	PUNCT
cana-5235	88	13	(	(	PUNCT
cana-5235	88	14	2.1	2.1	NUM
cana-5235	88	15	)	)	PUNCT
cana-5235	88	16	𝜕𝑡𝑢𝑗	𝜕𝑡𝑢𝑗	ADV
cana-5235	88	17	+	+	NUM
cana-5235	88	18	𝑢𝑗𝜕𝑥𝑢𝑗	𝑢𝑗𝜕𝑥𝑢𝑗	X
cana-5235	88	19	+	+	X
cana-5235	88	20	𝑣𝑗𝜕𝑦𝑢𝑗	𝑣𝑗𝜕𝑦𝑢𝑗	NOUN
cana-5235	88	21	=	=	SYM
cana-5235	88	22	−	−	NOUN
cana-5235	88	23	1	1	NUM
cana-5235	88	24	𝜌𝑗	𝜌𝑗	ADP
cana-5235	88	25	𝜕𝑥𝑝𝑗	𝜕𝑥𝑝𝑗	PROPN
cana-5235	88	26	+	+	SYM
cana-5235	88	27	𝜈𝑗[𝜕𝑥𝑥	𝜈𝑗[𝜕𝑥𝑥	SYM
cana-5235	88	28	2	2	NUM
cana-5235	88	29	𝑢𝑗	𝑢𝑗	NOUN
cana-5235	88	30	+	+	CCONJ
cana-5235	88	31	𝜕𝑦𝑦	𝜕𝑦𝑦	PROPN
cana-5235	88	32	2	2	NUM
cana-5235	88	33	𝑢𝑗	𝑢𝑗	NOUN
cana-5235	88	34	]	]	PUNCT
cana-5235	88	35	+	+	CCONJ
cana-5235	88	36	𝑔sin𝜃	𝑔sin𝜃	NOUN
cana-5235	88	37	,	,	PUNCT
cana-5235	88	38	(	(	PUNCT
cana-5235	88	39	2.2	2.2	NUM
cana-5235	88	40	)	)	PUNCT
cana-5235	88	41	𝜕𝑡𝑣𝑗	𝜕𝑡𝑣𝑗	NOUN
cana-5235	88	42	+	+	CCONJ
cana-5235	88	43	𝑢𝑗𝜕𝑥𝑣𝑗	𝑢𝑗𝜕𝑥𝑣𝑗	NOUN
cana-5235	88	44	+	+	CCONJ
cana-5235	88	45	𝑣𝑗𝜕𝑦𝑣𝑗	𝑣𝑗𝜕𝑦𝑣𝑗	X
cana-5235	88	46	=	=	PUNCT
cana-5235	88	47	−	−	PROPN
cana-5235	88	48	1	1	NUM
cana-5235	88	49	𝜌𝑗	𝜌𝑗	ADP
cana-5235	88	50	𝜕𝑦𝑝𝑗	𝜕𝑦𝑝𝑗	PROPN
cana-5235	89	1	+	+	PUNCT
cana-5235	89	2	𝜈𝑗[𝜕𝑥𝑥	𝜈𝑗[𝜕𝑥𝑥	X
cana-5235	89	3	2	2	NUM
cana-5235	89	4	𝑣𝑗	𝑣𝑗	ADP
cana-5235	89	5	+	+	CCONJ
cana-5235	89	6	𝜕𝑦𝑦	𝜕𝑦𝑦	ADP
cana-5235	89	7	2	2	NUM
cana-5235	89	8	𝑣𝑗	𝑣𝑗	NOUN
cana-5235	89	9	]	]	PUNCT
cana-5235	89	10	−	−	NOUN
cana-5235	89	11	𝑔cos𝜃	𝑔cos𝜃	NOUN
cana-5235	89	12	,	,	PUNCT
cana-5235	89	13	(	(	PUNCT
cana-5235	89	14	2.3	2.3	NUM
cana-5235	89	15	)	)	PUNCT
cana-5235	89	16	figure	figure	NOUN
cana-5235	89	17	1	1	NUM
cana-5235	89	18	:	:	PUNCT
cana-5235	89	19	schematic	schematic	ADJ
cana-5235	89	20	diagram	diagram	NOUN
cana-5235	89	21	for	for	ADP
cana-5235	89	22	a	a	DET
cana-5235	89	23	two	two	NUM
cana-5235	89	24	-	-	PUNCT
cana-5235	89	25	layer	layer	NOUN
cana-5235	89	26	thin	thin	ADJ
cana-5235	89	27	film	film	NOUN
cana-5235	89	28	flow	flow	NOUN
cana-5235	89	29	down	down	ADP
cana-5235	89	30	in	in	ADP
cana-5235	89	31	an	an	DET
cana-5235	89	32	inclined	inclined	ADJ
cana-5235	89	33	slippery	slippery	ADJ
cana-5235	89	34	plane	plane	NOUN
cana-5235	89	35	in	in	ADP
cana-5235	89	36	the	the	DET
cana-5235	89	37	presence	presence	NOUN
cana-5235	89	38	of	of	ADP
cana-5235	89	39	an	an	DET
cana-5235	89	40	insoluble	insoluble	ADJ
cana-5235	89	41	surfactant	surfactant	NOUN
cana-5235	89	42	at	at	ADP
cana-5235	89	43	the	the	DET
cana-5235	89	44	free	free	ADJ
cana-5235	89	45	surface	surface	NOUN
cana-5235	89	46	.	.	PUNCT
cana-5235	90	1	where	where	SCONJ
cana-5235	90	2	𝑗	𝑗	ADJ
cana-5235	90	3	=	=	SYM
cana-5235	90	4	1	1	NUM
cana-5235	90	5	and	and	CCONJ
cana-5235	90	6	𝑗	𝑗	NOUN
cana-5235	90	7	=	=	SYM
cana-5235	90	8	2	2	NUM
cana-5235	90	9	denote	denote	VERB
cana-5235	90	10	the	the	DET
cana-5235	90	11	upper	upper	ADJ
cana-5235	90	12	and	and	CCONJ
cana-5235	90	13	lower	low	ADJ
cana-5235	90	14	layer	layer	NOUN
cana-5235	90	15	fluids	fluid	NOUN
cana-5235	90	16	respectively	respectively	ADV
cana-5235	90	17	,	,	PUNCT
cana-5235	90	18	and	and	CCONJ
cana-5235	90	19	𝑔	𝑔	PROPN
cana-5235	90	20	be	be	AUX
cana-5235	90	21	the	the	DET
cana-5235	90	22	acceleration	acceleration	NOUN
cana-5235	90	23	due	due	ADP
cana-5235	90	24	to	to	ADP
cana-5235	90	25	gravity	gravity	NOUN
cana-5235	90	26	.	.	PUNCT
cana-5235	91	1	in	in	ADP
cana-5235	91	2	the	the	DET
cana-5235	91	3	upper	upper	ADJ
cana-5235	91	4	layer	layer	NOUN
cana-5235	91	5	,	,	PUNCT
cana-5235	91	6	the	the	DET
cana-5235	91	7	surface	surface	NOUN
cana-5235	91	8	is	be	AUX
cana-5235	91	9	covered	cover	VERB
cana-5235	91	10	by	by	ADP
cana-5235	91	11	the	the	DET
cana-5235	91	12	monolayer	monolayer	NOUN
cana-5235	91	13	insoluble	insoluble	ADJ
cana-5235	91	14	surfactant	surfactant	NOUN
cana-5235	91	15	with	with	ADP
cana-5235	91	16	concentration	concentration	NOUN
cana-5235	91	17	γ(𝑥	γ(𝑥	PROPN
cana-5235	91	18	,	,	PUNCT
cana-5235	91	19	𝑡	𝑡	NOUN
cana-5235	91	20	)	)	PUNCT
cana-5235	91	21	,	,	PUNCT
cana-5235	91	22	which	which	PRON
cana-5235	91	23	diffuses	diffuse	VERB
cana-5235	91	24	on	on	ADP
cana-5235	91	25	the	the	DET
cana-5235	91	26	free	free	ADJ
cana-5235	91	27	surface	surface	NOUN
cana-5235	91	28	.	.	PUNCT
cana-5235	92	1	but	but	CCONJ
cana-5235	92	2	,	,	PUNCT
cana-5235	92	3	there	there	PRON
cana-5235	92	4	is	be	VERB
cana-5235	92	5	no	no	DET
cana-5235	92	6	much	much	ADJ
cana-5235	92	7	penetration	penetration	NOUN
cana-5235	92	8	in	in	ADP
cana-5235	92	9	the	the	DET
cana-5235	92	10	bulk	bulk	ADJ
cana-5235	92	11	fluid	fluid	NOUN
cana-5235	92	12	.	.	PUNCT
cana-5235	93	1	now	now	ADV
cana-5235	93	2	,	,	PUNCT
cana-5235	93	3	the	the	DET
cana-5235	93	4	local	local	ADJ
cana-5235	93	5	surface	surface	NOUN
cana-5235	93	6	tension	tension	NOUN
cana-5235	93	7	on	on	ADP
cana-5235	93	8	the	the	DET
cana-5235	93	9	free	free	ADJ
cana-5235	93	10	surface	surface	NOUN
cana-5235	93	11	(	(	PUNCT
cana-5235	93	12	𝜎1	𝜎1	ADJ
cana-5235	93	13	)	)	PUNCT
cana-5235	93	14	varies	vary	VERB
cana-5235	93	15	with	with	ADP
cana-5235	93	16	respect	respect	NOUN
cana-5235	93	17	to	to	ADP
cana-5235	93	18	the	the	DET
cana-5235	93	19	local	local	ADJ
cana-5235	93	20	surfactant	surfactant	ADJ
cana-5235	93	21	concentration	concentration	NOUN
cana-5235	93	22	(	(	PUNCT
cana-5235	93	23	𝜎𝑐	𝜎𝑐	PROPN
cana-5235	93	24	)	)	PUNCT
cana-5235	93	25	.	.	PUNCT
cana-5235	94	1	the	the	DET
cana-5235	94	2	relation	relation	NOUN
cana-5235	94	3	between	between	ADP
cana-5235	94	4	the	the	DET
cana-5235	94	5	surface	surface	NOUN
cana-5235	94	6	concentration	concentration	NOUN
cana-5235	94	7	and	and	CCONJ
cana-5235	94	8	tension	tension	NOUN
cana-5235	94	9	(	(	PUNCT
cana-5235	94	10	gibbs	gibbs	PROPN
cana-5235	94	11	relation	relation	PROPN
cana-5235	94	12	)	)	PUNCT
cana-5235	94	13	is	be	AUX
cana-5235	94	14	given	give	VERB
cana-5235	94	15	by	by	ADP
cana-5235	94	16	,	,	PUNCT
cana-5235	94	17	𝜎𝑐	𝜎𝑐	PROPN
cana-5235	94	18	−	−	PROPN
cana-5235	94	19	𝜎1	𝜎1	PROPN
cana-5235	94	20	=	=	PUNCT
cana-5235	94	21	γ	γ	X
cana-5235	94	22	𝑅𝑇	𝑅𝑇	PROPN
cana-5235	94	23	,	,	PUNCT
cana-5235	94	24	(	(	PUNCT
cana-5235	94	25	2.4	2.4	NUM
cana-5235	94	26	)	)	PUNCT
cana-5235	94	27	where	where	SCONJ
cana-5235	94	28	and	and	CCONJ
cana-5235	94	29	are	be	AUX
cana-5235	94	30	the	the	DET
cana-5235	94	31	ideal	ideal	ADJ
cana-5235	94	32	gas	gas	NOUN
cana-5235	94	33	constant	constant	ADJ
cana-5235	94	34	and	and	CCONJ
cana-5235	94	35	absolute	absolute	ADJ
cana-5235	94	36	temperature	temperature	NOUN
cana-5235	94	37	respectively	respectively	ADV
cana-5235	94	38	.	.	PUNCT
cana-5235	95	1	thus	thus	ADV
cana-5235	95	2	,	,	PUNCT
cana-5235	95	3	the	the	DET
cana-5235	95	4	linear	linear	ADJ
cana-5235	95	5	equation	equation	NOUN
cana-5235	95	6	is	be	AUX
cana-5235	95	7	given	give	VERB
cana-5235	95	8	by	by	ADP
cana-5235	95	9	𝜎1	𝜎1	PROPN
cana-5235	95	10	=	=	SYM
cana-5235	95	11	𝜎𝑐	𝜎𝑐	PROPN
cana-5235	95	12	(	(	PUNCT
cana-5235	95	13	1	1	NUM
cana-5235	95	14	−	−	NOUN
cana-5235	95	15	𝛾	𝛾	ADP
cana-5235	95	16	γ	γ	X
cana-5235	95	17	γ0	γ0	PROPN
cana-5235	95	18	)	)	PUNCT
cana-5235	95	19	,	,	PUNCT
cana-5235	95	20	(	(	PUNCT
cana-5235	95	21	2.5	2.5	NUM
cana-5235	95	22	)	)	PUNCT
cana-5235	95	23	where	where	SCONJ
cana-5235	95	24	𝛾	𝛾	NOUN
cana-5235	95	25	=	=	SYM
cana-5235	95	26	γ0𝑅𝑇/𝜎𝑐	γ0𝑅𝑇/𝜎𝑐	NOUN
cana-5235	95	27	,	,	PUNCT
cana-5235	95	28	which	which	PRON
cana-5235	95	29	is	be	AUX
cana-5235	95	30	related	relate	VERB
cana-5235	95	31	to	to	ADP
cana-5235	95	32	the	the	DET
cana-5235	95	33	surface	surface	NOUN
cana-5235	95	34	elasticity	elasticity	NOUN
cana-5235	95	35	𝐸	𝐸	PROPN
cana-5235	95	36	=	=	SYM
cana-5235	95	37	𝛾𝜎𝑐/γ0	𝛾𝜎𝑐/γ0	PROPN
cana-5235	95	38	.	.	PUNCT
cana-5235	96	1	the	the	DET
cana-5235	96	2	reference	reference	NOUN
cana-5235	96	3	surfactant	surfactant	ADJ
cana-5235	96	4	concentration	concentration	NOUN
cana-5235	96	5	and	and	CCONJ
cana-5235	96	6	surface	surface	NOUN
cana-5235	96	7	tension	tension	NOUN
cana-5235	96	8	are	be	AUX
cana-5235	96	9	denoted	denote	VERB
cana-5235	96	10	as	as	ADP
cana-5235	96	11	γ0	γ0	NOUN
cana-5235	96	12	and	and	CCONJ
cana-5235	96	13	𝜎0	𝜎0	NOUN
cana-5235	96	14	,	,	PUNCT
cana-5235	96	15	respectively	respectively	ADV
cana-5235	96	16	.	.	PUNCT
cana-5235	97	1	using	use	VERB
cana-5235	97	2	the	the	DET
cana-5235	97	3	taylor	taylor	PROPN
cana-5235	97	4	series	series	PROPN
cana-5235	97	5	expansion	expansion	NOUN
cana-5235	97	6	about	about	ADP
cana-5235	97	7	γ0	γ0	NOUN
cana-5235	97	8	,	,	PUNCT
cana-5235	97	9	the	the	DET
cana-5235	97	10	local	local	ADJ
cana-5235	97	11	surface	surface	NOUN
cana-5235	97	12	tension	tension	NOUN
cana-5235	97	13	is	be	AUX
cana-5235	97	14	given	give	VERB
cana-5235	97	15	as	as	ADP
cana-5235	97	16	𝜎1	𝜎1	PROPN
cana-5235	97	17	=	=	SYM
cana-5235	97	18	𝜎0	𝜎0	NOUN
cana-5235	97	19	−	−	PROPN
cana-5235	97	20	𝐸(γ	𝐸(γ	X
cana-5235	97	21	−	−	X
cana-5235	97	22	γ0	γ0	NOUN
cana-5235	97	23	)	)	PUNCT
cana-5235	97	24	.	.	PUNCT
cana-5235	98	1	(	(	PUNCT
cana-5235	98	2	2.6	2.6	NUM
cana-5235	98	3	)	)	PUNCT
cana-5235	98	4	the	the	DET
cana-5235	98	5	boundary	boundary	ADJ
cana-5235	98	6	conditions	condition	NOUN
cana-5235	98	7	associated	associate	VERB
cana-5235	98	8	with	with	ADP
cana-5235	98	9	the	the	DET
cana-5235	98	10	upper	upper	ADJ
cana-5235	98	11	layer	layer	NOUN
cana-5235	98	12	fluid	fluid	NOUN
cana-5235	98	13	such	such	ADJ
cana-5235	98	14	as	as	ADP
cana-5235	98	15	kinematic	kinematic	ADJ
cana-5235	98	16	condition	condition	NOUN
cana-5235	98	17	,	,	PUNCT
cana-5235	98	18	tangential	tangential	ADJ
cana-5235	98	19	and	and	CCONJ
cana-5235	98	20	normal	normal	ADJ
cana-5235	98	21	stress	stress	NOUN
cana-5235	98	22	balances	balance	NOUN
cana-5235	98	23	,	,	PUNCT
cana-5235	98	24	are	be	AUX
cana-5235	98	25	given	give	VERB
cana-5235	98	26	by	by	ADP
cana-5235	98	27	𝑣1	𝑣1	NOUN
cana-5235	98	28	=	=	SYM
cana-5235	98	29	𝜕𝑡ℎ1	𝜕𝑡ℎ1	PROPN
cana-5235	98	30	+	+	CCONJ
cana-5235	98	31	𝑢1𝜕𝑥ℎ1	𝑢1𝜕𝑥ℎ1	X
cana-5235	98	32	at	at	ADP
cana-5235	98	33	𝑦	𝑦	NOUN
cana-5235	98	34	=	=	PUNCT
cana-5235	98	35	ℎ	ℎ	X
cana-5235	98	36	1(𝑥	1(𝑥	NUM
cana-5235	98	37	,	,	PUNCT
cana-5235	98	38	𝑡	𝑡	NOUN
cana-5235	98	39	)	)	PUNCT
cana-5235	98	40	,	,	PUNCT
cana-5235	98	41	(	(	PUNCT
cana-5235	98	42	2.7	2.7	NUM
cana-5235	98	43	)	)	PUNCT
cana-5235	98	44	𝜇1[−4𝜕𝑥𝑢1𝜕𝑥ℎ1	𝜇1[−4𝜕𝑥𝑢1𝜕𝑥ℎ1	PUNCT
cana-5235	99	1	+	+	PUNCT
cana-5235	99	2	[	[	X
cana-5235	99	3	𝜕𝑦𝑢1	𝜕𝑦𝑢1	ADJ
cana-5235	99	4	+	+	ADJ
cana-5235	99	5	𝜕𝑥𝑣1][1	𝜕𝑥𝑣1][1	NOUN
cana-5235	99	6	−	−	PROPN
cana-5235	99	7	(	(	PUNCT
cana-5235	99	8	𝜕𝑥ℎ1)2	𝜕𝑥ℎ1)2	PROPN
cana-5235	99	9	]	]	X
cana-5235	99	10	]	]	PUNCT
cana-5235	99	11	=	=	PUNCT
cana-5235	100	1	[	[	X
cana-5235	100	2	𝜕𝑥𝜎1	𝜕𝑥𝜎1	NOUN
cana-5235	100	3	+	+	NOUN
cana-5235	100	4	𝜏	𝜏	X
cana-5235	100	5	]	]	PUNCT
cana-5235	100	6	√1	√1	PROPN
cana-5235	100	7	+	+	CCONJ
cana-5235	100	8	(	(	PUNCT
cana-5235	100	9	𝜕𝑥ℎ1)2	𝜕𝑥ℎ1)2	VERB
cana-5235	100	10	at	at	ADP
cana-5235	100	11	𝑦	𝑦	NOUN
cana-5235	100	12	=	=	SYM
cana-5235	100	13	ℎ1(𝑥	ℎ1(𝑥	PROPN
cana-5235	100	14	,	,	PUNCT
cana-5235	100	15	𝑡	𝑡	PROPN
cana-5235	100	16	)	)	PUNCT
cana-5235	100	17	,	,	PUNCT
cana-5235	100	18	(	(	PUNCT
cana-5235	100	19	2.8	2.8	NUM
cana-5235	100	20	)	)	PUNCT
cana-5235	100	21	communications	communication	NOUN
cana-5235	100	22	on	on	ADP
cana-5235	100	23	applied	apply	VERB
cana-5235	100	24	nonlinear	nonlinear	ADJ
cana-5235	100	25	analysis	analysis	NOUN
cana-5235	100	26	issn	issn	NOUN
cana-5235	100	27	:	:	PUNCT
cana-5235	100	28	1074	1074	NUM
cana-5235	100	29	-	-	PUNCT
cana-5235	100	30	133x	133x	NUM
cana-5235	100	31	vol	vol	VERB
cana-5235	100	32	32	32	NUM
cana-5235	100	33	no	no	NOUN
cana-5235	100	34	.	.	PUNCT
cana-5235	101	1	10s	10	NOUN
cana-5235	101	2	(	(	PUNCT
cana-5235	101	3	2025	2025	NUM
cana-5235	101	4	)	)	PUNCT
cana-5235	101	5	1327	1327	NUM
cana-5235	101	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5235	101	7	𝑝1	𝑝1	NOUN
cana-5235	101	8	=	=	SYM
cana-5235	101	9	2𝜇1	2𝜇1	PROPN
cana-5235	102	1	[	[	X
cana-5235	102	2	1+(𝜕𝑥ℎ1)2	1+(𝜕𝑥ℎ1)2	NUM
cana-5235	102	3	]	]	X
cana-5235	102	4	[	[	X
cana-5235	102	5	𝜕𝑥	𝜕𝑥	NOUN
cana-5235	102	6	𝑢1	𝑢1	PROPN
cana-5235	102	7	(	(	PUNCT
cana-5235	102	8	𝜕𝑥	𝜕𝑥	X
cana-5235	102	9	ℎ1)2	ℎ1)2	NUM
cana-5235	102	10	−	−	PROPN
cana-5235	102	11	(	(	PUNCT
cana-5235	102	12	𝜕𝑦	𝜕𝑦	PROPN
cana-5235	102	13	𝑢1	𝑢1	PROPN
cana-5235	102	14	+	+	CCONJ
cana-5235	102	15	𝜕𝑥𝑣1	𝜕𝑥𝑣1	NOUN
cana-5235	102	16	)	)	PUNCT
cana-5235	102	17	𝜕𝑥	𝜕𝑥	NOUN
cana-5235	103	1	ℎ1	ℎ1	PROPN
cana-5235	103	2	+	+	CCONJ
cana-5235	103	3	𝜕𝑦	𝜕𝑦	PROPN
cana-5235	103	4	𝑣1	𝑣1	NOUN
cana-5235	103	5	]	]	PUNCT
cana-5235	103	6	−	−	PROPN
cana-5235	103	7	𝜎1	𝜎1	ADJ
cana-5235	103	8	𝜕𝑥𝑥	𝜕𝑥𝑥	NOUN
cana-5235	103	9	2	2	NUM
cana-5235	103	10	ℎ1	ℎ1	PROPN
cana-5235	104	1	[	[	X
cana-5235	104	2	1+𝜕𝑥	1+𝜕𝑥	VERB
cana-5235	104	3	ℎ1]3/2	ℎ1]3/2	ADV
cana-5235	104	4	at	at	ADP
cana-5235	104	5	𝑦	𝑦	NOUN
cana-5235	104	6	=	=	SYM
cana-5235	104	7	ℎ1(𝑥	ℎ1(𝑥	PROPN
cana-5235	104	8	,	,	PUNCT
cana-5235	104	9	𝑡	𝑡	PROPN
cana-5235	104	10	)	)	PUNCT
cana-5235	104	11	,	,	PUNCT
cana-5235	104	12	(	(	PUNCT
cana-5235	104	13	2.9	2.9	NUM
cana-5235	104	14	)	)	PUNCT
cana-5235	104	15	where	where	SCONJ
cana-5235	104	16	𝜏	𝜏	NOUN
cana-5235	104	17	is	be	AUX
cana-5235	104	18	the	the	DET
cana-5235	104	19	external	external	ADJ
cana-5235	104	20	shear	shear	NOUN
cana-5235	104	21	imposed	impose	VERB
cana-5235	104	22	on	on	ADP
cana-5235	104	23	the	the	DET
cana-5235	104	24	fluid	fluid	ADJ
cana-5235	104	25	flow	flow	NOUN
cana-5235	104	26	.	.	PUNCT
cana-5235	105	1	in	in	ADP
cana-5235	105	2	the	the	DET
cana-5235	105	3	case	case	NOUN
cana-5235	105	4	of	of	ADP
cana-5235	105	5	lower	low	ADJ
cana-5235	105	6	layer	layer	NOUN
cana-5235	105	7	fluid	fluid	NOUN
cana-5235	105	8	,	,	PUNCT
cana-5235	105	9	the	the	DET
cana-5235	105	10	kinematic	kinematic	ADJ
cana-5235	105	11	condition	condition	NOUN
cana-5235	105	12	along	along	ADP
cana-5235	105	13	with	with	ADP
cana-5235	105	14	the	the	DET
cana-5235	105	15	balance	balance	NOUN
cana-5235	105	16	of	of	ADP
cana-5235	105	17	velocities	velocity	NOUN
cana-5235	105	18	,	,	PUNCT
cana-5235	105	19	tangential	tangential	ADJ
cana-5235	105	20	and	and	CCONJ
cana-5235	105	21	normal	normal	ADJ
cana-5235	105	22	stresses	stress	NOUN
cana-5235	105	23	,	,	PUNCT
cana-5235	105	24	are	be	AUX
cana-5235	105	25	given	give	VERB
cana-5235	105	26	by	by	ADP
cana-5235	105	27	,	,	PUNCT
cana-5235	105	28	𝑢1	𝑢1	PROPN
cana-5235	105	29	=	=	PROPN
cana-5235	105	30	𝑢2	𝑢2	PROPN
cana-5235	105	31	and	and	CCONJ
cana-5235	105	32	𝑣1	𝑣1	NOUN
cana-5235	105	33	=	=	PROPN
cana-5235	105	34	𝑣2	𝑣2	PROPN
cana-5235	105	35	at	at	ADP
cana-5235	105	36	𝑦	𝑦	NOUN
cana-5235	105	37	=	=	SYM
cana-5235	105	38	ℎ2(𝑥	ℎ2(𝑥	PROPN
cana-5235	105	39	,	,	PUNCT
cana-5235	105	40	𝑡	𝑡	NOUN
cana-5235	105	41	)	)	PUNCT
cana-5235	105	42	,	,	PUNCT
cana-5235	105	43	(	(	PUNCT
cana-5235	105	44	2.10	2.10	NUM
cana-5235	105	45	)	)	PUNCT
cana-5235	105	46	𝑣2	𝑣2	NOUN
cana-5235	105	47	=	=	PUNCT
cana-5235	106	1	𝜕𝑡	𝜕𝑡	NOUN
cana-5235	106	2	ℎ2	ℎ2	NOUN
cana-5235	106	3	+	+	CCONJ
cana-5235	106	4	𝑢2	𝑢2	PROPN
cana-5235	106	5	𝜕𝑥	𝜕𝑥	NOUN
cana-5235	106	6	ℎ2	ℎ2	NOUN
cana-5235	106	7	at	at	ADP
cana-5235	106	8	𝑦	𝑦	NOUN
cana-5235	106	9	=	=	PUNCT
cana-5235	106	10	ℎ	ℎ	X
cana-5235	106	11	2(𝑥	2(𝑥	NUM
cana-5235	106	12	,	,	PUNCT
cana-5235	106	13	𝑡	𝑡	NOUN
cana-5235	106	14	)	)	PUNCT
cana-5235	106	15	,	,	PUNCT
cana-5235	106	16	(	(	PUNCT
cana-5235	106	17	2.11	2.11	NUM
cana-5235	106	18	)	)	PUNCT
cana-5235	106	19	𝜇2	𝜇2	NOUN
cana-5235	107	1	[	[	X
cana-5235	107	2	(	(	PUNCT
cana-5235	107	3	𝜕𝑦	𝜕𝑦	PROPN
cana-5235	107	4	𝑢2	𝑢2	PROPN
cana-5235	107	5	+	+	CCONJ
cana-5235	107	6	𝜕𝑥	𝜕𝑥	X
cana-5235	107	7	𝑣2)(1	𝑣2)(1	ADP
cana-5235	107	8	−	−	PROPN
cana-5235	107	9	(	(	PUNCT
cana-5235	107	10	𝜕𝑥	𝜕𝑥	X
cana-5235	107	11	ℎ2)2	ℎ2)2	NUM
cana-5235	107	12	)	)	PUNCT
cana-5235	107	13	−	−	PROPN
cana-5235	107	14	4	4	NUM
cana-5235	107	15	𝜕𝑥𝑢2	𝜕𝑥𝑢2	X
cana-5235	107	16	𝜕𝑥ℎ2	𝜕𝑥ℎ2	X
cana-5235	107	17	]	]	PUNCT
cana-5235	107	18	=	=	SYM
cana-5235	107	19	𝜇1	𝜇1	NOUN
cana-5235	107	20	[	[	X
cana-5235	107	21	(	(	PUNCT
cana-5235	107	22	𝜕𝑦	𝜕𝑦	NOUN
cana-5235	107	23	𝑢1	𝑢1	PROPN
cana-5235	107	24	+	+	CCONJ
cana-5235	107	25	𝜕𝑥	𝜕𝑥	X
cana-5235	107	26	𝑣1)(1	𝑣1)(1	PROPN
cana-5235	107	27	−	−	PROPN
cana-5235	107	28	(	(	PUNCT
cana-5235	107	29	𝜕𝑥	𝜕𝑥	X
cana-5235	107	30	ℎ1)2	ℎ1)2	NUM
cana-5235	107	31	)	)	PUNCT
cana-5235	107	32	−	−	PROPN
cana-5235	107	33	4𝜕𝑥	4𝜕𝑥	PROPN
cana-5235	107	34	𝑢1𝜕𝑥	𝑢1𝜕𝑥	NOUN
cana-5235	107	35	ℎ1	ℎ1	PROPN
cana-5235	107	36	]	]	PUNCT
cana-5235	107	37	at	at	ADP
cana-5235	107	38	𝑦	𝑦	NOUN
cana-5235	107	39	=	=	SYM
cana-5235	107	40	ℎ2(𝑥	ℎ2(𝑥	PROPN
cana-5235	107	41	,	,	PUNCT
cana-5235	107	42	𝑡	𝑡	NOUN
cana-5235	107	43	)	)	PUNCT
cana-5235	107	44	,	,	PUNCT
cana-5235	107	45	(	(	PUNCT
cana-5235	107	46	2.12	2.12	NUM
cana-5235	107	47	)	)	PUNCT
cana-5235	107	48	𝑝1	𝑝1	NOUN
cana-5235	107	49	+	+	CCONJ
cana-5235	107	50	2	2	NUM
cana-5235	107	51	𝜇1	𝜇1	NOUN
cana-5235	107	52	[	[	X
cana-5235	107	53	1+(𝜕𝑥ℎ1)2	1+(𝜕𝑥ℎ1)2	NUM
cana-5235	107	54	]	]	X
cana-5235	108	1	[	[	X
cana-5235	108	2	𝜕𝑥𝑢1(1	𝜕𝑥𝑢1(1	ADJ
cana-5235	108	3	−	−	PROPN
cana-5235	108	4	(	(	PUNCT
cana-5235	108	5	𝜕𝑥ℎ1)2	𝜕𝑥ℎ1)2	PROPN
cana-5235	108	6	)	)	PUNCT
cana-5235	108	7	+	+	CCONJ
cana-5235	108	8	𝜕𝑥ℎ1	𝜕𝑥ℎ1	NOUN
cana-5235	108	9	(	(	PUNCT
cana-5235	108	10	𝜕𝑦𝑢1	𝜕𝑦𝑢1	PROPN
cana-5235	108	11	+	+	SYM
cana-5235	108	12	𝜕𝑥𝑣1	𝜕𝑥𝑣1	NOUN
cana-5235	108	13	)	)	PUNCT
cana-5235	108	14	]	]	PUNCT
cana-5235	109	1	+	+	CCONJ
cana-5235	109	2	𝜎2	𝜎2	NOUN
cana-5235	109	3	𝜕𝑥𝑥	𝜕𝑥𝑥	SYM
cana-5235	109	4	2	2	NUM
cana-5235	109	5	ℎ1	ℎ1	PROPN
cana-5235	109	6	[	[	X
cana-5235	109	7	1+(𝜕𝑥ℎ1)2]3/2	1+(𝜕𝑥ℎ1)2]3/2	NOUN
cana-5235	109	8	=	=	SYM
cana-5235	109	9	𝑝2	𝑝2	NOUN
cana-5235	109	10	+	+	CCONJ
cana-5235	109	11	2	2	NUM
cana-5235	109	12	𝜇2	𝜇2	NOUN
cana-5235	109	13	[	[	X
cana-5235	109	14	1+(𝜕𝑥ℎ2)2	1+(𝜕𝑥ℎ2)2	NUM
cana-5235	109	15	]	]	X
cana-5235	109	16	[	[	X
cana-5235	109	17	𝜕𝑥𝑢2(1	𝜕𝑥𝑢2(1	NOUN
cana-5235	109	18	−	−	PROPN
cana-5235	109	19	(	(	PUNCT
cana-5235	109	20	𝜕𝑥ℎ2)2	𝜕𝑥ℎ2)2	PROPN
cana-5235	109	21	)	)	PUNCT
cana-5235	109	22	+	+	CCONJ
cana-5235	109	23	(	(	PUNCT
cana-5235	109	24	𝜕𝑦𝑢2	𝜕𝑦𝑢2	NOUN
cana-5235	109	25	+	+	CCONJ
cana-5235	109	26	𝜕𝑥𝑣2	𝜕𝑥𝑣2	NOUN
cana-5235	109	27	)	)	PUNCT
cana-5235	109	28	]	]	PUNCT
cana-5235	109	29	at	at	ADP
cana-5235	109	30	𝑦	𝑦	NOUN
cana-5235	109	31	=	=	SYM
cana-5235	109	32	ℎ2(𝑥	ℎ2(𝑥	PROPN
cana-5235	109	33	,	,	PUNCT
cana-5235	109	34	𝑡	𝑡	PROPN
cana-5235	109	35	)	)	PUNCT
cana-5235	109	36	.	.	PUNCT
cana-5235	110	1	(	(	PUNCT
cana-5235	110	2	2.13	2.13	NUM
cana-5235	110	3	)	)	PUNCT
cana-5235	110	4	where	where	SCONJ
cana-5235	110	5	𝜎2	𝜎2	NOUN
cana-5235	110	6	represents	represent	VERB
cana-5235	110	7	the	the	DET
cana-5235	110	8	interfacial	interfacial	ADJ
cana-5235	110	9	tension	tension	NOUN
cana-5235	110	10	between	between	ADP
cana-5235	110	11	the	the	DET
cana-5235	110	12	two	two	NUM
cana-5235	110	13	layers	layer	NOUN
cana-5235	110	14	.	.	PUNCT
cana-5235	111	1	the	the	DET
cana-5235	111	2	boundary	boundary	ADJ
cana-5235	111	3	conditions	condition	NOUN
cana-5235	111	4	at	at	ADP
cana-5235	111	5	slippery	slippery	ADJ
cana-5235	111	6	bottom	bottom	NOUN
cana-5235	111	7	are	be	AUX
cana-5235	111	8	given	give	VERB
cana-5235	111	9	by	by	ADP
cana-5235	111	10	,	,	PUNCT
cana-5235	111	11	𝑢2	𝑢2	PROPN
cana-5235	111	12	=	=	PROPN
cana-5235	111	13	𝛽	𝛽	PROPN
cana-5235	111	14	𝜕𝑦	𝜕𝑦	NOUN
cana-5235	111	15	𝑢2	𝑢2	PROPN
cana-5235	111	16	and	and	CCONJ
cana-5235	111	17	𝑣2	𝑣2	NOUN
cana-5235	111	18	=	=	PUNCT
cana-5235	111	19	0	0	PROPN
cana-5235	112	1	at	at	ADP
cana-5235	112	2	𝑦	𝑦	NOUN
cana-5235	112	3	=	=	SYM
cana-5235	112	4	𝐻	𝐻	PROPN
cana-5235	112	5	,	,	PUNCT
cana-5235	112	6	(	(	PUNCT
cana-5235	112	7	2.14	2.14	NUM
cana-5235	112	8	)	)	PUNCT
cana-5235	112	9	where	where	SCONJ
cana-5235	112	10	𝛽	𝛽	NOUN
cana-5235	112	11	be	be	AUX
cana-5235	112	12	the	the	DET
cana-5235	112	13	slip	slip	NOUN
cana-5235	112	14	parameter	parameter	NOUN
cana-5235	112	15	having	have	VERB
cana-5235	112	16	range	range	NOUN
cana-5235	112	17	as	as	ADP
cana-5235	112	18	0	0	NUM
cana-5235	112	19	≤	≤	NUM
cana-5235	112	20	𝛽	𝛽	NOUN
cana-5235	112	21	≤	≤	NOUN
cana-5235	112	22	1	1	NUM
cana-5235	112	23	.	.	PUNCT
cana-5235	113	1	the	the	DET
cana-5235	113	2	reference	reference	NOUN
cana-5235	113	3	length	length	NOUN
cana-5235	113	4	and	and	CCONJ
cana-5235	113	5	velocity	velocity	NOUN
cana-5235	113	6	scale	scale	NOUN
cana-5235	113	7	are	be	AUX
cana-5235	113	8	chosen	choose	VERB
cana-5235	113	9	as	as	ADP
cana-5235	113	10	𝐻	𝐻	PROPN
cana-5235	113	11	and	and	CCONJ
cana-5235	113	12	𝑉	𝑉	PROPN
cana-5235	113	13	,	,	PUNCT
cana-5235	113	14	respectively	respectively	ADV
cana-5235	113	15	.	.	PUNCT
cana-5235	114	1	further	far	ADV
cana-5235	114	2	,	,	PUNCT
cana-5235	114	3	the	the	DET
cana-5235	114	4	chosen	choose	VERB
cana-5235	114	5	scale	scale	NOUN
cana-5235	114	6	of	of	ADP
cana-5235	114	7	velocity	velocity	NOUN
cana-5235	114	8	is	be	AUX
cana-5235	114	9	the	the	DET
cana-5235	114	10	maximum	maximum	ADJ
cana-5235	114	11	value	value	NOUN
cana-5235	114	12	of	of	ADP
cana-5235	114	13	velocity	velocity	NOUN
cana-5235	114	14	for	for	ADP
cana-5235	114	15	an	an	DET
cana-5235	114	16	uniform	uniform	ADJ
cana-5235	114	17	nusselt	nusselt	NOUN
cana-5235	114	18	film	film	NOUN
cana-5235	114	19	over	over	ADP
cana-5235	114	20	the	the	DET
cana-5235	114	21	rigid	rigid	ADJ
cana-5235	114	22	substrate	substrate	NOUN
cana-5235	114	23	,	,	PUNCT
cana-5235	114	24	which	which	PRON
cana-5235	114	25	is	be	AUX
cana-5235	114	26	defined	define	VERB
cana-5235	114	27	as	as	ADP
cana-5235	114	28	𝑉	𝑉	PROPN
cana-5235	114	29	=	=	NOUN
cana-5235	114	30	𝑔𝐻2sin𝜃/2𝜈1	𝑔𝐻2sin𝜃/2𝜈1	NOUN
cana-5235	114	31	,	,	PUNCT
cana-5235	114	32	with	with	ADP
cana-5235	114	33	𝜈1	𝜈1	NOUN
cana-5235	114	34	being	be	AUX
cana-5235	114	35	the	the	DET
cana-5235	114	36	kinematic	kinematic	ADJ
cana-5235	114	37	viscosity	viscosity	NOUN
cana-5235	114	38	of	of	ADP
cana-5235	114	39	upper	upper	ADJ
cana-5235	114	40	layer	layer	NOUN
cana-5235	114	41	fluid	fluid	NOUN
cana-5235	114	42	.	.	PUNCT
cana-5235	115	1	now	now	ADV
cana-5235	115	2	,	,	PUNCT
cana-5235	115	3	the	the	DET
cana-5235	115	4	governing	govern	VERB
cana-5235	115	5	equations	equation	NOUN
cana-5235	115	6	along	along	ADP
cana-5235	115	7	with	with	ADP
cana-5235	115	8	the	the	DET
cana-5235	115	9	boundary	boundary	ADJ
cana-5235	115	10	conditions	condition	NOUN
cana-5235	115	11	are	be	AUX
cana-5235	115	12	made	make	VERB
cana-5235	115	13	dimensionless	dimensionless	NOUN
cana-5235	115	14	using	use	VERB
cana-5235	115	15	the	the	DET
cana-5235	115	16	following	follow	VERB
cana-5235	115	17	non	non	ADJ
cana-5235	115	18	-	-	ADJ
cana-5235	115	19	dimensional	dimensional	ADJ
cana-5235	115	20	variables	variable	NOUN
cana-5235	115	21	,	,	PUNCT
cana-5235	115	22	are	be	AUX
cana-5235	115	23	given	give	VERB
cana-5235	115	24	as	as	ADP
cana-5235	115	25	�	�	PROPN
cana-5235	115	26	̅	̅	NOUN
cana-5235	115	27	�	�	NOUN
cana-5235	115	28	=	=	PUNCT
cana-5235	115	29	𝑥	𝑥	PROPN
cana-5235	115	30	𝐻	𝐻	PROPN
cana-5235	115	31	,	,	PUNCT
cana-5235	115	32	�	�	NOUN
cana-5235	115	33	̅	̅	NOUN
cana-5235	115	34	�	�	NOUN
cana-5235	115	35	=	=	SYM
cana-5235	115	36	𝑦	𝑦	SYM
cana-5235	115	37	𝐻	𝐻	PROPN
cana-5235	115	38	,	,	PUNCT
cana-5235	115	39	�	�	NOUN
cana-5235	115	40	̅	̅	NOUN
cana-5235	115	41	�	�	NOUN
cana-5235	115	42	𝑗	𝑗	NOUN
cana-5235	115	43	=	=	SYM
cana-5235	115	44	𝑢𝑗	𝑢𝑗	PROPN
cana-5235	115	45	𝑉	𝑉	PROPN
cana-5235	115	46	,	,	PUNCT
cana-5235	115	47	�	�	PROPN
cana-5235	115	48	̅	̅	NOUN
cana-5235	115	49	�	�	NOUN
cana-5235	115	50	𝑗	𝑗	NOUN
cana-5235	115	51	=	=	SYM
cana-5235	115	52	𝑣𝑗	𝑣𝑗	ADP
cana-5235	115	53	𝑉	𝑉	PROPN
cana-5235	115	54	,	,	PUNCT
cana-5235	115	55	𝑡̅	𝑡̅	PROPN
cana-5235	115	56	=	=	SYM
cana-5235	115	57	𝑡𝑉	𝑡𝑉	PROPN
cana-5235	115	58	𝐻	𝐻	PROPN
cana-5235	115	59	,	,	PUNCT
cana-5235	115	60	�	�	NOUN
cana-5235	115	61	̅	̅	NOUN
cana-5235	115	62	�	�	NOUN
cana-5235	115	63	𝑗	𝑗	NOUN
cana-5235	115	64	=	=	SYM
cana-5235	115	65	𝑝𝑗	𝑝𝑗	NOUN
cana-5235	115	66	𝜌𝑗𝑉2	𝜌𝑗𝑉2	NOUN
cana-5235	115	67	,	,	PUNCT
cana-5235	115	68	ℎ̅𝑗	ℎ̅𝑗	PROPN
cana-5235	115	69	=	=	NOUN
cana-5235	115	70	ℎ𝑗	ℎ𝑗	PROPN
cana-5235	115	71	𝐻	𝐻	PROPN
cana-5235	115	72	,	,	PUNCT
cana-5235	115	73	�	�	NOUN
cana-5235	115	74	̅	̅	NOUN
cana-5235	115	75	�	�	NOUN
cana-5235	115	76	=	=	SYM
cana-5235	115	77	𝑑	𝑑	PROPN
cana-5235	115	78	𝐻	𝐻	PROPN
cana-5235	115	79	,	,	PUNCT
cana-5235	115	80	γ̅	γ̅	PUNCT
cana-5235	115	81	=	=	SYM
cana-5235	115	82	γ	γ	X
cana-5235	115	83	γ0	γ0	PROPN
cana-5235	115	84	,	,	PUNCT
cana-5235	115	85	�	�	PROPN
cana-5235	115	86	̅	̅	NOUN
cana-5235	115	87	�	�	NOUN
cana-5235	115	88	𝑗	𝑗	NOUN
cana-5235	115	89	=	=	SYM
cana-5235	115	90	𝜎𝑗	𝜎𝑗	PROPN
cana-5235	115	91	𝜎0	𝜎0	NOUN
cana-5235	115	92	.	.	PUNCT
cana-5235	116	1	the	the	DET
cana-5235	116	2	set	set	NOUN
cana-5235	116	3	of	of	ADP
cana-5235	116	4	non	non	ADJ
cana-5235	116	5	-	-	ADJ
cana-5235	116	6	dimensional	dimensional	ADJ
cana-5235	116	7	form	form	NOUN
cana-5235	116	8	of	of	ADP
cana-5235	116	9	governing	govern	VERB
cana-5235	116	10	equations	equation	NOUN
cana-5235	116	11	and	and	CCONJ
cana-5235	116	12	boundary	boundary	ADJ
cana-5235	116	13	conditions	condition	NOUN
cana-5235	116	14	for	for	ADP
cana-5235	116	15	the	the	DET
cana-5235	116	16	two	two	NUM
cana-5235	116	17	-	-	PUNCT
cana-5235	116	18	layer	layer	NOUN
cana-5235	116	19	fluid	fluid	NOUN
cana-5235	116	20	system	system	NOUN
cana-5235	116	21	are	be	AUX
cana-5235	116	22	given	give	VERB
cana-5235	116	23	by	by	ADP
cana-5235	116	24	𝜕𝑥𝑢𝑗	𝜕𝑥𝑢𝑗	NOUN
cana-5235	116	25	+	+	CCONJ
cana-5235	116	26	𝜕𝑦𝑣𝑗	𝜕𝑦𝑣𝑗	NUM
cana-5235	116	27	=	=	SYM
cana-5235	116	28	0	0	NUM
cana-5235	116	29	,	,	PUNCT
cana-5235	116	30	(	(	PUNCT
cana-5235	116	31	2.15	2.15	NUM
cana-5235	116	32	)	)	PUNCT
cana-5235	116	33	𝜕𝑡𝑢𝑗	𝜕𝑡𝑢𝑗	ADV
cana-5235	116	34	+	+	CCONJ
cana-5235	116	35	𝑢𝑗	𝑢𝑗	NOUN
cana-5235	116	36	𝜕𝑥𝑢𝑗	𝜕𝑥𝑢𝑗	ADV
cana-5235	116	37	+	+	CCONJ
cana-5235	116	38	𝑣𝑗	𝑣𝑗	ADP
cana-5235	116	39	𝜕𝑦𝑢𝑗	𝜕𝑦𝑢𝑗	NOUN
cana-5235	116	40	=	=	SYM
cana-5235	116	41	−𝜕𝑥𝑝𝑗	−𝜕𝑥𝑝𝑗	X
cana-5235	116	42	+	+	CCONJ
cana-5235	116	43	1	1	NUM
cana-5235	116	44	𝑅𝑒𝑗	𝑅𝑒𝑗	PROPN
cana-5235	116	45	(	(	PUNCT
cana-5235	116	46	𝜕𝑥𝑥	𝜕𝑥𝑥	NOUN
cana-5235	116	47	2	2	NUM
cana-5235	116	48	𝑢𝑗	𝑢𝑗	NOUN
cana-5235	116	49	+	+	CCONJ
cana-5235	116	50	𝜕𝑦𝑦	𝜕𝑦𝑦	PROPN
cana-5235	116	51	2	2	NUM
cana-5235	116	52	𝑢𝑗	𝑢𝑗	NOUN
cana-5235	116	53	)	)	PUNCT
cana-5235	116	54	+	+	CCONJ
cana-5235	117	1	𝐺	𝐺	PROPN
cana-5235	117	2	,	,	PUNCT
cana-5235	117	3	(	(	PUNCT
cana-5235	117	4	2.16	2.16	NUM
cana-5235	117	5	)	)	PUNCT
cana-5235	117	6	𝜕𝑡𝑣𝑗	𝜕𝑡𝑣𝑗	NOUN
cana-5235	117	7	+	+	CCONJ
cana-5235	117	8	𝑢𝑗𝜕𝑥𝑣𝑗	𝑢𝑗𝜕𝑥𝑣𝑗	NOUN
cana-5235	117	9	+	+	CCONJ
cana-5235	117	10	𝑣𝑗𝜕𝑦𝑣𝑗	𝑣𝑗𝜕𝑦𝑣𝑗	ADJ
cana-5235	117	11	=	=	ADJ
cana-5235	117	12	−𝜕𝑥𝑝𝑗	−𝜕𝑥𝑝𝑗	X
cana-5235	117	13	+	+	CCONJ
cana-5235	117	14	1	1	NUM
cana-5235	117	15	𝑅𝑒𝑗	𝑅𝑒𝑗	PROPN
cana-5235	117	16	(	(	PUNCT
cana-5235	117	17	𝜕𝑥𝑥	𝜕𝑥𝑥	X
cana-5235	117	18	2	2	NUM
cana-5235	117	19	𝑣𝑗	𝑣𝑗	ADP
cana-5235	117	20	+	+	CCONJ
cana-5235	117	21	𝜕𝑦𝑦	𝜕𝑦𝑦	ADP
cana-5235	117	22	2	2	NUM
cana-5235	117	23	𝑣𝑗	𝑣𝑗	NOUN
cana-5235	117	24	)	)	PUNCT
cana-5235	117	25	−	−	PROPN
cana-5235	118	1	𝐺	𝐺	PROPN
cana-5235	118	2	cot𝜃	cot𝜃	NOUN
cana-5235	118	3	,	,	PUNCT
cana-5235	118	4	(	(	PUNCT
cana-5235	118	5	2.17	2.17	NUM
cana-5235	118	6	)	)	PUNCT
cana-5235	118	7	𝑣𝑗	𝑣𝑗	ADP
cana-5235	118	8	=	=	SYM
cana-5235	118	9	𝜕𝑡ℎ𝑗	𝜕𝑡ℎ𝑗	NOUN
cana-5235	118	10	+	+	X
cana-5235	118	11	𝑢𝑗𝜕𝑥ℎ𝑗	𝑢𝑗𝜕𝑥ℎ𝑗	NOUN
cana-5235	118	12	at	at	ADP
cana-5235	118	13	𝑦	𝑦	NOUN
cana-5235	118	14	=	=	PUNCT
cana-5235	118	15	ℎ𝑗	ℎ𝑗	PROPN
cana-5235	118	16	(	(	PUNCT
cana-5235	118	17	𝑥	𝑥	PROPN
cana-5235	118	18	,	,	PUNCT
cana-5235	118	19	𝑡	𝑡	NOUN
cana-5235	118	20	)	)	PUNCT
cana-5235	118	21	,	,	PUNCT
cana-5235	118	22	(	(	PUNCT
cana-5235	118	23	2.18	2.18	NUM
cana-5235	118	24	)	)	PUNCT
cana-5235	118	25	−4𝜕𝑥𝑢1𝜕𝑥ℎ1	−4𝜕𝑥𝑢1𝜕𝑥ℎ1	PRON
cana-5235	118	26	+	+	CCONJ
cana-5235	118	27	(	(	PUNCT
cana-5235	118	28	𝜕𝑦𝑢1	𝜕𝑦𝑢1	PROPN
cana-5235	118	29	+	+	NOUN
cana-5235	118	30	𝜕𝑥𝑣1)(1	𝜕𝑥𝑣1)(1	PROPN
cana-5235	118	31	−	−	PROPN
cana-5235	118	32	(	(	PUNCT
cana-5235	118	33	𝜕𝑥ℎ1)2	𝜕𝑥ℎ1)2	NOUN
cana-5235	118	34	)	)	PUNCT
cana-5235	118	35	=	=	PUNCT
cana-5235	119	1	[	[	X
cana-5235	119	2	−	−	X
cana-5235	119	3	𝑀𝑎	𝑀𝑎	PROPN
cana-5235	119	4	𝐶𝑎	𝐶𝑎	PROPN
cana-5235	119	5	𝜕𝑥γ	𝜕𝑥γ	VERB
cana-5235	119	6	𝜏	𝜏	NOUN
cana-5235	119	7	]	]	PUNCT
cana-5235	119	8	√1	√1	PROPN
cana-5235	119	9	+	+	CCONJ
cana-5235	119	10	(	(	PUNCT
cana-5235	119	11	𝜕𝑥ℎ1)2	𝜕𝑥ℎ1)2	VERB
cana-5235	119	12	at	at	ADP
cana-5235	119	13	𝑦	𝑦	NOUN
cana-5235	119	14	=	=	SYM
cana-5235	119	15	ℎ1(𝑥	ℎ1(𝑥	PROPN
cana-5235	119	16	,	,	PUNCT
cana-5235	119	17	𝑡	𝑡	PROPN
cana-5235	119	18	)	)	PUNCT
cana-5235	119	19	,	,	PUNCT
cana-5235	119	20	(	(	PUNCT
cana-5235	119	21	2.19	2.19	NUM
cana-5235	119	22	)	)	PUNCT
cana-5235	119	23	𝑅𝑒	𝑅𝑒	VERB
cana-5235	119	24	𝑝1	𝑝1	NOUN
cana-5235	119	25	=	=	SYM
cana-5235	119	26	2	2	NUM
cana-5235	119	27	(	(	PUNCT
cana-5235	119	28	1+(𝜕𝑥ℎ1)2	1+(𝜕𝑥ℎ1)2	NUM
cana-5235	119	29	)	)	PUNCT
cana-5235	120	1	[	[	X
cana-5235	120	2	𝜕𝑥𝑢1	𝜕𝑥𝑢1	X
cana-5235	120	3	(	(	PUNCT
cana-5235	120	4	𝜕𝑥ℎ1)2	𝜕𝑥ℎ1)2	VERB
cana-5235	120	5	−	−	PROPN
cana-5235	120	6	(	(	PUNCT
cana-5235	120	7	𝜕𝑦𝑢1	𝜕𝑦𝑢1	NUM
cana-5235	120	8	+	+	SYM
cana-5235	120	9	𝜕𝑥𝑣1	𝜕𝑥𝑣1	NOUN
cana-5235	120	10	)	)	PUNCT
cana-5235	120	11	𝜕𝑥ℎ1	𝜕𝑥ℎ1	PROPN
cana-5235	121	1	+	+	PUNCT
cana-5235	121	2	𝜕𝑥𝑣1	𝜕𝑥𝑣1	X
cana-5235	121	3	]	]	X
cana-5235	121	4	−	−	PROPN
cana-5235	122	1	[	[	X
cana-5235	122	2	1−𝑀𝑎(γ−1	1−𝑀𝑎(γ−1	NUM
cana-5235	122	3	)	)	PUNCT
cana-5235	122	4	]	]	PUNCT
cana-5235	122	5	𝜕𝑥𝑥	𝜕𝑥𝑥	X
cana-5235	123	1	2	2	NUM
cana-5235	123	2	ℎ1	ℎ1	PROPN
cana-5235	123	3	𝐶𝑎	𝐶𝑎	PROPN
cana-5235	123	4	[	[	X
cana-5235	123	5	1+(𝜕𝑥ℎ)2]3/2	1+(𝜕𝑥ℎ)2]3/2	NUM
cana-5235	123	6	at	at	ADP
cana-5235	123	7	𝑦	𝑦	NOUN
cana-5235	123	8	=	=	SYM
cana-5235	123	9	ℎ1(𝑥	ℎ1(𝑥	PROPN
cana-5235	123	10	,	,	PUNCT
cana-5235	123	11	𝑡	𝑡	PROPN
cana-5235	123	12	)	)	PUNCT
cana-5235	123	13	,	,	PUNCT
cana-5235	123	14	(	(	PUNCT
cana-5235	123	15	2.20	2.20	NUM
cana-5235	123	16	)	)	PUNCT
cana-5235	123	17	𝜕𝑡γ	𝜕𝑡γ	PUNCT
cana-5235	124	1	+	+	CCONJ
cana-5235	124	2	𝑢1	𝑢1	PROPN
cana-5235	124	3	𝜕𝑡γ	𝜕𝑡γ	PART
cana-5235	124	4	+	+	PUNCT
cana-5235	124	5	γ𝜕𝑥𝑢1	γ𝜕𝑥𝑢1	X
cana-5235	125	1	=	=	SYM
cana-5235	125	2	1	1	NUM
cana-5235	125	3	𝛼	𝛼	X
cana-5235	125	4	𝐶𝑎	𝐶𝑎	PROPN
cana-5235	125	5	𝜕𝑥𝑥	𝜕𝑥𝑥	NOUN
cana-5235	125	6	2	2	NUM
cana-5235	125	7	γ	γ	NOUN
cana-5235	125	8	at	at	ADP
cana-5235	125	9	𝑦	𝑦	NOUN
cana-5235	125	10	=	=	SYM
cana-5235	125	11	ℎ1(𝑥	ℎ1(𝑥	PROPN
cana-5235	125	12	,	,	PUNCT
cana-5235	125	13	𝑡	𝑡	PROPN
cana-5235	125	14	)	)	PUNCT
cana-5235	125	15	,	,	PUNCT
cana-5235	125	16	(	(	PUNCT
cana-5235	125	17	2.21	2.21	NUM
cana-5235	125	18	)	)	PUNCT
cana-5235	125	19	communications	communication	NOUN
cana-5235	125	20	on	on	ADP
cana-5235	125	21	applied	apply	VERB
cana-5235	125	22	nonlinear	nonlinear	ADJ
cana-5235	125	23	analysis	analysis	NOUN
cana-5235	125	24	issn	issn	NOUN
cana-5235	125	25	:	:	PUNCT
cana-5235	125	26	1074	1074	NUM
cana-5235	125	27	-	-	PUNCT
cana-5235	125	28	133x	133x	NUM
cana-5235	125	29	vol	vol	VERB
cana-5235	125	30	32	32	NUM
cana-5235	125	31	no	no	NOUN
cana-5235	125	32	.	.	PUNCT
cana-5235	126	1	10s	10	NOUN
cana-5235	126	2	(	(	PUNCT
cana-5235	126	3	2025	2025	NUM
cana-5235	126	4	)	)	PUNCT
cana-5235	126	5	1328	1328	NUM
cana-5235	126	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5235	126	7	𝑢1	𝑢1	PROPN
cana-5235	126	8	=	=	PROPN
cana-5235	126	9	𝑢2	𝑢2	PROPN
cana-5235	126	10	and	and	CCONJ
cana-5235	126	11	𝑣1	𝑣1	NOUN
cana-5235	126	12	=	=	PROPN
cana-5235	126	13	𝑣2	𝑣2	PROPN
cana-5235	126	14	at	at	ADP
cana-5235	126	15	𝑦	𝑦	NOUN
cana-5235	126	16	=	=	SYM
cana-5235	126	17	ℎ2(𝑥	ℎ2(𝑥	PROPN
cana-5235	126	18	,	,	PUNCT
cana-5235	126	19	𝑡	𝑡	NOUN
cana-5235	126	20	)	)	PUNCT
cana-5235	126	21	,	,	PUNCT
cana-5235	126	22	(	(	PUNCT
cana-5235	126	23	2.22	2.22	NUM
cana-5235	126	24	)	)	PUNCT
cana-5235	126	25	−4	−4	X
cana-5235	126	26	𝜕𝑥𝑢1	𝜕𝑥𝑢1	NOUN
cana-5235	126	27	𝜕𝑥ℎ1	𝜕𝑥ℎ1	NUM
cana-5235	126	28	+	+	CCONJ
cana-5235	126	29	(	(	PUNCT
cana-5235	126	30	𝜕𝑦𝑢1	𝜕𝑦𝑢1	PROPN
cana-5235	126	31	+	+	NOUN
cana-5235	126	32	𝜕𝑥𝑣1)(1	𝜕𝑥𝑣1)(1	PROPN
cana-5235	126	33	−	−	PROPN
cana-5235	126	34	(	(	PUNCT
cana-5235	126	35	𝜕𝑥ℎ1)2	𝜕𝑥ℎ1)2	PROPN
cana-5235	126	36	)	)	PUNCT
cana-5235	126	37	=	=	PUNCT
cana-5235	127	1	𝑚	𝑚	X
cana-5235	127	2	[	[	X
cana-5235	127	3	−4	−4	X
cana-5235	127	4	𝜕𝑥𝑢2	𝜕𝑥𝑢2	X
cana-5235	127	5	𝜕𝑥ℎ2	𝜕𝑥ℎ2	X
cana-5235	127	6	+	+	CCONJ
cana-5235	127	7	(	(	PUNCT
cana-5235	127	8	𝜕𝑦𝑢2	𝜕𝑦𝑢2	NOUN
cana-5235	127	9	+	+	CCONJ
cana-5235	128	1	𝜕𝑥𝑣2)(1	𝜕𝑥𝑣2)(1	PROPN
cana-5235	128	2	−	−	PROPN
cana-5235	128	3	(	(	PUNCT
cana-5235	128	4	𝜕𝑥ℎ2)2	𝜕𝑥ℎ2)2	PROPN
cana-5235	128	5	)	)	PUNCT
cana-5235	128	6	]	]	PUNCT
cana-5235	128	7	at	at	ADP
cana-5235	128	8	𝑦	𝑦	NOUN
cana-5235	128	9	=	=	SYM
cana-5235	128	10	ℎ2(𝑥	ℎ2(𝑥	PROPN
cana-5235	128	11	,	,	PUNCT
cana-5235	128	12	𝑡	𝑡	NOUN
cana-5235	128	13	)	)	PUNCT
cana-5235	128	14	,	,	PUNCT
cana-5235	128	15	(	(	PUNCT
cana-5235	128	16	2.23	2.23	NUM
cana-5235	128	17	)	)	PUNCT
cana-5235	128	18	𝑝1	𝑝1	NOUN
cana-5235	128	19	+	+	CCONJ
cana-5235	128	20	2	2	NUM
cana-5235	128	21	𝑅𝑒1	𝑅𝑒1	NOUN
cana-5235	128	22	(	(	PUNCT
cana-5235	128	23	1+(𝜕𝑥ℎ1)2	1+(𝜕𝑥ℎ1)2	NUM
cana-5235	128	24	)	)	PUNCT
cana-5235	129	1	[	[	X
cana-5235	129	2	(	(	PUNCT
cana-5235	129	3	𝜕𝑦𝑢1	𝜕𝑦𝑢1	NUM
cana-5235	129	4	+	+	SYM
cana-5235	129	5	𝜕𝑥𝑣1	𝜕𝑥𝑣1	NOUN
cana-5235	129	6	)	)	PUNCT
cana-5235	129	7	𝜕𝑥ℎ1	𝜕𝑥ℎ1	PROPN
cana-5235	129	8	−	−	PROPN
cana-5235	129	9	𝜕𝑥𝑢1	𝜕𝑥𝑢1	NOUN
cana-5235	129	10	(	(	PUNCT
cana-5235	129	11	𝜕𝑥ℎ1)2	𝜕𝑥ℎ1)2	VERB
cana-5235	129	12	−	−	NOUN
cana-5235	129	13	𝜕𝑦𝑣1	𝜕𝑦𝑣1	NOUN
cana-5235	129	14	]	]	X
cana-5235	129	15	=	=	SYM
cana-5235	129	16	𝑟	𝑟	NOUN
cana-5235	129	17	𝑝2	𝑝2	NOUN
cana-5235	129	18	+	+	CCONJ
cana-5235	129	19	2	2	NUM
cana-5235	129	20	𝑅𝑒1	𝑅𝑒1	NOUN
cana-5235	129	21	(	(	PUNCT
cana-5235	129	22	1+(𝜕𝑥ℎ2)2	1+(𝜕𝑥ℎ2)2	NUM
cana-5235	129	23	)	)	PUNCT
cana-5235	130	1	[	[	X
cana-5235	130	2	(	(	PUNCT
cana-5235	130	3	𝜕𝑦𝑢2	𝜕𝑦𝑢2	NOUN
cana-5235	130	4	+	+	CCONJ
cana-5235	130	5	𝜕𝑥𝑣2	𝜕𝑥𝑣2	NOUN
cana-5235	130	6	)	)	PUNCT
cana-5235	130	7	𝜕𝑥ℎ2	𝜕𝑥ℎ2	NOUN
cana-5235	130	8	−	−	PROPN
cana-5235	130	9	𝜕𝑥𝑢2	𝜕𝑥𝑢2	PROPN
cana-5235	130	10	(	(	PUNCT
cana-5235	130	11	𝜕𝑥ℎ2)2	𝜕𝑥ℎ2)2	PROPN
cana-5235	130	12	−	−	PROPN
cana-5235	130	13	𝜕𝑦𝑣2	𝜕𝑦𝑣2	X
cana-5235	130	14	]	]	PUNCT
cana-5235	131	1	−	−	PROPN
cana-5235	131	2	𝑊𝑒	𝑊𝑒	ADJ
cana-5235	131	3	𝜕𝑥𝑥	𝜕𝑥𝑥	SYM
cana-5235	131	4	2	2	NUM
cana-5235	131	5	ℎ2	ℎ2	NOUN
cana-5235	131	6	[	[	X
cana-5235	131	7	1+(𝜕𝑥ℎ2)2	1+(𝜕𝑥ℎ2)2	NUM
cana-5235	131	8	]	]	X
cana-5235	131	9	at	at	ADP
cana-5235	131	10	𝑦	𝑦	NOUN
cana-5235	131	11	=	=	SYM
cana-5235	131	12	ℎ2(𝑥	ℎ2(𝑥	PROPN
cana-5235	131	13	,	,	PUNCT
cana-5235	131	14	𝑡	𝑡	X
cana-5235	131	15	)	)	PUNCT
cana-5235	131	16	(	(	PUNCT
cana-5235	131	17	2.24	2.24	NUM
cana-5235	131	18	)	)	PUNCT
cana-5235	131	19	𝑢2	𝑢2	PROPN
cana-5235	131	20	=	=	SYM
cana-5235	131	21	𝛽	𝛽	PROPN
cana-5235	131	22	𝜕𝑦𝑢2	𝜕𝑦𝑢2	NOUN
cana-5235	131	23	and	and	CCONJ
cana-5235	131	24	𝑣2	𝑣2	NOUN
cana-5235	131	25	=	=	PUNCT
cana-5235	131	26	0	0	PROPN
cana-5235	131	27	at	at	ADP
cana-5235	131	28	𝑦	𝑦	NOUN
cana-5235	131	29	=	=	SYM
cana-5235	131	30	𝐻	𝐻	PROPN
cana-5235	131	31	,	,	PUNCT
cana-5235	131	32	(	(	PUNCT
cana-5235	131	33	2.25	2.25	NUM
cana-5235	131	34	)	)	PUNCT
cana-5235	131	35	where	where	SCONJ
cana-5235	131	36	𝑚	𝑚	NOUN
cana-5235	131	37	=	=	SYM
cana-5235	131	38	𝜇2/𝜇1	𝜇2/𝜇1	NOUN
cana-5235	131	39	and	and	CCONJ
cana-5235	131	40	𝑟	𝑟	NOUN
cana-5235	131	41	=	=	SYM
cana-5235	131	42	𝜌2/𝜌1	𝜌2/𝜌1	PROPN
cana-5235	131	43	be	be	VERB
cana-5235	131	44	the	the	DET
cana-5235	131	45	viscosity	viscosity	NOUN
cana-5235	131	46	and	and	CCONJ
cana-5235	131	47	density	density	NOUN
cana-5235	131	48	ratios	ratio	NOUN
cana-5235	131	49	.	.	PUNCT
cana-5235	132	1	the	the	DET
cana-5235	132	2	other	other	ADJ
cana-5235	132	3	parameters	parameter	NOUN
cana-5235	132	4	are	be	AUX
cana-5235	132	5	given	give	VERB
cana-5235	132	6	as	as	SCONJ
cana-5235	132	7	follows	follow	VERB
cana-5235	132	8	:	:	PUNCT
cana-5235	132	9	marangoninumber	marangoninumber	PROPN
cana-5235	132	10	𝑀𝑎	𝑀𝑎	PROPN
cana-5235	132	11	=	=	PROPN
cana-5235	132	12	𝐸γ0	𝐸γ0	NOUN
cana-5235	132	13	𝜎0	𝜎0	NOUN
cana-5235	132	14	,	,	PUNCT
cana-5235	132	15	reynoldsnumber	reynoldsnumber	NOUN
cana-5235	132	16	𝑅𝑒1	𝑅𝑒1	NOUN
cana-5235	132	17	=	=	PUNCT
cana-5235	132	18	𝑉𝐻	𝑉𝐻	PROPN
cana-5235	132	19	𝜈1	𝜈1	NOUN
cana-5235	132	20	,	,	PUNCT
cana-5235	132	21	capillarynumber	capillarynumber	VERB
cana-5235	132	22	𝐶𝑎	𝐶𝑎	PROPN
cana-5235	132	23	=	=	SYM
cana-5235	132	24	𝑉𝜇1	𝑉𝜇1	NOUN
cana-5235	132	25	𝜎0	𝜎0	NOUN
cana-5235	132	26	,	,	PUNCT
cana-5235	132	27	surfactantsurfaceconstant	surfactantsurfaceconstant	ADJ
cana-5235	132	28	𝛼	𝛼	NOUN
cana-5235	132	29	=	=	SYM
cana-5235	132	30	𝜎0𝐻	𝜎0𝐻	NUM
cana-5235	132	31	𝜇1	𝜇1	PROPN
cana-5235	132	32	,	,	PUNCT
cana-5235	132	33	webernumber	webernumber	PROPN
cana-5235	133	1	𝑊𝑒	𝑊𝑒	NOUN
cana-5235	133	2	=	=	SYM
cana-5235	133	3	𝜎2	𝜎2	NOUN
cana-5235	133	4	𝜌	𝜌	ADP
cana-5235	133	5	𝑔𝐻2	𝑔𝐻2	NOUN
cana-5235	133	6	.	.	PUNCT
cana-5235	134	1	2.1	2.1	NUM
cana-5235	134	2	base	base	NOUN
cana-5235	134	3	solution	solution	NOUN
cana-5235	134	4	and	and	CCONJ
cana-5235	134	5	stability	stability	NOUN
cana-5235	134	6	equation	equation	NOUN
cana-5235	134	7	the	the	DET
cana-5235	134	8	base	base	NOUN
cana-5235	134	9	state	state	NOUN
cana-5235	134	10	solution	solution	NOUN
cana-5235	134	11	corresponding	correspond	VERB
cana-5235	134	12	to	to	ADP
cana-5235	134	13	the	the	DET
cana-5235	134	14	two	two	NUM
cana-5235	134	15	-	-	PUNCT
cana-5235	134	16	layer	layer	NOUN
cana-5235	134	17	fluid	fluid	NOUN
cana-5235	134	18	system	system	NOUN
cana-5235	134	19	in	in	ADP
cana-5235	134	20	the	the	DET
cana-5235	134	21	case	case	NOUN
cana-5235	134	22	of	of	ADP
cana-5235	134	23	velocity	velocity	NOUN
cana-5235	134	24	and	and	CCONJ
cana-5235	134	25	pressure	pressure	NOUN
cana-5235	134	26	are	be	AUX
cana-5235	134	27	obtained	obtain	VERB
cana-5235	134	28	by	by	ADP
cana-5235	134	29	assuming	assume	VERB
cana-5235	134	30	𝑢1	𝑢1	PROPN
cana-5235	134	31	=	=	SYM
cana-5235	134	32	(	(	PUNCT
cana-5235	134	33	𝑈1𝐵(𝑦),0	𝑈1𝐵(𝑦),0	PROPN
cana-5235	134	34	)	)	PUNCT
cana-5235	134	35	,	,	PUNCT
cana-5235	134	36	𝑢2	𝑢2	PROPN
cana-5235	134	37	=	=	SYM
cana-5235	134	38	(	(	PUNCT
cana-5235	134	39	𝑈2𝐵(𝑦),0	𝑈2𝐵(𝑦),0	PROPN
cana-5235	134	40	)	)	PUNCT
cana-5235	134	41	,	,	PUNCT
cana-5235	134	42	𝑝1	𝑝1	NOUN
cana-5235	134	43	=	=	SYM
cana-5235	134	44	(	(	PUNCT
cana-5235	134	45	𝑃1𝐵(𝑦),0	𝑃1𝐵(𝑦),0	PROPN
cana-5235	134	46	)	)	PUNCT
cana-5235	134	47	and	and	CCONJ
cana-5235	134	48	𝑝2	𝑝2	NOUN
cana-5235	134	49	=	=	SYM
cana-5235	134	50	(	(	PUNCT
cana-5235	134	51	𝑃2𝐵(𝑦),0	𝑃2𝐵(𝑦),0	PROPN
cana-5235	134	52	)	)	PUNCT
cana-5235	134	53	,	,	PUNCT
cana-5235	134	54	where	where	SCONJ
cana-5235	134	55	𝑈1𝐵(𝑦	𝑈1𝐵(𝑦	NOUN
cana-5235	134	56	)	)	PUNCT
cana-5235	134	57	,	,	PUNCT
cana-5235	134	58	𝑃1𝐵(𝑦	𝑃1𝐵(𝑦	NUM
cana-5235	134	59	)	)	PUNCT
cana-5235	134	60	,	,	PUNCT
cana-5235	134	61	𝑈2𝐵(𝑦	𝑈2𝐵(𝑦	PROPN
cana-5235	134	62	)	)	PUNCT
cana-5235	134	63	,	,	PUNCT
cana-5235	134	64	and	and	CCONJ
cana-5235	134	65	𝑃2𝐵(𝑦	𝑃2𝐵(𝑦	NOUN
cana-5235	134	66	)	)	PUNCT
cana-5235	134	67	denote	denote	VERB
cana-5235	134	68	the	the	DET
cana-5235	134	69	base	base	ADJ
cana-5235	134	70	state	state	NOUN
cana-5235	134	71	velocity	velocity	NOUN
cana-5235	134	72	and	and	CCONJ
cana-5235	134	73	pressure	pressure	NOUN
cana-5235	134	74	in	in	ADP
cana-5235	134	75	upper	upper	ADJ
cana-5235	134	76	and	and	CCONJ
cana-5235	134	77	lower	low	ADJ
cana-5235	134	78	layers	layer	NOUN
cana-5235	134	79	.	.	PUNCT
cana-5235	135	1	by	by	ADP
cana-5235	135	2	applying	apply	VERB
cana-5235	135	3	these	these	DET
cana-5235	135	4	assumptions	assumption	NOUN
cana-5235	135	5	in	in	ADP
cana-5235	135	6	the	the	DET
cana-5235	135	7	above	above	ADJ
cana-5235	135	8	system	system	NOUN
cana-5235	135	9	of	of	ADP
cana-5235	135	10	equations	equation	NOUN
cana-5235	135	11	(	(	PUNCT
cana-5235	135	12	2.15)–(2.25	2.15)–(2.25	NUM
cana-5235	135	13	)	)	PUNCT
cana-5235	135	14	yield	yield	VERB
cana-5235	135	15	the	the	DET
cana-5235	135	16	following	follow	VERB
cana-5235	135	17	solutions	solution	NOUN
cana-5235	135	18	𝑈1𝐵(𝑦	𝑈1𝐵(𝑦	NOUN
cana-5235	135	19	)	)	PUNCT
cana-5235	136	1	=	=	PUNCT
cana-5235	137	1	−𝑦2	−𝑦2	PROPN
cana-5235	137	2	+	+	CCONJ
cana-5235	137	3	𝜏	𝜏	PUNCT
cana-5235	137	4	𝑦	𝑦	NOUN
cana-5235	137	5	+	+	X
cana-5235	138	1	[	[	X
cana-5235	138	2	(	(	PUNCT
cana-5235	138	3	2𝑑2	2𝑑2	NUM
cana-5235	138	4	−	−	NOUN
cana-5235	138	5	𝜏	𝜏	NOUN
cana-5235	138	6	𝑑	𝑑	NOUN
cana-5235	138	7	−	−	NUM
cana-5235	138	8	2𝑑	2𝑑	NUM
cana-5235	138	9	)	)	PUNCT
cana-5235	139	1	(	(	PUNCT
cana-5235	139	2	1	1	NUM
cana-5235	139	3	−	−	NUM
cana-5235	139	4	1	1	NUM
cana-5235	139	5	𝑚	𝑚	NOUN
cana-5235	139	6	)	)	PUNCT
cana-5235	140	1	+	+	CCONJ
cana-5235	140	2	(	(	PUNCT
cana-5235	140	3	1	1	NUM
cana-5235	140	4	−	−	NOUN
cana-5235	140	5	𝜏	𝜏	NOUN
cana-5235	140	6	𝑚	𝑚	NOUN
cana-5235	140	7	)	)	PUNCT
cana-5235	140	8	]	]	PUNCT
cana-5235	141	1	+	+	PUNCT
cana-5235	141	2	𝛽	𝛽	NOUN
cana-5235	141	3	[	[	X
cana-5235	141	4	2𝑑	2𝑑	NUM
cana-5235	141	5	(	(	PUNCT
cana-5235	141	6	1	1	NUM
cana-5235	141	7	−	−	NUM
cana-5235	141	8	1	1	NUM
cana-5235	141	9	𝑚	𝑚	NOUN
cana-5235	141	10	)	)	PUNCT
cana-5235	142	1	+	+	CCONJ
cana-5235	142	2	𝜏	𝜏	ADP
cana-5235	142	3	𝑚	𝑚	X
cana-5235	142	4	−	−	PROPN
cana-5235	142	5	2	2	NUM
cana-5235	142	6	]	]	PUNCT
cana-5235	142	7	,	,	PUNCT
cana-5235	142	8	(	(	PUNCT
cana-5235	142	9	2.26	2.26	NUM
cana-5235	142	10	)	)	PUNCT
cana-5235	142	11	𝑈2𝐵(𝑦	𝑈2𝐵(𝑦	PROPN
cana-5235	142	12	)	)	PUNCT
cana-5235	142	13	=	=	PUNCT
cana-5235	143	1	−𝑦2	−𝑦2	PROPN
cana-5235	143	2	+	+	PUNCT
cana-5235	144	1	[	[	X
cana-5235	144	2	2𝑑	2𝑑	NUM
cana-5235	144	3	(	(	PUNCT
cana-5235	144	4	1	1	NUM
cana-5235	144	5	−	−	NUM
cana-5235	144	6	1	1	NUM
cana-5235	144	7	𝑚	𝑚	NOUN
cana-5235	144	8	)	)	PUNCT
cana-5235	144	9	+	+	CCONJ
cana-5235	144	10	𝜏	𝜏	PART
cana-5235	144	11	𝑚	𝑚	X
cana-5235	144	12	]	]	PUNCT
cana-5235	144	13	𝑦	𝑦	NOUN
cana-5235	144	14	+	+	PUNCT
cana-5235	145	1	[	[	X
cana-5235	145	2	1	1	NUM
cana-5235	145	3	−	−	NUM
cana-5235	145	4	2𝑑	2𝑑	NOUN
cana-5235	145	5	(	(	PUNCT
cana-5235	145	6	1	1	NUM
cana-5235	145	7	−	−	NUM
cana-5235	145	8	1	1	NUM
cana-5235	145	9	𝑚	𝑚	NOUN
cana-5235	145	10	)	)	PUNCT
cana-5235	145	11	−	−	PROPN
cana-5235	145	12	𝜏	𝜏	X
cana-5235	145	13	𝑚	𝑚	X
cana-5235	145	14	]	]	PUNCT
cana-5235	146	1	+	+	PUNCT
cana-5235	146	2	𝛽	𝛽	NOUN
cana-5235	146	3	[	[	X
cana-5235	146	4	2𝑑(1	2𝑑(1	NUM
cana-5235	146	5	−	−	NOUN
cana-5235	146	6	1	1	NUM
cana-5235	146	7	𝑚	𝑚	NOUN
cana-5235	146	8	)	)	PUNCT
cana-5235	147	1	+	+	CCONJ
cana-5235	147	2	𝜏	𝜏	ADP
cana-5235	147	3	𝑚	𝑚	X
cana-5235	147	4	−	−	PROPN
cana-5235	147	5	2	2	NUM
cana-5235	147	6	]	]	PUNCT
cana-5235	147	7	,	,	PUNCT
cana-5235	147	8	(	(	PUNCT
cana-5235	147	9	2.27	2.27	NUM
cana-5235	147	10	)	)	PUNCT
cana-5235	147	11	𝑃1𝐵(𝑦	𝑃1𝐵(𝑦	NUM
cana-5235	147	12	)	)	PUNCT
cana-5235	147	13	=	=	SYM
cana-5235	148	1	−	−	PROPN
cana-5235	148	2	cos𝜃	cos𝜃	NOUN
cana-5235	148	3	𝐹𝑟2	𝐹𝑟2	VERB
cana-5235	148	4	𝑦	𝑦	NOUN
cana-5235	148	5	,	,	PUNCT
cana-5235	148	6	(	(	PUNCT
cana-5235	148	7	2.28	2.28	NUM
cana-5235	148	8	)	)	PUNCT
cana-5235	148	9	𝑃2𝐵(𝑦	𝑃2𝐵(𝑦	NOUN
cana-5235	148	10	)	)	PUNCT
cana-5235	148	11	=	=	SYM
cana-5235	149	1	−	−	PROPN
cana-5235	149	2	cos𝜃	cos𝜃	NOUN
cana-5235	149	3	𝐹𝑟2	𝐹𝑟2	VERB
cana-5235	149	4	𝑦	𝑦	NOUN
cana-5235	149	5	+	+	CCONJ
cana-5235	149	6	(	(	PUNCT
cana-5235	149	7	𝑟−1	𝑟−1	PROPN
cana-5235	149	8	𝑟	𝑟	NOUN
cana-5235	149	9	)	)	PUNCT
cana-5235	149	10	cos𝜃	cos𝜃	NOUN
cana-5235	149	11	𝐹𝑟2	𝐹𝑟2	NOUN
cana-5235	149	12	𝑑.	𝑑.	NOUN
cana-5235	149	13	(	(	PUNCT
cana-5235	149	14	2.29	2.29	NUM
cana-5235	149	15	)	)	PUNCT
cana-5235	149	16	it	it	PRON
cana-5235	149	17	is	be	AUX
cana-5235	149	18	worth	worth	ADJ
cana-5235	149	19	to	to	PART
cana-5235	149	20	be	be	AUX
cana-5235	149	21	noted	note	VERB
cana-5235	149	22	that	that	SCONJ
cana-5235	149	23	the	the	DET
cana-5235	149	24	behavior	behavior	NOUN
cana-5235	149	25	of	of	ADP
cana-5235	149	26	base	base	NOUN
cana-5235	149	27	flow	flow	NOUN
cana-5235	149	28	velocity	velocity	NOUN
cana-5235	149	29	and	and	CCONJ
cana-5235	149	30	pressure	pressure	NOUN
cana-5235	149	31	do	do	AUX
cana-5235	149	32	not	not	PART
cana-5235	149	33	alter	alter	VERB
cana-5235	149	34	due	due	ADP
cana-5235	149	35	to	to	ADP
cana-5235	149	36	the	the	DET
cana-5235	149	37	presence	presence	NOUN
cana-5235	149	38	of	of	ADP
cana-5235	149	39	insoluble	insoluble	ADJ
cana-5235	149	40	surfactant	surfactant	NOUN
cana-5235	149	41	.	.	PUNCT
cana-5235	150	1	however	however	ADV
cana-5235	150	2	,	,	PUNCT
cana-5235	150	3	the	the	DET
cana-5235	150	4	base	base	NOUN
cana-5235	150	5	velocity	velocity	NOUN
cana-5235	150	6	depends	depend	VERB
cana-5235	150	7	on	on	ADP
cana-5235	150	8	the	the	DET
cana-5235	150	9	slip	slip	NOUN
cana-5235	150	10	parameter	parameter	NOUN
cana-5235	150	11	and	and	CCONJ
cana-5235	150	12	shear	shear	NOUN
cana-5235	150	13	stress	stress	NOUN
cana-5235	150	14	.	.	PUNCT
cana-5235	151	1	by	by	ADP
cana-5235	151	2	considering	consider	VERB
cana-5235	151	3	𝛽	𝛽	NOUN
cana-5235	151	4	=	=	SYM
cana-5235	151	5	0	0	PROPN
cana-5235	151	6	and	and	CCONJ
cana-5235	151	7	𝜏	𝜏	X
cana-5235	151	8	=	=	SYM
cana-5235	151	9	0	0	NUM
cana-5235	151	10	,	,	PUNCT
cana-5235	151	11	the	the	DET
cana-5235	151	12	base	base	NOUN
cana-5235	151	13	profiles	profile	NOUN
cana-5235	151	14	are	be	AUX
cana-5235	151	15	similar	similar	ADJ
cana-5235	151	16	to	to	ADP
cana-5235	151	17	that	that	PRON
cana-5235	151	18	in	in	ADP
cana-5235	151	19	the	the	DET
cana-5235	151	20	case	case	NOUN
cana-5235	151	21	of	of	ADP
cana-5235	151	22	two	two	NUM
cana-5235	151	23	-	-	PUNCT
cana-5235	151	24	layer	layer	NOUN
cana-5235	151	25	film	film	NOUN
cana-5235	151	26	flow	flow	VERB
cana-5235	151	27	down	down	ADP
cana-5235	151	28	the	the	DET
cana-5235	151	29	inclined	inclined	ADJ
cana-5235	151	30	plane	plane	NOUN
cana-5235	151	31	in	in	ADP
cana-5235	151	32	the	the	DET
cana-5235	151	33	absence	absence	NOUN
cana-5235	151	34	of	of	ADP
cana-5235	151	35	shear	shear	NOUN
cana-5235	151	36	stress	stress	NOUN
cana-5235	151	37	for	for	ADP
cana-5235	151	38	rigid	rigid	ADJ
cana-5235	151	39	bottom	bottom	NOUN
cana-5235	151	40	.	.	PUNCT
cana-5235	152	1	on	on	ADP
cana-5235	152	2	the	the	DET
cana-5235	152	3	other	other	ADJ
cana-5235	152	4	hand	hand	NOUN
cana-5235	152	5	,	,	PUNCT
cana-5235	152	6	for	for	ADP
cana-5235	152	7	𝑑	𝑑	PROPN
cana-5235	152	8	=	=	SYM
cana-5235	152	9	0	0	NUM
cana-5235	152	10	and	and	CCONJ
cana-5235	152	11	𝑚	𝑚	X
cana-5235	152	12	=	=	SYM
cana-5235	152	13	1	1	NUM
cana-5235	152	14	,	,	PUNCT
cana-5235	152	15	the	the	DET
cana-5235	152	16	base	base	NOUN
cana-5235	152	17	velocity	velocity	NOUN
cana-5235	152	18	profile	profile	NOUN
cana-5235	152	19	in	in	ADP
cana-5235	152	20	eq	eq	ADP
cana-5235	152	21	.	.	PUNCT
cana-5235	153	1	(	(	PUNCT
cana-5235	153	2	2.26	2.26	NUM
cana-5235	153	3	)	)	PUNCT
cana-5235	153	4	is	be	AUX
cana-5235	153	5	same	same	ADJ
cana-5235	153	6	as	as	ADP
cana-5235	153	7	the	the	DET
cana-5235	153	8	velocity	velocity	NOUN
cana-5235	153	9	profile	profile	NOUN
cana-5235	153	10	for	for	ADP
cana-5235	153	11	homogeneous	homogeneous	ADJ
cana-5235	153	12	fluid	fluid	ADJ
cana-5235	153	13	flow	flow	NOUN
cana-5235	153	14	in	in	ADP
cana-5235	153	15	the	the	DET
cana-5235	153	16	presence	presence	NOUN
cana-5235	153	17	of	of	ADP
cana-5235	153	18	external	external	ADJ
cana-5235	153	19	shear	shear	NOUN
cana-5235	153	20	stress	stress	NOUN
cana-5235	153	21	.	.	PUNCT
cana-5235	154	1	further	far	ADV
cana-5235	154	2	,	,	PUNCT
cana-5235	154	3	an	an	DET
cana-5235	154	4	infinitesimal	infinitesimal	ADJ
cana-5235	154	5	disturbance	disturbance	NOUN
cana-5235	154	6	is	be	AUX
cana-5235	154	7	applied	apply	VERB
cana-5235	154	8	on	on	ADP
cana-5235	154	9	the	the	DET
cana-5235	154	10	system	system	NOUN
cana-5235	154	11	and	and	CCONJ
cana-5235	154	12	the	the	DET
cana-5235	154	13	physical	physical	ADJ
cana-5235	154	14	quantities	quantity	NOUN
cana-5235	154	15	can	can	AUX
cana-5235	154	16	be	be	AUX
cana-5235	154	17	written	write	VERB
cana-5235	154	18	as	as	ADP
cana-5235	154	19	the	the	DET
cana-5235	154	20	sum	sum	NOUN
cana-5235	154	21	of	of	ADP
cana-5235	154	22	initial	initial	ADJ
cana-5235	154	23	and	and	CCONJ
cana-5235	154	24	perturbed	perturb	VERB
cana-5235	154	25	state	state	NOUN
cana-5235	154	26	.	.	PUNCT
cana-5235	155	1	substituting	substitute	VERB
cana-5235	155	2	𝑢𝑗(𝑥	𝑢𝑗(𝑥	PROPN
cana-5235	155	3	,	,	PUNCT
cana-5235	155	4	𝑦	𝑦	NOUN
cana-5235	155	5	,	,	PUNCT
cana-5235	155	6	𝑡	𝑡	NOUN
cana-5235	155	7	)	)	PUNCT
cana-5235	155	8	=	=	SYM
cana-5235	155	9	𝑈𝑗𝐵(𝑦	𝑈𝑗𝐵(𝑦	PROPN
cana-5235	155	10	)	)	PUNCT
cana-5235	155	11	+	+	NUM
cana-5235	155	12	�	�	PROPN
cana-5235	155	13	̃	̃	NOUN
cana-5235	155	14	�	�	NOUN
cana-5235	155	15	𝑗(𝑥	𝑗(𝑥	X
cana-5235	155	16	,	,	PUNCT
cana-5235	155	17	𝑦	𝑦	NOUN
cana-5235	155	18	,	,	PUNCT
cana-5235	155	19	𝑡	𝑡	NOUN
cana-5235	155	20	)	)	PUNCT
cana-5235	155	21	,	,	PUNCT
cana-5235	155	22	𝑣𝑗(𝑥	𝑣𝑗(𝑥	ADP
cana-5235	155	23	,	,	PUNCT
cana-5235	155	24	𝑦	𝑦	NOUN
cana-5235	155	25	,	,	PUNCT
cana-5235	155	26	𝑡	𝑡	NOUN
cana-5235	155	27	)	)	PUNCT
cana-5235	155	28	=	=	SYM
cana-5235	155	29	�	�	PROPN
cana-5235	155	30	̃	̃	PROPN
cana-5235	155	31	�	�	NOUN
cana-5235	155	32	𝑗(𝑥	𝑗(𝑥	X
cana-5235	155	33	,	,	PUNCT
cana-5235	155	34	𝑦	𝑦	NOUN
cana-5235	155	35	,	,	PUNCT
cana-5235	155	36	𝑡	𝑡	NOUN
cana-5235	155	37	)	)	PUNCT
cana-5235	155	38	,	,	PUNCT
cana-5235	155	39	𝑝𝑗(𝑥	𝑝𝑗(𝑥	X
cana-5235	155	40	,	,	PUNCT
cana-5235	155	41	𝑦	𝑦	NOUN
cana-5235	155	42	,	,	PUNCT
cana-5235	155	43	𝑡	𝑡	NOUN
cana-5235	155	44	)	)	PUNCT
cana-5235	155	45	=	=	SYM
cana-5235	155	46	𝑃𝑗𝐵(𝑦	𝑃𝑗𝐵(𝑦	PROPN
cana-5235	155	47	)	)	PUNCT
cana-5235	155	48	+	+	NUM
cana-5235	155	49	𝑝𝑗(𝑥	𝑝𝑗(𝑥	X
cana-5235	155	50	,	,	PUNCT
cana-5235	155	51	𝑦	𝑦	NOUN
cana-5235	155	52	,	,	PUNCT
cana-5235	155	53	𝑡	𝑡	NOUN
cana-5235	155	54	)	)	PUNCT
cana-5235	155	55	,	,	PUNCT
cana-5235	155	56	ℎ1(𝑥	ℎ1(𝑥	PROPN
cana-5235	155	57	,	,	PUNCT
cana-5235	155	58	𝑡	𝑡	NOUN
cana-5235	155	59	)	)	PUNCT
cana-5235	155	60	=	=	SYM
cana-5235	155	61	ℎ̃1(𝑥	ℎ̃1(𝑥	PROPN
cana-5235	155	62	,	,	PUNCT
cana-5235	155	63	𝑡	𝑡	PROPN
cana-5235	155	64	)	)	PUNCT
cana-5235	155	65	,	,	PUNCT
cana-5235	155	66	ℎ2(𝑥	ℎ2(𝑥	PROPN
cana-5235	155	67	,	,	PUNCT
cana-5235	155	68	𝑡	𝑡	X
cana-5235	155	69	)	)	PUNCT
cana-5235	155	70	=	=	SYM
cana-5235	155	71	𝑑	𝑑	PROPN
cana-5235	155	72	±	±	NUM
cana-5235	155	73	ℎ̃2(𝑥	ℎ̃2(𝑥	PROPN
cana-5235	155	74	,	,	PUNCT
cana-5235	155	75	𝑡	𝑡	NOUN
cana-5235	155	76	)	)	PUNCT
cana-5235	155	77	and	and	CCONJ
cana-5235	155	78	γ(𝑥	γ(𝑥	PROPN
cana-5235	155	79	,	,	PUNCT
cana-5235	155	80	𝑡	𝑡	X
cana-5235	155	81	)	)	PUNCT
cana-5235	155	82	=	=	SYM
cana-5235	155	83	1	1	NUM
cana-5235	155	84	+	+	NUM
cana-5235	155	85	γ̃	γ̃	PROPN
cana-5235	155	86	in	in	ADP
cana-5235	155	87	the	the	DET
cana-5235	155	88	governing	govern	VERB
cana-5235	155	89	equations	equation	NOUN
cana-5235	155	90	along	along	ADP
cana-5235	155	91	with	with	ADP
cana-5235	155	92	the	the	DET
cana-5235	155	93	boundary	boundary	ADJ
cana-5235	155	94	conditions	condition	NOUN
cana-5235	155	95	.	.	PUNCT
cana-5235	156	1	let	let	VERB
cana-5235	156	2	the	the	DET
cana-5235	156	3	normal	normal	ADJ
cana-5235	156	4	solution	solution	NOUN
cana-5235	156	5	for	for	ADP
cana-5235	156	6	the	the	DET
cana-5235	156	7	two	two	NUM
cana-5235	156	8	-	-	PUNCT
cana-5235	156	9	dimensional	dimensional	ADJ
cana-5235	156	10	two	two	NUM
cana-5235	156	11	-	-	PUNCT
cana-5235	156	12	layer	layer	NOUN
cana-5235	156	13	fluid	fluid	NOUN
cana-5235	156	14	flows	flow	NOUN
cana-5235	156	15	are	be	AUX
cana-5235	156	16	given	give	VERB
cana-5235	156	17	as	as	SCONJ
cana-5235	156	18	communications	communication	NOUN
cana-5235	156	19	on	on	ADP
cana-5235	156	20	applied	apply	VERB
cana-5235	156	21	nonlinear	nonlinear	ADJ
cana-5235	156	22	analysis	analysis	NOUN
cana-5235	156	23	issn	issn	NOUN
cana-5235	156	24	:	:	PUNCT
cana-5235	156	25	1074	1074	NUM
cana-5235	156	26	-	-	PUNCT
cana-5235	156	27	133x	133x	NUM
cana-5235	156	28	vol	vol	VERB
cana-5235	156	29	32	32	NUM
cana-5235	156	30	no	no	NOUN
cana-5235	156	31	.	.	PUNCT
cana-5235	157	1	10s	10	NOUN
cana-5235	157	2	(	(	PUNCT
cana-5235	157	3	2025	2025	NUM
cana-5235	157	4	)	)	PUNCT
cana-5235	157	5	1329	1329	NUM
cana-5235	157	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5235	157	7	�	�	PROPN
cana-5235	157	8	̃	̃	PROPN
cana-5235	157	9	�	�	NOUN
cana-5235	157	10	𝑗(𝑥	𝑗(𝑥	X
cana-5235	157	11	,	,	PUNCT
cana-5235	157	12	𝑦	𝑦	NOUN
cana-5235	157	13	,	,	PUNCT
cana-5235	157	14	𝑡	𝑡	NOUN
cana-5235	157	15	)	)	PUNCT
cana-5235	157	16	=	=	SYM
cana-5235	157	17	𝜙𝑗(𝑦	𝜙𝑗(𝑦	X
cana-5235	157	18	)	)	PUNCT
cana-5235	157	19	ei𝑘(𝑥−𝑐𝑡	ei𝑘(𝑥−𝑐𝑡	ADJ
cana-5235	157	20	)	)	PUNCT
cana-5235	157	21	,	,	PUNCT
cana-5235	157	22	(	(	PUNCT
cana-5235	157	23	2.30	2.30	NUM
cana-5235	157	24	)	)	PUNCT
cana-5235	157	25	γ̃(𝑥	γ̃(𝑥	PROPN
cana-5235	157	26	,	,	PUNCT
cana-5235	157	27	𝑦	𝑦	NOUN
cana-5235	157	28	,	,	PUNCT
cana-5235	157	29	𝑡	𝑡	NOUN
cana-5235	157	30	)	)	PUNCT
cana-5235	157	31	=	=	SYM
cana-5235	157	32	γ(𝑦	γ(𝑦	NOUN
cana-5235	157	33	)	)	PUNCT
cana-5235	157	34	ei𝑘(𝑥−𝑐𝑡	ei𝑘(𝑥−𝑐𝑡	NOUN
cana-5235	157	35	)	)	PUNCT
cana-5235	157	36	,	,	PUNCT
cana-5235	157	37	(	(	PUNCT
cana-5235	157	38	2.31	2.31	NUM
cana-5235	157	39	)	)	PUNCT
cana-5235	157	40	ℎ̃𝑗(𝑥	ℎ̃𝑗(𝑥	PROPN
cana-5235	157	41	,	,	PUNCT
cana-5235	157	42	𝑦	𝑦	NOUN
cana-5235	157	43	,	,	PUNCT
cana-5235	157	44	𝑡	𝑡	NOUN
cana-5235	157	45	)	)	PUNCT
cana-5235	157	46	=	=	SYM
cana-5235	157	47	𝜂𝑗(𝑦	𝜂𝑗(𝑦	X
cana-5235	157	48	)	)	PUNCT
cana-5235	157	49	ei𝑘(𝑥−𝑐𝑡	ei𝑘(𝑥−𝑐𝑡	ADJ
cana-5235	157	50	)	)	PUNCT
cana-5235	157	51	,	,	PUNCT
cana-5235	157	52	(	(	PUNCT
cana-5235	157	53	2.32	2.32	NUM
cana-5235	157	54	)	)	PUNCT
cana-5235	157	55	where	where	SCONJ
cana-5235	157	56	𝑘	𝑘	X
cana-5235	157	57	,	,	PUNCT
cana-5235	157	58	𝑐	𝑐	PROPN
cana-5235	157	59	and	and	CCONJ
cana-5235	157	60	�	�	PROPN
cana-5235	157	61	̃	̃	PROPN
cana-5235	157	62	�	�	NOUN
cana-5235	157	63	𝑗	𝑗	NOUN
cana-5235	157	64	are	be	AUX
cana-5235	157	65	the	the	DET
cana-5235	157	66	wavenumber	wavenumber	NOUN
cana-5235	157	67	,	,	PUNCT
cana-5235	157	68	complex	complex	ADJ
cana-5235	157	69	wave	wave	NOUN
cana-5235	157	70	speed	speed	NOUN
cana-5235	157	71	and	and	CCONJ
cana-5235	157	72	stream	stream	NOUN
cana-5235	157	73	function	function	NOUN
cana-5235	157	74	,	,	PUNCT
cana-5235	157	75	respectively	respectively	ADV
cana-5235	157	76	and	and	CCONJ
cana-5235	157	77	i	i	PRON
cana-5235	157	78	≡	≡	PROPN
cana-5235	157	79	√−1	√−1	VERB
cana-5235	157	80	.	.	PUNCT
cana-5235	158	1	using	use	VERB
cana-5235	158	2	eqs	eqs	PROPN
cana-5235	158	3	.	.	PUNCT
cana-5235	159	1	(	(	PUNCT
cana-5235	159	2	2.30)–(2.32	2.30)–(2.32	NUM
cana-5235	159	3	)	)	PUNCT
cana-5235	159	4	in	in	ADP
cana-5235	159	5	the	the	DET
cana-5235	159	6	governing	govern	VERB
cana-5235	159	7	equations	equation	NOUN
cana-5235	159	8	and	and	CCONJ
cana-5235	159	9	boundary	boundary	ADJ
cana-5235	159	10	conditions	condition	NOUN
cana-5235	159	11	(	(	PUNCT
cana-5235	159	12	2.15)–(2.25	2.15)–(2.25	NUM
cana-5235	159	13	)	)	PUNCT
cana-5235	159	14	yield	yield	VERB
cana-5235	159	15	the	the	DET
cana-5235	159	16	following	follow	VERB
cana-5235	159	17	orr	orr	PROPN
cana-5235	159	18	-	-	PUNCT
cana-5235	159	19	sommerfeld	sommerfeld	ADJ
cana-5235	159	20	system	system	NOUN
cana-5235	159	21	for	for	ADP
cana-5235	159	22	both	both	CCONJ
cana-5235	159	23	upper	upper	ADJ
cana-5235	159	24	and	and	CCONJ
cana-5235	159	25	lower	low	ADJ
cana-5235	159	26	layers	layer	NOUN
cana-5235	159	27	,	,	PUNCT
cana-5235	159	28	(	(	PUNCT
cana-5235	159	29	𝐷2	𝐷2	PROPN
cana-5235	159	30	−	−	ADP
cana-5235	159	31	𝑘2)2	𝑘2)2	NOUN
cana-5235	159	32	𝜙𝑗	𝜙𝑗	NOUN
cana-5235	160	1	−	−	PROPN
cana-5235	160	2	𝑅𝑒𝑗[i	𝑅𝑒𝑗[i	ADP
cana-5235	160	3	𝑘	𝑘	X
cana-5235	160	4	(	(	PUNCT
cana-5235	160	5	𝑈𝑗𝐵	𝑈𝑗𝐵	PROPN
cana-5235	160	6	−	−	PROPN
cana-5235	160	7	𝑐	𝑐	NOUN
cana-5235	160	8	)	)	PUNCT
cana-5235	160	9	(	(	PUNCT
cana-5235	160	10	𝐷2	𝐷2	PROPN
cana-5235	160	11	−	−	PROPN
cana-5235	160	12	𝑘2	𝑘2	PROPN
cana-5235	160	13	)	)	PUNCT
cana-5235	161	1	𝜙𝑗	𝜙𝑗	PROPN
cana-5235	161	2	−	−	PROPN
cana-5235	161	3	i𝑘	i𝑘	NOUN
cana-5235	161	4	𝑈′′𝑗𝐵	𝑈′′𝑗𝐵	PROPN
cana-5235	161	5	𝜙𝑗	𝜙𝑗	PROPN
cana-5235	161	6	]	]	X
cana-5235	161	7	=	=	SYM
cana-5235	161	8	0	0	NUM
cana-5235	161	9	,	,	PUNCT
cana-5235	161	10	(	(	PUNCT
cana-5235	161	11	2.33	2.33	NUM
cana-5235	161	12	)	)	PUNCT
cana-5235	161	13	𝜙𝑗	𝜙𝑗	NOUN
cana-5235	162	1	+	+	X
cana-5235	162	2	𝜂𝑗	𝜂𝑗	X
cana-5235	162	3	(	(	PUNCT
cana-5235	162	4	𝑈𝑗𝐵	𝑈𝑗𝐵	PROPN
cana-5235	162	5	−	−	PROPN
cana-5235	162	6	𝑐	𝑐	NOUN
cana-5235	162	7	)	)	PUNCT
cana-5235	162	8	=	=	SYM
cana-5235	162	9	0	0	NUM
cana-5235	163	1	at	at	ADP
cana-5235	163	2	𝑦	𝑦	NOUN
cana-5235	163	3	=	=	SYM
cana-5235	163	4	0	0	PUNCT
cana-5235	164	1	(	(	PUNCT
cana-5235	164	2	for	for	ADP
cana-5235	164	3	𝑗	𝑗	NOUN
cana-5235	164	4	=	=	SYM
cana-5235	164	5	1	1	NUM
cana-5235	164	6	)	)	PUNCT
cana-5235	164	7	and	and	CCONJ
cana-5235	164	8	𝑦	𝑦	NOUN
cana-5235	164	9	=	=	SYM
cana-5235	164	10	𝑑	𝑑	X
cana-5235	164	11	(	(	PUNCT
cana-5235	164	12	for	for	ADP
cana-5235	164	13	𝑗	𝑗	NOUN
cana-5235	164	14	=	=	SYM
cana-5235	164	15	2	2	NUM
cana-5235	164	16	)	)	PUNCT
cana-5235	164	17	,	,	PUNCT
cana-5235	164	18	(	(	PUNCT
cana-5235	164	19	2.34	2.34	NUM
cana-5235	164	20	)	)	PUNCT
cana-5235	164	21	𝐷𝜙1	𝐷𝜙1	NOUN
cana-5235	165	1	+	+	X
cana-5235	165	2	γ	γ	X
cana-5235	165	3	[	[	X
cana-5235	165	4	(	(	PUNCT
cana-5235	165	5	𝑈1𝐵	𝑈1𝐵	PROPN
cana-5235	165	6	−	−	PROPN
cana-5235	165	7	𝑐	𝑐	NOUN
cana-5235	165	8	)	)	PUNCT
cana-5235	165	9	−	−	PROPN
cana-5235	165	10	i𝑘	i𝑘	PRON
cana-5235	165	11	𝛼𝐶𝑎	𝛼𝐶𝑎	X
cana-5235	165	12	]	]	PUNCT
cana-5235	166	1	=	=	SYM
cana-5235	166	2	0	0	NUM
cana-5235	167	1	at	at	ADP
cana-5235	167	2	𝑦	𝑦	NOUN
cana-5235	167	3	=	=	SYM
cana-5235	167	4	0	0	NUM
cana-5235	167	5	,	,	PUNCT
cana-5235	167	6	(	(	PUNCT
cana-5235	167	7	2.35	2.35	NUM
cana-5235	167	8	)	)	PUNCT
cana-5235	167	9	𝑈′′1𝐵	𝑈′′1𝐵	PROPN
cana-5235	167	10	𝜂1	𝜂1	NOUN
cana-5235	167	11	+	+	CCONJ
cana-5235	167	12	(	(	PUNCT
cana-5235	167	13	𝐷2	𝐷2	PROPN
cana-5235	167	14	+	+	CCONJ
cana-5235	167	15	𝑘2	𝑘2	PROPN
cana-5235	167	16	)	)	PUNCT
cana-5235	167	17	𝜙1	𝜙1	NOUN
cana-5235	167	18	+	+	CCONJ
cana-5235	167	19	i𝑘𝑀𝑎	i𝑘𝑀𝑎	VERB
cana-5235	167	20	𝐶𝑎	𝐶𝑎	PROPN
cana-5235	167	21	γ	γ	NOUN
cana-5235	167	22	=	=	SYM
cana-5235	167	23	0	0	NUM
cana-5235	167	24	at	at	ADP
cana-5235	167	25	𝑦	𝑦	NOUN
cana-5235	167	26	=	=	SYM
cana-5235	167	27	0	0	NUM
cana-5235	167	28	,	,	PUNCT
cana-5235	167	29	(	(	PUNCT
cana-5235	167	30	2.36	2.36	NUM
cana-5235	167	31	)	)	PUNCT
cana-5235	167	32	𝐷3𝜙1	𝐷3𝜙1	NOUN
cana-5235	168	1	+	+	CCONJ
cana-5235	168	2	[	[	X
cana-5235	168	3	𝑅𝑒1i𝑘(𝑐	𝑅𝑒1i𝑘(𝑐	X
cana-5235	168	4	−	−	NOUN
cana-5235	168	5	𝑈1𝐵	𝑈1𝐵	NUM
cana-5235	168	6	)	)	PUNCT
cana-5235	169	1	−	−	PROPN
cana-5235	169	2	3𝑘2]𝐷𝜙1	3𝑘2]𝐷𝜙1	NUM
cana-5235	170	1	−	−	PROPN
cana-5235	170	2	i𝑘𝑅𝑒1𝑈′	i𝑘𝑅𝑒1𝑈′	ADJ
cana-5235	170	3	1𝐵𝜙1	1𝐵𝜙1	NUM
cana-5235	170	4	−[2i𝑘cot𝜃	−[2i𝑘cot𝜃	NOUN
cana-5235	170	5	+	+	CCONJ
cana-5235	170	6	2𝑈′1𝐵	2𝑈′1𝐵	PROPN
cana-5235	170	7	𝑘2	𝑘2	NOUN
cana-5235	170	8	+	+	CCONJ
cana-5235	170	9	i𝑘3	i𝑘3	VERB
cana-5235	170	10	𝐶𝑎	𝐶𝑎	PROPN
cana-5235	170	11	]	]	PUNCT
cana-5235	170	12	𝜂1	𝜂1	NOUN
cana-5235	170	13	=	=	SYM
cana-5235	170	14	0	0	NUM
cana-5235	170	15	at	at	ADP
cana-5235	170	16	𝑦	𝑦	NOUN
cana-5235	170	17	=	=	SYM
cana-5235	170	18	0	0	NUM
cana-5235	170	19	,	,	PUNCT
cana-5235	170	20	(	(	PUNCT
cana-5235	170	21	2.37	2.37	NUM
cana-5235	170	22	)	)	PUNCT
cana-5235	170	23	(	(	PUNCT
cana-5235	170	24	𝐷2	𝐷2	PROPN
cana-5235	170	25	+	+	CCONJ
cana-5235	170	26	𝑘2	𝑘2	PROPN
cana-5235	170	27	)	)	PUNCT
cana-5235	170	28	𝜙1	𝜙1	NOUN
cana-5235	170	29	=	=	SYM
cana-5235	170	30	(	(	PUNCT
cana-5235	170	31	𝑈′′1𝐵	𝑈′′1𝐵	PROPN
cana-5235	170	32	+	+	CCONJ
cana-5235	170	33	𝑚	𝑚	ADP
cana-5235	170	34	𝑈′′2𝐵	𝑈′′2𝐵	PROPN
cana-5235	170	35	)	)	PUNCT
cana-5235	170	36	𝜂2	𝜂2	VERB
cana-5235	170	37	+	+	CCONJ
cana-5235	170	38	𝑚	𝑚	X
cana-5235	170	39	(	(	PUNCT
cana-5235	170	40	𝐷2	𝐷2	PROPN
cana-5235	170	41	+	+	CCONJ
cana-5235	170	42	𝑘2	𝑘2	PROPN
cana-5235	170	43	)	)	PUNCT
cana-5235	170	44	𝜙2	𝜙2	NOUN
cana-5235	170	45	at	at	ADP
cana-5235	170	46	𝑦	𝑦	NOUN
cana-5235	170	47	=	=	SYM
cana-5235	170	48	𝑑	𝑑	PROPN
cana-5235	170	49	,	,	PUNCT
cana-5235	170	50	(	(	PUNCT
cana-5235	170	51	2.38	2.38	NUM
cana-5235	170	52	)	)	PUNCT
cana-5235	170	53	𝐷𝜙1	𝐷𝜙1	NOUN
cana-5235	171	1	=	=	PUNCT
cana-5235	172	1	[	[	X
cana-5235	172	2	𝑈′1𝐵	𝑈′1𝐵	PRON
cana-5235	172	3	+	+	NOUN
cana-5235	172	4	𝑈′2𝐵	𝑈′2𝐵	PROPN
cana-5235	172	5	]	]	X
cana-5235	172	6	𝜂2	𝜂2	X
cana-5235	172	7	+	+	NUM
cana-5235	172	8	𝐷𝜙2	𝐷𝜙2	NOUN
cana-5235	172	9	at	at	ADP
cana-5235	172	10	𝑦	𝑦	PROPN
cana-5235	172	11	=	=	SYM
cana-5235	172	12	𝑑	𝑑	PROPN
cana-5235	172	13	,	,	PUNCT
cana-5235	172	14	(	(	PUNCT
cana-5235	172	15	2.39	2.39	NUM
cana-5235	172	16	)	)	PUNCT
cana-5235	172	17	𝜙1	𝜙1	NOUN
cana-5235	172	18	=	=	SYM
cana-5235	172	19	𝜙2	𝜙2	NOUN
cana-5235	172	20	at	at	ADP
cana-5235	172	21	𝑦	𝑦	NOUN
cana-5235	172	22	=	=	SYM
cana-5235	172	23	𝑑	𝑑	PROPN
cana-5235	172	24	,	,	PUNCT
cana-5235	172	25	(	(	PUNCT
cana-5235	172	26	2.40	2.40	NUM
cana-5235	172	27	)	)	PUNCT
cana-5235	172	28	2𝑘2	2𝑘2	NUM
cana-5235	172	29	𝑈′	𝑈′	ADJ
cana-5235	172	30	1𝐵	1𝐵	NOUN
cana-5235	172	31	𝜂1	𝜂1	NOUN
cana-5235	172	32	+	+	CCONJ
cana-5235	172	33	[	[	X
cana-5235	172	34	3𝑘2𝐷	3𝑘2𝐷	NUM
cana-5235	172	35	−	−	NOUN
cana-5235	172	36	𝐷3	𝐷3	NOUN
cana-5235	172	37	+	+	CCONJ
cana-5235	172	38	i𝑘𝑅𝑒1((𝑈1𝐵	i𝑘𝑅𝑒1((𝑈1𝐵	NOUN
cana-5235	172	39	−	−	NOUN
cana-5235	172	40	𝑐)𝐷	𝑐)𝐷	ADJ
cana-5235	172	41	−	−	NUM
cana-5235	172	42	𝑈′	𝑈′	ADJ
cana-5235	172	43	1𝐵	1𝐵	NOUN
cana-5235	172	44	)	)	PUNCT
cana-5235	172	45	]	]	PUNCT
cana-5235	173	1	=	=	PUNCT
cana-5235	173	2	(	(	PUNCT
cana-5235	173	3	2icot𝜃	2icot𝜃	NUM
cana-5235	173	4	(	(	PUNCT
cana-5235	173	5	𝑟	𝑟	NOUN
cana-5235	173	6	+	+	CCONJ
cana-5235	173	7	1	1	X
cana-5235	173	8	)	)	PUNCT
cana-5235	173	9	+	+	NUM
cana-5235	173	10	2𝑚𝑘2𝑈′	2𝑚𝑘2𝑈′	NUM
cana-5235	173	11	2𝐵	2𝐵	NOUN
cana-5235	173	12	−	−	NOUN
cana-5235	173	13	i𝑘3	i𝑘3	VERB
cana-5235	173	14	𝑊𝑒	𝑊𝑒	DET
cana-5235	173	15	𝑅𝑒1	𝑅𝑒1	NOUN
cana-5235	173	16	)	)	PUNCT
cana-5235	173	17	𝜂2	𝜂2	PROPN
cana-5235	173	18	+	+	PROPN
cana-5235	174	1	[	[	X
cana-5235	174	2	𝑚	𝑚	X
cana-5235	174	3	(	(	PUNCT
cana-5235	174	4	3𝑘2𝐷	3𝑘2𝐷	NUM
cana-5235	174	5	−	−	PROPN
cana-5235	174	6	𝐷3	𝐷3	PROPN
cana-5235	174	7	)	)	PUNCT
cana-5235	175	1	+	+	CCONJ
cana-5235	175	2	𝑟𝑅𝑒1	𝑟𝑅𝑒1	PROPN
cana-5235	175	3	(	(	PUNCT
cana-5235	175	4	i𝑘(𝑈2𝐵	i𝑘(𝑈2𝐵	PROPN
cana-5235	175	5	−	−	PROPN
cana-5235	175	6	𝑐	𝑐	NOUN
cana-5235	175	7	)	)	PUNCT
cana-5235	175	8	𝐷	𝐷	NOUN
cana-5235	175	9	−	−	PROPN
cana-5235	175	10	i𝑘𝑈′	i𝑘𝑈′	ADP
cana-5235	175	11	2𝐵	2𝐵	NOUN
cana-5235	175	12	)	)	PUNCT
cana-5235	175	13	]	]	PUNCT
cana-5235	175	14	𝜙2	𝜙2	NOUN
cana-5235	175	15	at	at	ADP
cana-5235	175	16	𝑦	𝑦	NOUN
cana-5235	175	17	=	=	SYM
cana-5235	175	18	𝑑	𝑑	PROPN
cana-5235	175	19	,	,	PUNCT
cana-5235	175	20	(	(	PUNCT
cana-5235	175	21	2.41	2.41	NUM
cana-5235	175	22	)	)	PUNCT
cana-5235	175	23	𝜙2	𝜙2	NOUN
cana-5235	175	24	=	=	SYM
cana-5235	175	25	0	0	NUM
cana-5235	175	26	and	and	CCONJ
cana-5235	175	27	𝐷𝜙2	𝐷𝜙2	NOUN
cana-5235	175	28	=	=	SYM
cana-5235	175	29	𝛽	𝛽	PROPN
cana-5235	175	30	𝐷2𝜙2	𝐷2𝜙2	PROPN
cana-5235	175	31	at	at	ADP
cana-5235	175	32	𝑦	𝑦	NOUN
cana-5235	175	33	=	=	SYM
cana-5235	175	34	1	1	NUM
cana-5235	175	35	,	,	PUNCT
cana-5235	175	36	(	(	PUNCT
cana-5235	175	37	2.42	2.42	NUM
cana-5235	175	38	)	)	PUNCT
cana-5235	175	39	where	where	SCONJ
cana-5235	175	40	𝐷	𝐷	NOUN
cana-5235	175	41	denote	denote	VERB
cana-5235	175	42	the	the	DET
cana-5235	175	43	derivative	derivative	NOUN
cana-5235	175	44	with	with	ADP
cana-5235	175	45	respect	respect	NOUN
cana-5235	175	46	to	to	ADP
cana-5235	175	47	𝑦.	𝑦.	PROPN
cana-5235	175	48	3	3	NUM
cana-5235	175	49	numerical	numerical	ADJ
cana-5235	175	50	results	result	NOUN
cana-5235	175	51	here	here	ADV
cana-5235	175	52	,	,	PUNCT
cana-5235	175	53	the	the	DET
cana-5235	175	54	spectral	spectral	ADJ
cana-5235	175	55	collocation	collocation	NOUN
cana-5235	175	56	method	method	NOUN
cana-5235	175	57	[	[	X
cana-5235	175	58	33	33	NUM
cana-5235	175	59	]	]	PUNCT
cana-5235	175	60	is	be	AUX
cana-5235	175	61	employed	employ	VERB
cana-5235	175	62	to	to	PART
cana-5235	175	63	solve	solve	VERB
cana-5235	175	64	the	the	DET
cana-5235	175	65	orr	orr	PROPN
cana-5235	175	66	-	-	PUNCT
cana-5235	175	67	sommerfeld	sommerfeld	ADJ
cana-5235	175	68	system	system	NOUN
cana-5235	175	69	(	(	PUNCT
cana-5235	175	70	eqs.(2.33	eqs.(2.33	NOUN
cana-5235	175	71	)	)	PUNCT
cana-5235	175	72	–	–	PUNCT
cana-5235	175	73	(	(	PUNCT
cana-5235	175	74	2.42	2.42	NUM
cana-5235	175	75	)	)	PUNCT
cana-5235	175	76	)	)	PUNCT
cana-5235	175	77	by	by	ADP
cana-5235	175	78	matlab	matlab	PROPN
cana-5235	175	79	(	(	PUNCT
cana-5235	175	80	2014a	2014a	NUM
cana-5235	175	81	)	)	PUNCT
cana-5235	175	82	.	.	PUNCT
cana-5235	176	1	the	the	DET
cana-5235	176	2	entire	entire	ADJ
cana-5235	176	3	domain	domain	NOUN
cana-5235	176	4	splits	split	VERB
cana-5235	176	5	into	into	ADP
cana-5235	176	6	the	the	DET
cana-5235	176	7	two	two	NUM
cana-5235	176	8	sub	sub	NOUN
cana-5235	176	9	-	-	NOUN
cana-5235	176	10	domain	domain	NOUN
cana-5235	176	11	,	,	PUNCT
cana-5235	176	12	which	which	PRON
cana-5235	176	13	are	be	AUX
cana-5235	176	14	discretized	discretize	VERB
cana-5235	176	15	with	with	ADP
cana-5235	176	16	𝑛-points	𝑛-point	NOUN
cana-5235	176	17	using	use	VERB
cana-5235	176	18	the	the	DET
cana-5235	176	19	chebyshev	chebyshev	NOUN
cana-5235	176	20	polynomials	polynomial	NOUN
cana-5235	176	21	as	as	SCONJ
cana-5235	176	22	given	give	VERB
cana-5235	176	23	by	by	ADP
cana-5235	176	24	𝑦𝑗	𝑦𝑗	NOUN
cana-5235	176	25	=	=	SYM
cana-5235	176	26	0.5	0.5	NUM
cana-5235	176	27	(	(	PUNCT
cana-5235	176	28	cos[𝜋	cos[𝜋	PROPN
cana-5235	176	29	(	(	PUNCT
cana-5235	176	30	𝑗−1	𝑗−1	PROPN
cana-5235	176	31	)	)	PUNCT
cana-5235	176	32	(	(	PUNCT
cana-5235	176	33	𝑛−1	𝑛−1	PROPN
cana-5235	176	34	)	)	PUNCT
cana-5235	176	35	]	]	PUNCT
cana-5235	177	1	+	+	CCONJ
cana-5235	177	2	1	1	X
cana-5235	177	3	)	)	PUNCT
cana-5235	177	4	where	where	SCONJ
cana-5235	177	5	𝑗	𝑗	NOUN
cana-5235	177	6	=	=	SYM
cana-5235	177	7	1,2,3	1,2,3	NUM
cana-5235	177	8	,	,	PUNCT
cana-5235	177	9	…	…	PUNCT
cana-5235	177	10	𝑛.	𝑛.	NOUN
cana-5235	177	11	in	in	ADP
cana-5235	177	12	order	order	NOUN
cana-5235	177	13	to	to	PART
cana-5235	177	14	implement	implement	VERB
cana-5235	177	15	this	this	DET
cana-5235	177	16	method	method	NOUN
cana-5235	177	17	,	,	PUNCT
cana-5235	177	18	the	the	DET
cana-5235	177	19	sub	sub	NOUN
cana-5235	177	20	-	-	NOUN
cana-5235	177	21	domains	domain	NOUN
cana-5235	177	22	such	such	ADJ
cana-5235	177	23	as	as	ADP
cana-5235	177	24	[	[	X
cana-5235	177	25	0	0	NUM
cana-5235	177	26	,	,	PUNCT
cana-5235	177	27	𝑑	𝑑	NOUN
cana-5235	177	28	]	]	PUNCT
cana-5235	177	29	and	and	CCONJ
cana-5235	177	30	[	[	X
cana-5235	177	31	𝑑	𝑑	NOUN
cana-5235	177	32	,	,	PUNCT
cana-5235	177	33	1	1	NUM
cana-5235	177	34	]	]	PUNCT
cana-5235	177	35	are	be	AUX
cana-5235	177	36	transformed	transform	VERB
cana-5235	177	37	to	to	ADP
cana-5235	177	38	the	the	DET
cana-5235	177	39	computational	computational	ADJ
cana-5235	177	40	interval	interval	NOUN
cana-5235	178	1	[	[	X
cana-5235	178	2	−1,1	−1,1	X
cana-5235	178	3	]	]	X
cana-5235	178	4	(	(	PUNCT
cana-5235	178	5	[	[	X
cana-5235	178	6	10	10	NUM
cana-5235	178	7	]	]	NUM
cana-5235	178	8	)	)	PUNCT
cana-5235	178	9	.	.	PUNCT
cana-5235	179	1	further	far	ADV
cana-5235	179	2	,	,	PUNCT
cana-5235	179	3	the	the	DET
cana-5235	179	4	complex	complex	ADJ
cana-5235	179	5	phase	phase	NOUN
cana-5235	179	6	velocity	velocity	NOUN
cana-5235	179	7	𝑐	𝑐	NOUN
cana-5235	179	8	=	=	SYM
cana-5235	179	9	𝑐𝑟	𝑐𝑟	PROPN
cana-5235	180	1	+	+	NUM
cana-5235	180	2	i𝑐𝑖	i𝑐𝑖	NOUN
cana-5235	180	3	is	be	AUX
cana-5235	180	4	obtained	obtain	VERB
cana-5235	180	5	from	from	ADP
cana-5235	180	6	the	the	DET
cana-5235	180	7	orr	orr	PROPN
cana-5235	180	8	-	-	PUNCT
cana-5235	180	9	sommerfeld	sommerfeld	ADJ
cana-5235	180	10	system	system	NOUN
cana-5235	180	11	,	,	PUNCT
cana-5235	180	12	from	from	ADP
cana-5235	180	13	which	which	PRON
cana-5235	180	14	the	the	DET
cana-5235	180	15	non	non	ADJ
cana-5235	180	16	-	-	ADJ
cana-5235	180	17	dimensional	dimensional	ADJ
cana-5235	180	18	scaled	scale	VERB
cana-5235	180	19	parameter	parameter	NOUN
cana-5235	180	20	known	know	VERB
cana-5235	180	21	as	as	ADP
cana-5235	180	22	growth	growth	NOUN
cana-5235	180	23	rate	rate	NOUN
cana-5235	180	24	(	(	PUNCT
cana-5235	180	25	𝜔𝑖	𝜔𝑖	ADP
cana-5235	180	26	=	=	PUNCT
cana-5235	180	27	𝑘𝑐𝑖	𝑘𝑐𝑖	NOUN
cana-5235	180	28	)	)	PUNCT
cana-5235	180	29	is	be	AUX
cana-5235	180	30	derived	derive	VERB
cana-5235	180	31	.	.	PUNCT
cana-5235	181	1	using	use	VERB
cana-5235	181	2	the	the	DET
cana-5235	181	3	special	special	ADJ
cana-5235	181	4	process	process	NOUN
cana-5235	181	5	,	,	PUNCT
cana-5235	181	6	the	the	DET
cana-5235	181	7	extra	extra	ADJ
cana-5235	181	8	eigenvalues	eigenvalue	NOUN
cana-5235	181	9	are	be	AUX
cana-5235	181	10	eliminated	eliminate	VERB
cana-5235	181	11	,	,	PUNCT
cana-5235	181	12	which	which	PRON
cana-5235	181	13	,	,	PUNCT
cana-5235	181	14	in	in	ADP
cana-5235	181	15	turns	turn	NOUN
cana-5235	181	16	,	,	PUNCT
cana-5235	181	17	increases	increase	VERB
cana-5235	181	18	the	the	DET
cana-5235	181	19	accuracy	accuracy	NOUN
cana-5235	181	20	of	of	ADP
cana-5235	181	21	obtained	obtain	VERB
cana-5235	181	22	eigenvalues	eigenvalue	NOUN
cana-5235	181	23	.	.	PUNCT
cana-5235	182	1	in	in	ADP
cana-5235	182	2	fig	fig	NOUN
cana-5235	182	3	.	.	PUNCT
cana-5235	183	1	2	2	NUM
cana-5235	183	2	,	,	PUNCT
cana-5235	183	3	the	the	DET
cana-5235	183	4	present	present	ADJ
cana-5235	183	5	result	result	NOUN
cana-5235	183	6	is	be	AUX
cana-5235	183	7	validated	validate	VERB
cana-5235	183	8	with	with	ADP
cana-5235	183	9	the	the	DET
cana-5235	183	10	result	result	NOUN
cana-5235	183	11	of	of	ADP
cana-5235	183	12	chin	chin	PROPN
cana-5235	183	13	et	et	PROPN
cana-5235	183	14	al	al	PROPN
cana-5235	183	15	.	.	PUNCT
cana-5235	184	1	[	[	X
cana-5235	184	2	34	34	NUM
cana-5235	184	3	]	]	PUNCT
cana-5235	184	4	in	in	ADP
cana-5235	184	5	the	the	DET
cana-5235	184	6	case	case	NOUN
cana-5235	184	7	of	of	ADP
cana-5235	184	8	homogeneous	homogeneous	ADJ
cana-5235	184	9	fluid	fluid	NOUN
cana-5235	184	10	(	(	PUNCT
cana-5235	184	11	𝑑	𝑑	NOUN
cana-5235	184	12	=	=	SYM
cana-5235	184	13	1	1	NUM
cana-5235	184	14	,	,	PUNCT
cana-5235	184	15	𝑚	𝑚	X
cana-5235	184	16	=	=	SYM
cana-5235	184	17	1	1	NUM
cana-5235	184	18	,	,	PUNCT
cana-5235	184	19	𝐶𝑎	𝐶𝑎	PROPN
cana-5235	184	20	=	=	SYM
cana-5235	184	21	0.0169	0.0169	NUM
cana-5235	184	22	,	,	PUNCT
cana-5235	184	23	𝜏	𝜏	X
cana-5235	184	24	=	=	SYM
cana-5235	184	25	0	0	NUM
cana-5235	184	26	,	,	PUNCT
cana-5235	184	27	𝛽	𝛽	NOUN
cana-5235	184	28	=	=	SYM
cana-5235	184	29	0	0	NUM
cana-5235	184	30	,	,	PUNCT
cana-5235	184	31	𝜃	𝜃	X
cana-5235	184	32	=	=	SYM
cana-5235	184	33	4∘	4∘	NOUN
cana-5235	184	34	and	and	CCONJ
cana-5235	184	35	𝑅𝑒1	𝑅𝑒1	NOUN
cana-5235	184	36	=	=	SYM
cana-5235	184	37	2500	2500	NUM
cana-5235	184	38	)	)	PUNCT
cana-5235	184	39	.	.	PUNCT
cana-5235	185	1	the	the	DET
cana-5235	185	2	result	result	NOUN
cana-5235	185	3	depicts	depict	VERB
cana-5235	185	4	that	that	SCONJ
cana-5235	185	5	the	the	DET
cana-5235	185	6	dispersion	dispersion	NOUN
cana-5235	185	7	curve	curve	NOUN
cana-5235	185	8	for	for	ADP
cana-5235	185	9	single	single	ADJ
cana-5235	185	10	layer	layer	NOUN
cana-5235	185	11	fluid	fluid	NOUN
cana-5235	185	12	(	(	PUNCT
cana-5235	185	13	𝑘𝑐𝑖	𝑘𝑐𝑖	NOUN
cana-5235	185	14	vs	vs	ADP
cana-5235	185	15	𝑘	𝑘	PROPN
cana-5235	185	16	)	)	PUNCT
cana-5235	185	17	obtained	obtain	VERB
cana-5235	185	18	from	from	ADP
cana-5235	185	19	the	the	DET
cana-5235	185	20	present	present	ADJ
cana-5235	185	21	theory	theory	NOUN
cana-5235	185	22	,	,	PUNCT
cana-5235	185	23	matches	match	VERB
cana-5235	185	24	precisely	precisely	ADV
cana-5235	185	25	with	with	ADP
cana-5235	185	26	the	the	DET
cana-5235	185	27	existing	exist	VERB
cana-5235	185	28	result	result	NOUN
cana-5235	185	29	of	of	ADP
cana-5235	185	30	chin	chin	PROPN
cana-5235	185	31	et	et	PROPN
cana-5235	185	32	al	al	PROPN
cana-5235	185	33	.	.	PUNCT
cana-5235	186	1	[	[	X
cana-5235	186	2	34	34	NUM
cana-5235	186	3	]	]	PUNCT
cana-5235	186	4	.	.	PUNCT
cana-5235	187	1	moreover	moreover	ADV
cana-5235	187	2	,	,	PUNCT
cana-5235	187	3	the	the	DET
cana-5235	187	4	nature	nature	NOUN
cana-5235	187	5	of	of	ADP
cana-5235	187	6	growth	growth	NOUN
cana-5235	187	7	rate	rate	NOUN
cana-5235	187	8	is	be	AUX
cana-5235	187	9	two	two	NUM
cana-5235	187	10	-	-	ADJ
cana-5235	187	11	fold	fold	ADJ
cana-5235	187	12	and	and	CCONJ
cana-5235	187	13	becomes	become	VERB
cana-5235	187	14	more	more	ADV
cana-5235	187	15	stable	stable	ADJ
cana-5235	187	16	for	for	ADP
cana-5235	187	17	the	the	DET
cana-5235	187	18	wavenumber	wavenumber	NOUN
cana-5235	187	19	𝑘	𝑘	PRON
cana-5235	187	20	≥	≥	NOUN
cana-5235	187	21	1.5	1.5	NUM
cana-5235	187	22	.	.	PUNCT
cana-5235	188	1	in	in	ADP
cana-5235	188	2	the	the	DET
cana-5235	188	3	case	case	NOUN
cana-5235	188	4	of	of	ADP
cana-5235	188	5	the	the	DET
cana-5235	188	6	two	two	NUM
cana-5235	188	7	-	-	PUNCT
cana-5235	188	8	layer	layer	NOUN
cana-5235	188	9	fluid	fluid	NOUN
cana-5235	188	10	,	,	PUNCT
cana-5235	188	11	the	the	DET
cana-5235	188	12	dispersion	dispersion	NOUN
cana-5235	188	13	curves	curve	VERB
cana-5235	188	14	for	for	ADP
cana-5235	188	15	different	different	ADJ
cana-5235	188	16	interface	interface	NOUN
cana-5235	188	17	position	position	NOUN
cana-5235	188	18	(	(	PUNCT
cana-5235	188	19	𝑑	𝑑	NOUN
cana-5235	188	20	)	)	PUNCT
cana-5235	188	21	communications	communication	NOUN
cana-5235	188	22	on	on	ADP
cana-5235	188	23	applied	apply	VERB
cana-5235	188	24	nonlinear	nonlinear	ADJ
cana-5235	188	25	analysis	analysis	NOUN
cana-5235	188	26	issn	issn	NOUN
cana-5235	188	27	:	:	PUNCT
cana-5235	188	28	1074	1074	NUM
cana-5235	188	29	-	-	PUNCT
cana-5235	188	30	133x	133x	NUM
cana-5235	188	31	vol	vol	VERB
cana-5235	188	32	32	32	NUM
cana-5235	188	33	no	no	NOUN
cana-5235	188	34	.	.	PUNCT
cana-5235	189	1	10s	10	NOUN
cana-5235	189	2	(	(	PUNCT
cana-5235	189	3	2025	2025	NUM
cana-5235	189	4	)	)	PUNCT
cana-5235	189	5	1330	1330	NUM
cana-5235	189	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5235	189	7	and	and	CCONJ
cana-5235	189	8	viscosity	viscosity	NOUN
cana-5235	189	9	ratio	ratio	NOUN
cana-5235	189	10	(	(	PUNCT
cana-5235	189	11	𝑚	𝑚	NOUN
cana-5235	189	12	)	)	PUNCT
cana-5235	189	13	are	be	AUX
cana-5235	189	14	plotted	plot	VERB
cana-5235	189	15	in	in	ADP
cana-5235	189	16	figs	fig	NOUN
cana-5235	189	17	.	.	PUNCT
cana-5235	190	1	3(a	3(a	NUM
cana-5235	190	2	)	)	PUNCT
cana-5235	190	3	and	and	CCONJ
cana-5235	190	4	(	(	PUNCT
cana-5235	190	5	b	b	NOUN
cana-5235	190	6	)	)	PUNCT
cana-5235	190	7	,	,	PUNCT
cana-5235	190	8	respectively	respectively	ADV
cana-5235	190	9	.	.	PUNCT
cana-5235	191	1	the	the	DET
cana-5235	191	2	patterns	pattern	NOUN
cana-5235	191	3	are	be	AUX
cana-5235	191	4	two	two	NUM
cana-5235	191	5	-	-	PUNCT
cana-5235	191	6	fold	fold	ADJ
cana-5235	191	7	,	,	PUNCT
cana-5235	191	8	which	which	PRON
cana-5235	191	9	are	be	AUX
cana-5235	191	10	similar	similar	ADJ
cana-5235	191	11	to	to	ADP
cana-5235	191	12	the	the	DET
cana-5235	191	13	single	single	ADJ
cana-5235	191	14	-	-	PUNCT
cana-5235	191	15	layer	layer	NOUN
cana-5235	191	16	fluid	fluid	NOUN
cana-5235	191	17	flow	flow	NOUN
cana-5235	191	18	as	as	ADP
cana-5235	191	19	in	in	ADP
cana-5235	191	20	fig	fig	NOUN
cana-5235	191	21	.	.	PUNCT
cana-5235	192	1	2	2	X
cana-5235	192	2	.	.	PUNCT
cana-5235	192	3	however	however	ADV
cana-5235	192	4	,	,	PUNCT
cana-5235	192	5	the	the	DET
cana-5235	192	6	long	long	ADJ
cana-5235	192	7	wave	wave	NOUN
cana-5235	192	8	stability	stability	NOUN
cana-5235	192	9	is	be	AUX
cana-5235	192	10	more	more	ADV
cana-5235	192	11	as	as	ADP
cana-5235	192	12	figure	figure	NOUN
cana-5235	192	13	2	2	NUM
cana-5235	192	14	:	:	PUNCT
cana-5235	192	15	validation	validation	NOUN
cana-5235	192	16	of	of	ADP
cana-5235	192	17	free	free	ADJ
cana-5235	192	18	surface	surface	NOUN
cana-5235	192	19	single	single	ADJ
cana-5235	192	20	layer	layer	NOUN
cana-5235	192	21	dispersion	dispersion	NOUN
cana-5235	192	22	curve	curve	NOUN
cana-5235	192	23	with	with	ADP
cana-5235	192	24	the	the	DET
cana-5235	192	25	existing	exist	VERB
cana-5235	192	26	theory	theory	NOUN
cana-5235	192	27	of	of	ADP
cana-5235	192	28	[	[	X
cana-5235	192	29	34	34	NUM
cana-5235	192	30	]	]	PUNCT
cana-5235	192	31	by	by	ADP
cana-5235	192	32	considering	consider	VERB
cana-5235	192	33	𝒅	𝒅	X
cana-5235	192	34	=	=	NOUN
cana-5235	192	35	𝟏	𝟏	PROPN
cana-5235	192	36	,	,	PUNCT
cana-5235	192	37	𝒎	𝒎	X
cana-5235	192	38	=	=	SYM
cana-5235	192	39	𝟏	𝟏	PROPN
cana-5235	192	40	,	,	PUNCT
cana-5235	192	41	𝑪𝒂	𝑪𝒂	PROPN
cana-5235	192	42	=	=	SYM
cana-5235	192	43	𝟎.	𝟎.	NOUN
cana-5235	192	44	𝟎𝟏𝟔𝟗	𝟎𝟏𝟔𝟗	NUM
cana-5235	192	45	,	,	PUNCT
cana-5235	192	46	𝝉	𝝉	X
cana-5235	192	47	=	=	SYM
cana-5235	192	48	𝟎	𝟎	PROPN
cana-5235	192	49	,	,	PUNCT
cana-5235	192	50	𝜷	𝜷	NOUN
cana-5235	192	51	=	=	SYM
cana-5235	192	52	𝟎	𝟎	NUM
cana-5235	192	53	and	and	CCONJ
cana-5235	192	54	𝑹𝒆𝟏	𝑹𝒆𝟏	NOUN
cana-5235	192	55	=	=	SYM
cana-5235	192	56	𝟐𝟓𝟎𝟎.	𝟐𝟓𝟎𝟎.	ADJ
cana-5235	192	57	compared	compare	VERB
cana-5235	192	58	to	to	ADP
cana-5235	192	59	that	that	PRON
cana-5235	192	60	for	for	ADP
cana-5235	192	61	single	single	ADJ
cana-5235	192	62	-	-	PUNCT
cana-5235	192	63	layer	layer	NOUN
cana-5235	192	64	fluid	fluid	NOUN
cana-5235	192	65	i.e.	i.e.	ADV
cana-5235	192	66	,	,	PUNCT
cana-5235	192	67	the	the	DET
cana-5235	192	68	growth	growth	NOUN
cana-5235	192	69	rate	rate	NOUN
cana-5235	192	70	of	of	ADP
cana-5235	192	71	dominant	dominant	ADJ
cana-5235	192	72	disturbance	disturbance	NOUN
cana-5235	192	73	increases	increase	NOUN
cana-5235	192	74	and	and	CCONJ
cana-5235	192	75	attains	attain	NOUN
cana-5235	192	76	maximum	maximum	ADJ
cana-5235	192	77	,	,	PUNCT
cana-5235	192	78	then	then	ADV
cana-5235	192	79	befall	befall	NOUN
cana-5235	192	80	for	for	ADP
cana-5235	192	81	the	the	DET
cana-5235	192	82	smaller	small	ADJ
cana-5235	192	83	values	value	NOUN
cana-5235	192	84	of	of	ADP
cana-5235	192	85	𝑘.	𝑘.	NOUN
cana-5235	192	86	while	while	SCONJ
cana-5235	192	87	increasing	increase	VERB
cana-5235	192	88	the	the	DET
cana-5235	192	89	interface	interface	NOUN
cana-5235	192	90	position	position	NOUN
cana-5235	192	91	(	(	PUNCT
cana-5235	192	92	𝑑	𝑑	NOUN
cana-5235	192	93	)	)	PUNCT
cana-5235	192	94	as	as	ADP
cana-5235	192	95	in	in	ADP
cana-5235	192	96	fig	fig	NOUN
cana-5235	192	97	.	.	PUNCT
cana-5235	193	1	3(a	3(a	NUM
cana-5235	193	2	)	)	PUNCT
cana-5235	193	3	,	,	PUNCT
cana-5235	193	4	the	the	DET
cana-5235	193	5	growth	growth	NOUN
cana-5235	193	6	rate	rate	NOUN
cana-5235	193	7	increases	increase	NOUN
cana-5235	193	8	.	.	PUNCT
cana-5235	194	1	this	this	DET
cana-5235	194	2	result	result	NOUN
cana-5235	194	3	in	in	ADP
cana-5235	194	4	more	more	ADJ
cana-5235	194	5	perturbed	perturb	VERB
cana-5235	194	6	wave	wave	NOUN
cana-5235	194	7	when	when	SCONJ
cana-5235	194	8	the	the	DET
cana-5235	194	9	interface	interface	NOUN
cana-5235	194	10	is	be	AUX
cana-5235	194	11	closer	close	ADJ
cana-5235	194	12	to	to	ADP
cana-5235	194	13	the	the	DET
cana-5235	194	14	slippery	slippery	ADJ
cana-5235	194	15	bottom	bottom	NOUN
cana-5235	194	16	.	.	PUNCT
cana-5235	195	1	on	on	ADP
cana-5235	195	2	the	the	DET
cana-5235	195	3	other	other	ADJ
cana-5235	195	4	hand	hand	NOUN
cana-5235	195	5	,	,	PUNCT
cana-5235	195	6	the	the	DET
cana-5235	195	7	growth	growth	NOUN
cana-5235	195	8	rate	rate	NOUN
cana-5235	195	9	increases	increase	NOUN
cana-5235	195	10	for	for	ADP
cana-5235	195	11	increase	increase	NOUN
cana-5235	195	12	in	in	ADP
cana-5235	195	13	the	the	DET
cana-5235	195	14	values	value	NOUN
cana-5235	195	15	of	of	ADP
cana-5235	195	16	𝑚	𝑚	PROPN
cana-5235	195	17	in	in	ADP
cana-5235	195	18	fig	fig	NOUN
cana-5235	195	19	.	.	PUNCT
cana-5235	196	1	3(b	3(b	NUM
cana-5235	196	2	)	)	PUNCT
cana-5235	196	3	due	due	ADP
cana-5235	196	4	to	to	ADP
cana-5235	196	5	the	the	DET
cana-5235	196	6	presence	presence	NOUN
cana-5235	196	7	of	of	ADP
cana-5235	196	8	less	less	ADJ
cana-5235	196	9	viscous	viscous	ADJ
cana-5235	196	10	fluid	fluid	NOUN
cana-5235	196	11	in	in	ADP
cana-5235	196	12	upper	upper	ADJ
cana-5235	196	13	layer	layer	NOUN
cana-5235	196	14	fluid	fluid	NOUN
cana-5235	196	15	,	,	PUNCT
cana-5235	196	16	which	which	PRON
cana-5235	196	17	destabilizes	destabilize	VERB
cana-5235	196	18	the	the	DET
cana-5235	196	19	flow	flow	NOUN
cana-5235	196	20	.	.	PUNCT
cana-5235	197	1	(	(	PUNCT
cana-5235	197	2	a	a	X
cana-5235	197	3	)	)	PUNCT
cana-5235	197	4	(	(	PUNCT
cana-5235	197	5	b	b	X
cana-5235	197	6	)	)	PUNCT
cana-5235	197	7	figure	figure	NOUN
cana-5235	197	8	3	3	NUM
cana-5235	197	9	:	:	PUNCT
cana-5235	197	10	growth	growth	NOUN
cana-5235	197	11	rate	rate	NOUN
cana-5235	197	12	against	against	ADP
cana-5235	197	13	the	the	DET
cana-5235	197	14	wavenumber	wavenumber	NOUN
cana-5235	197	15	for	for	ADP
cana-5235	197	16	different	different	ADJ
cana-5235	197	17	values	value	NOUN
cana-5235	197	18	of	of	ADP
cana-5235	197	19	(	(	PUNCT
cana-5235	197	20	a	a	PRON
cana-5235	197	21	)	)	PUNCT
cana-5235	197	22	interface	interface	NOUN
cana-5235	197	23	position	position	NOUN
cana-5235	197	24	𝒅	𝒅	NOUN
cana-5235	197	25	with	with	ADP
cana-5235	197	26	𝒎	𝒎	PROPN
cana-5235	197	27	=	=	SYM
cana-5235	197	28	𝟎.	𝟎.	X
cana-5235	197	29	𝟖	𝟖	X
cana-5235	197	30	and	and	CCONJ
cana-5235	197	31	(	(	PUNCT
cana-5235	197	32	b	b	NOUN
cana-5235	197	33	)	)	PUNCT
cana-5235	197	34	viscosity	viscosity	NOUN
cana-5235	197	35	ratio	ratio	NOUN
cana-5235	197	36	𝒎	𝒎	PROPN
cana-5235	197	37	with	with	ADP
cana-5235	197	38	𝒅	𝒅	NOUN
cana-5235	197	39	=	=	SYM
cana-5235	197	40	𝟎.	𝟎.	NOUN
cana-5235	197	41	𝟓	𝟓	NUM
cana-5235	197	42	,	,	PUNCT
cana-5235	197	43	and	and	CCONJ
cana-5235	197	44	the	the	DET
cana-5235	197	45	other	other	ADJ
cana-5235	197	46	parameters	parameter	NOUN
cana-5235	197	47	are	be	AUX
cana-5235	197	48	𝑪𝒂	𝑪𝒂	PROPN
cana-5235	197	49	=	=	PUNCT
cana-5235	197	50	𝟎.	𝟎.	X
cana-5235	197	51	𝟎𝟐	𝟎𝟐	NUM
cana-5235	197	52	,	,	PUNCT
cana-5235	197	53	𝑴𝒂	𝑴𝒂	PROPN
cana-5235	197	54	=	=	SYM
cana-5235	197	55	𝟎.	𝟎.	NOUN
cana-5235	197	56	𝟏	𝟏	NUM
cana-5235	197	57	,	,	PUNCT
cana-5235	197	58	𝑹𝒆𝟏	𝑹𝒆𝟏	NOUN
cana-5235	197	59	=	=	SYM
cana-5235	197	60	𝟓𝟎	𝟓𝟎	NUM
cana-5235	197	61	,	,	PUNCT
cana-5235	198	1	𝝉	𝝉	X
cana-5235	198	2	=	=	X
cana-5235	198	3	𝟎.	𝟎.	NOUN
cana-5235	198	4	𝟔	𝟔	NUM
cana-5235	198	5	and	and	CCONJ
cana-5235	198	6	𝜷	𝜷	NOUN
cana-5235	198	7	=	=	PUNCT
cana-5235	198	8	𝟎.	𝟎.	NOUN
cana-5235	198	9	𝟓.	𝟓.	PUNCT
cana-5235	198	10	the	the	DET
cana-5235	198	11	effect	effect	NOUN
cana-5235	198	12	of	of	ADP
cana-5235	198	13	insoluble	insoluble	ADJ
cana-5235	198	14	surfactant	surfactant	ADJ
cana-5235	198	15	concentration	concentration	NOUN
cana-5235	198	16	(	(	PUNCT
cana-5235	198	17	𝑀𝑎	𝑀𝑎	PROPN
cana-5235	198	18	)	)	PUNCT
cana-5235	198	19	on	on	ADP
cana-5235	198	20	the	the	DET
cana-5235	198	21	dispersion	dispersion	NOUN
cana-5235	198	22	curve	curve	NOUN
cana-5235	198	23	is	be	AUX
cana-5235	198	24	discussed	discuss	VERB
cana-5235	198	25	in	in	ADP
cana-5235	198	26	fig	fig	NOUN
cana-5235	198	27	.	.	PUNCT
cana-5235	199	1	4(a	4(a	NUM
cana-5235	199	2	)	)	PUNCT
cana-5235	199	3	.	.	PUNCT
cana-5235	200	1	the	the	DET
cana-5235	200	2	patterns	pattern	NOUN
cana-5235	200	3	resemble	resemble	VERB
cana-5235	200	4	as	as	ADP
cana-5235	200	5	in	in	ADP
cana-5235	200	6	fig	fig	NOUN
cana-5235	200	7	.	.	PUNCT
cana-5235	201	1	3	3	NUM
cana-5235	201	2	,	,	PUNCT
cana-5235	201	3	and	and	CCONJ
cana-5235	201	4	it	it	PRON
cana-5235	201	5	is	be	AUX
cana-5235	201	6	observed	observe	VERB
cana-5235	201	7	that	that	SCONJ
cana-5235	201	8	the	the	DET
cana-5235	201	9	presence	presence	NOUN
cana-5235	201	10	of	of	ADP
cana-5235	201	11	insoluble	insoluble	ADJ
cana-5235	201	12	surfactant	surfactant	ADJ
cana-5235	201	13	communications	communication	NOUN
cana-5235	201	14	on	on	ADP
cana-5235	201	15	applied	apply	VERB
cana-5235	201	16	nonlinear	nonlinear	ADJ
cana-5235	201	17	analysis	analysis	NOUN
cana-5235	201	18	issn	issn	NOUN
cana-5235	201	19	:	:	PUNCT
cana-5235	201	20	1074	1074	NUM
cana-5235	201	21	-	-	PUNCT
cana-5235	201	22	133x	133x	NUM
cana-5235	201	23	vol	vol	VERB
cana-5235	201	24	32	32	NUM
cana-5235	201	25	no	no	NOUN
cana-5235	201	26	.	.	PUNCT
cana-5235	202	1	10s	10	NOUN
cana-5235	202	2	(	(	PUNCT
cana-5235	202	3	2025	2025	NUM
cana-5235	202	4	)	)	PUNCT
cana-5235	202	5	1331	1331	NUM
cana-5235	202	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5235	202	7	decreases	decrease	VERB
cana-5235	202	8	the	the	DET
cana-5235	202	9	instability	instability	NOUN
cana-5235	202	10	.	.	PUNCT
cana-5235	203	1	further	far	ADV
cana-5235	203	2	,	,	PUNCT
cana-5235	203	3	the	the	DET
cana-5235	203	4	stability	stability	NOUN
cana-5235	203	5	enhances	enhance	VERB
cana-5235	203	6	for	for	ADP
cana-5235	203	7	the	the	DET
cana-5235	203	8	increase	increase	NOUN
cana-5235	203	9	in	in	ADP
cana-5235	203	10	the	the	DET
cana-5235	203	11	concentration	concentration	NOUN
cana-5235	203	12	of	of	ADP
cana-5235	203	13	insoluble	insoluble	ADJ
cana-5235	203	14	surfactant	surfactant	NOUN
cana-5235	203	15	𝑀𝑎.	𝑀𝑎.	PROPN
cana-5235	203	16	in	in	ADP
cana-5235	203	17	the	the	DET
cana-5235	203	18	case	case	NOUN
cana-5235	203	19	of	of	ADP
cana-5235	203	20	fig	fig	NOUN
cana-5235	203	21	.	.	PUNCT
cana-5235	204	1	4(b	4(b	NUM
cana-5235	204	2	)	)	PUNCT
cana-5235	204	3	,	,	PUNCT
cana-5235	204	4	the	the	DET
cana-5235	204	5	dispersion	dispersion	NOUN
cana-5235	204	6	curves	curve	NOUN
cana-5235	204	7	are	be	AUX
cana-5235	204	8	plotted	plot	VERB
cana-5235	204	9	for	for	ADP
cana-5235	204	10	different	different	ADJ
cana-5235	204	11	values	value	NOUN
cana-5235	204	12	of	of	ADP
cana-5235	204	13	density	density	NOUN
cana-5235	204	14	ratio	ratio	NOUN
cana-5235	204	15	𝑟.	𝑟.	NOUN
cana-5235	204	16	as	as	ADP
cana-5235	204	17	𝑟	𝑟	NOUN
cana-5235	204	18	increases	increase	NOUN
cana-5235	204	19	,	,	PUNCT
cana-5235	204	20	the	the	DET
cana-5235	204	21	instability	instability	NOUN
cana-5235	204	22	increases	increase	VERB
cana-5235	204	23	due	due	ADJ
cana-5235	204	24	to	to	PART
cana-5235	204	25	increase	increase	VERB
cana-5235	204	26	in	in	ADP
cana-5235	204	27	the	the	DET
cana-5235	204	28	value	value	NOUN
cana-5235	204	29	of	of	ADP
cana-5235	204	30	growth	growth	NOUN
cana-5235	204	31	rate	rate	NOUN
cana-5235	204	32	till	till	SCONJ
cana-5235	204	33	𝑘	𝑘	DET
cana-5235	204	34	≤	≤	NUM
cana-5235	204	35	0.09	0.09	NUM
cana-5235	204	36	.	.	PUNCT
cana-5235	205	1	after	after	ADP
cana-5235	205	2	that	that	SCONJ
cana-5235	205	3	the	the	DET
cana-5235	205	4	growth	growth	NOUN
cana-5235	205	5	rate	rate	NOUN
cana-5235	205	6	follows	follow	VERB
cana-5235	205	7	the	the	DET
cana-5235	205	8	reverse	reverse	ADJ
cana-5235	205	9	pattern	pattern	NOUN
cana-5235	205	10	for	for	ADP
cana-5235	205	11	increase	increase	NOUN
cana-5235	205	12	in	in	ADP
cana-5235	205	13	the	the	DET
cana-5235	205	14	values	value	NOUN
cana-5235	205	15	of	of	ADP
cana-5235	205	16	𝑟.	𝑟.	NOUN
cana-5235	205	17	this	this	PRON
cana-5235	205	18	is	be	AUX
cana-5235	205	19	due	due	ADJ
cana-5235	205	20	to	to	ADP
cana-5235	205	21	the	the	DET
cana-5235	205	22	rapid	rapid	ADJ
cana-5235	205	23	decline	decline	NOUN
cana-5235	205	24	of	of	ADP
cana-5235	205	25	the	the	DET
cana-5235	205	26	instability	instability	NOUN
cana-5235	205	27	for	for	ADP
cana-5235	205	28	higher	high	ADJ
cana-5235	205	29	wavenumbers	wavenumber	NOUN
cana-5235	205	30	𝑘	𝑘	X
cana-5235	205	31	>	>	X
cana-5235	205	32	0.09	0.09	NUM
cana-5235	205	33	,	,	PUNCT
cana-5235	205	34	but	but	CCONJ
cana-5235	205	35	the	the	DET
cana-5235	205	36	rate	rate	NOUN
cana-5235	205	37	of	of	ADP
cana-5235	205	38	befall	befall	NOUN
cana-5235	205	39	has	have	VERB
cana-5235	205	40	no	no	DET
cana-5235	205	41	major	major	ADJ
cana-5235	205	42	deviations	deviation	NOUN
cana-5235	205	43	for	for	ADP
cana-5235	205	44	larger	large	ADJ
cana-5235	205	45	values	value	NOUN
cana-5235	205	46	of	of	ADP
cana-5235	205	47	𝑟.	𝑟.	NOUN
cana-5235	205	48	(	(	PUNCT
cana-5235	205	49	a	a	X
cana-5235	205	50	)	)	PUNCT
cana-5235	205	51	(	(	PUNCT
cana-5235	205	52	b	b	X
cana-5235	205	53	)	)	PUNCT
cana-5235	205	54	figure	figure	NOUN
cana-5235	205	55	4	4	NUM
cana-5235	205	56	:	:	PUNCT
cana-5235	205	57	growth	growth	NOUN
cana-5235	205	58	rate	rate	NOUN
cana-5235	205	59	against	against	ADP
cana-5235	205	60	the	the	DET
cana-5235	205	61	wavenumber	wavenumber	NOUN
cana-5235	205	62	for	for	ADP
cana-5235	205	63	different	different	ADJ
cana-5235	205	64	values	value	NOUN
cana-5235	205	65	of	of	ADP
cana-5235	205	66	(	(	PUNCT
cana-5235	205	67	a	a	PRON
cana-5235	205	68	)	)	PUNCT
cana-5235	205	69	marangoni	marangoni	NOUN
cana-5235	205	70	number	number	NOUN
cana-5235	205	71	𝑴𝒂	𝑴𝒂	PROPN
cana-5235	205	72	with	with	ADP
cana-5235	205	73	𝒓	𝒓	PROPN
cana-5235	205	74	=	=	PUNCT
cana-5235	205	75	𝟎.	𝟎.	X
cana-5235	205	76	𝟔	𝟔	NUM
cana-5235	205	77	and	and	CCONJ
cana-5235	205	78	(	(	PUNCT
cana-5235	205	79	b	b	NOUN
cana-5235	205	80	)	)	PUNCT
cana-5235	205	81	density	density	NOUN
cana-5235	205	82	ratio	ratio	NOUN
cana-5235	205	83	𝒓	𝒓	PROPN
cana-5235	205	84	with	with	ADP
cana-5235	205	85	𝑴𝒂	𝑴𝒂	PROPN
cana-5235	205	86	=	=	SYM
cana-5235	205	87	𝟎.	𝟎.	NOUN
cana-5235	205	88	𝟏	𝟏	NUM
cana-5235	205	89	,	,	PUNCT
cana-5235	205	90	and	and	CCONJ
cana-5235	205	91	other	other	ADJ
cana-5235	205	92	parameters	parameter	NOUN
cana-5235	205	93	are	be	AUX
cana-5235	205	94	𝑪𝒂	𝑪𝒂	PROPN
cana-5235	205	95	=	=	PUNCT
cana-5235	205	96	𝟎.	𝟎.	X
cana-5235	205	97	𝟎𝟐	𝟎𝟐	NUM
cana-5235	205	98	,	,	PUNCT
cana-5235	205	99	𝒎	𝒎	X
cana-5235	205	100	=	=	SYM
cana-5235	205	101	𝟎.	𝟎.	X
cana-5235	205	102	𝟖	𝟖	NUM
cana-5235	205	103	,	,	PUNCT
cana-5235	205	104	𝑹𝒆𝟏	𝑹𝒆𝟏	NOUN
cana-5235	205	105	=	=	SYM
cana-5235	205	106	𝟓𝟎	𝟓𝟎	NUM
cana-5235	205	107	,	,	PUNCT
cana-5235	205	108	𝒅	𝒅	X
cana-5235	205	109	=	=	PRON
cana-5235	205	110	𝟎.	𝟎.	ADJ
cana-5235	205	111	𝟓	𝟓	NUM
cana-5235	205	112	,	,	PUNCT
cana-5235	205	113	𝝉	𝝉	X
cana-5235	205	114	=	=	X
cana-5235	205	115	𝟎.	𝟎.	NOUN
cana-5235	205	116	𝟔	𝟔	NUM
cana-5235	205	117	and	and	CCONJ
cana-5235	205	118	𝜷	𝜷	NOUN
cana-5235	205	119	=	=	PUNCT
cana-5235	205	120	𝟎.	𝟎.	PUNCT
cana-5235	205	121	𝟓.	𝟓.	PUNCT
cana-5235	205	122	(	(	PUNCT
cana-5235	205	123	(	(	PUNCT
cana-5235	205	124	a	a	NOUN
cana-5235	205	125	)	)	PUNCT
cana-5235	205	126	(	(	PUNCT
cana-5235	205	127	b	b	X
cana-5235	205	128	)	)	PUNCT
cana-5235	205	129	figure	figure	NOUN
cana-5235	205	130	5	5	NUM
cana-5235	205	131	:	:	PUNCT
cana-5235	205	132	growth	growth	NOUN
cana-5235	205	133	rate	rate	NOUN
cana-5235	205	134	against	against	ADP
cana-5235	205	135	the	the	DET
cana-5235	205	136	wavenumber	wavenumber	NOUN
cana-5235	205	137	for	for	ADP
cana-5235	205	138	different	different	ADJ
cana-5235	205	139	values	value	NOUN
cana-5235	205	140	of	of	ADP
cana-5235	205	141	(	(	PUNCT
cana-5235	205	142	a	a	X
cana-5235	205	143	)	)	PUNCT
cana-5235	205	144	shear	shear	NOUN
cana-5235	205	145	parameter	parameter	NOUN
cana-5235	205	146	𝝉	𝝉	NOUN
cana-5235	205	147	with	with	ADP
cana-5235	205	148	𝜷	𝜷	NOUN
cana-5235	205	149	=	=	PUNCT
cana-5235	205	150	𝟎.	𝟎.	X
cana-5235	205	151	𝟓	𝟓	NUM
cana-5235	205	152	and	and	CCONJ
cana-5235	205	153	(	(	PUNCT
cana-5235	205	154	b	b	NOUN
cana-5235	205	155	)	)	PUNCT
cana-5235	205	156	slip	slip	NOUN
cana-5235	205	157	parameter	parameter	NOUN
cana-5235	205	158	𝜷	𝜷	NOUN
cana-5235	205	159	with	with	ADP
cana-5235	205	160	𝝉	𝝉	PROPN
cana-5235	205	161	=	=	SYM
cana-5235	205	162	𝟎.	𝟎.	NUM
cana-5235	205	163	𝟔	𝟔	NUM
cana-5235	205	164	,	,	PUNCT
cana-5235	205	165	and	and	CCONJ
cana-5235	205	166	other	other	ADJ
cana-5235	205	167	parameters	parameter	NOUN
cana-5235	205	168	are	be	AUX
cana-5235	205	169	𝑪𝒂	𝑪𝒂	PROPN
cana-5235	205	170	=	=	PUNCT
cana-5235	205	171	𝟎.	𝟎.	X
cana-5235	205	172	𝟎𝟐	𝟎𝟐	NUM
cana-5235	205	173	,	,	PUNCT
cana-5235	205	174	𝒎	𝒎	X
cana-5235	205	175	=	=	SYM
cana-5235	205	176	𝟎.	𝟎.	X
cana-5235	205	177	𝟖	𝟖	NUM
cana-5235	205	178	,	,	PUNCT
cana-5235	205	179	𝑹𝒆𝟏	𝑹𝒆𝟏	NOUN
cana-5235	205	180	=	=	SYM
cana-5235	205	181	𝟓𝟎	𝟓𝟎	NUM
cana-5235	205	182	,	,	PUNCT
cana-5235	205	183	𝒅	𝒅	X
cana-5235	205	184	=	=	PRON
cana-5235	205	185	𝟎.	𝟎.	ADJ
cana-5235	205	186	𝟓	𝟓	NUM
cana-5235	205	187	,	,	PUNCT
cana-5235	205	188	𝑴𝒂	𝑴𝒂	PROPN
cana-5235	205	189	=	=	SYM
cana-5235	205	190	𝟎.	𝟎.	PUNCT
cana-5235	205	191	𝟏	𝟏	NUM
cana-5235	205	192	and	and	CCONJ
cana-5235	205	193	𝒓	𝒓	PROPN
cana-5235	205	194	=	=	PUNCT
cana-5235	205	195	𝟎.	𝟎.	PROPN
cana-5235	205	196	𝟔.	𝟔.	AUX
cana-5235	205	197	the	the	DET
cana-5235	205	198	effect	effect	NOUN
cana-5235	205	199	of	of	ADP
cana-5235	205	200	shear	shear	NOUN
cana-5235	205	201	parameter	parameter	NOUN
cana-5235	205	202	(	(	PUNCT
cana-5235	205	203	𝜏	𝜏	NOUN
cana-5235	205	204	)	)	PUNCT
cana-5235	205	205	and	and	CCONJ
cana-5235	205	206	slip	slip	VERB
cana-5235	205	207	parameter	parameter	NOUN
cana-5235	205	208	(	(	PUNCT
cana-5235	205	209	𝛽	𝛽	NOUN
cana-5235	205	210	)	)	PUNCT
cana-5235	205	211	on	on	ADP
cana-5235	205	212	the	the	DET
cana-5235	205	213	dispersion	dispersion	NOUN
cana-5235	205	214	curve	curve	NOUN
cana-5235	205	215	for	for	ADP
cana-5235	205	216	two	two	NUM
cana-5235	205	217	-	-	PUNCT
cana-5235	205	218	layer	layer	NOUN
cana-5235	205	219	film	film	NOUN
cana-5235	205	220	flow	flow	NOUN
cana-5235	205	221	are	be	AUX
cana-5235	205	222	illustrated	illustrate	VERB
cana-5235	205	223	in	in	ADP
cana-5235	205	224	figs	fig	NOUN
cana-5235	205	225	.	.	PUNCT
cana-5235	206	1	5(a	5(a	NUM
cana-5235	206	2	)	)	PUNCT
cana-5235	206	3	and	and	CCONJ
cana-5235	206	4	(	(	PUNCT
cana-5235	206	5	b	b	NOUN
cana-5235	206	6	)	)	PUNCT
cana-5235	206	7	,	,	PUNCT
cana-5235	206	8	respectively	respectively	ADV
cana-5235	206	9	.	.	PUNCT
cana-5235	207	1	as	as	SCONJ
cana-5235	207	2	the	the	DET
cana-5235	207	3	shear	shear	NOUN
cana-5235	207	4	imposed	impose	VERB
cana-5235	207	5	on	on	ADP
cana-5235	207	6	the	the	DET
cana-5235	207	7	upper	upper	ADJ
cana-5235	207	8	layer	layer	NOUN
cana-5235	207	9	communications	communication	NOUN
cana-5235	207	10	on	on	ADP
cana-5235	207	11	applied	apply	VERB
cana-5235	207	12	nonlinear	nonlinear	ADJ
cana-5235	207	13	analysis	analysis	NOUN
cana-5235	207	14	issn	issn	NOUN
cana-5235	207	15	:	:	PUNCT
cana-5235	207	16	1074	1074	NUM
cana-5235	207	17	-	-	PUNCT
cana-5235	207	18	133x	133x	NUM
cana-5235	207	19	vol	vol	VERB
cana-5235	207	20	32	32	NUM
cana-5235	207	21	no	no	NOUN
cana-5235	207	22	.	.	PUNCT
cana-5235	208	1	10s	10	NOUN
cana-5235	208	2	(	(	PUNCT
cana-5235	208	3	2025	2025	NUM
cana-5235	208	4	)	)	PUNCT
cana-5235	208	5	1332	1332	NUM
cana-5235	209	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5235	209	2	increases	increase	VERB
cana-5235	209	3	as	as	ADP
cana-5235	209	4	in	in	ADP
cana-5235	209	5	fig	fig	NOUN
cana-5235	209	6	.	.	PUNCT
cana-5235	210	1	5(a	5(a	NUM
cana-5235	210	2	)	)	PUNCT
cana-5235	210	3	,	,	PUNCT
cana-5235	210	4	the	the	DET
cana-5235	210	5	growth	growth	NOUN
cana-5235	210	6	rate	rate	NOUN
cana-5235	210	7	increases	increase	NOUN
cana-5235	210	8	for	for	ADP
cana-5235	210	9	wavenumber	wavenumber	NOUN
cana-5235	210	10	0	0	NUM
cana-5235	210	11	≤	≤	NOUN
cana-5235	210	12	𝑘	𝑘	DET
cana-5235	210	13	≤	≤	NOUN
cana-5235	210	14	0.038	0.038	NUM
cana-5235	210	15	and	and	CCONJ
cana-5235	210	16	it	it	PRON
cana-5235	210	17	decreases	decrease	VERB
cana-5235	210	18	for	for	ADP
cana-5235	210	19	the	the	DET
cana-5235	210	20	value	value	NOUN
cana-5235	210	21	of	of	ADP
cana-5235	210	22	𝑘	𝑘	PROPN
cana-5235	210	23	>	>	X
cana-5235	210	24	0.038	0.038	NUM
cana-5235	210	25	.	.	PUNCT
cana-5235	211	1	this	this	DET
cana-5235	211	2	bifurcation	bifurcation	NOUN
cana-5235	211	3	is	be	AUX
cana-5235	211	4	due	due	ADJ
cana-5235	211	5	to	to	ADP
cana-5235	211	6	the	the	DET
cana-5235	211	7	fact	fact	NOUN
cana-5235	211	8	that	that	SCONJ
cana-5235	211	9	the	the	DET
cana-5235	211	10	perturbed	perturb	VERB
cana-5235	211	11	wave	wave	NOUN
cana-5235	211	12	amplitude	amplitude	NOUN
cana-5235	211	13	exceeds	exceed	VERB
cana-5235	211	14	the	the	DET
cana-5235	211	15	applied	applied	ADJ
cana-5235	211	16	force	force	NOUN
cana-5235	211	17	for	for	ADP
cana-5235	211	18	0	0	NUM
cana-5235	211	19	≤	≤	NOUN
cana-5235	211	20	𝑘	𝑘	DET
cana-5235	211	21	≤	≤	NOUN
cana-5235	211	22	0.038	0.038	NUM
cana-5235	211	23	and	and	CCONJ
cana-5235	211	24	it	it	PRON
cana-5235	211	25	follows	follow	VERB
cana-5235	211	26	the	the	DET
cana-5235	211	27	reverse	reverse	ADJ
cana-5235	211	28	trends	trend	NOUN
cana-5235	211	29	for	for	ADP
cana-5235	211	30	𝑘	𝑘	PROPN
cana-5235	211	31	>	>	X
cana-5235	211	32	0.038	0.038	NUM
cana-5235	211	33	.	.	PUNCT
cana-5235	212	1	on	on	ADP
cana-5235	212	2	the	the	DET
cana-5235	212	3	other	other	ADJ
cana-5235	212	4	hand	hand	NOUN
cana-5235	212	5	,	,	PUNCT
cana-5235	212	6	in	in	ADP
cana-5235	212	7	the	the	DET
cana-5235	212	8	case	case	NOUN
cana-5235	212	9	of	of	ADP
cana-5235	212	10	fig	fig	NOUN
cana-5235	212	11	.	.	PUNCT
cana-5235	213	1	5(b	5(b	NUM
cana-5235	213	2	)	)	PUNCT
cana-5235	213	3	,	,	PUNCT
cana-5235	213	4	it	it	PRON
cana-5235	213	5	is	be	AUX
cana-5235	213	6	observed	observe	VERB
cana-5235	213	7	that	that	SCONJ
cana-5235	213	8	the	the	DET
cana-5235	213	9	fluid	fluid	ADJ
cana-5235	213	10	flow	flow	NOUN
cana-5235	213	11	destabilizes	destabilize	VERB
cana-5235	213	12	for	for	ADP
cana-5235	213	13	larger	large	ADJ
cana-5235	213	14	values	value	NOUN
cana-5235	213	15	of	of	ADP
cana-5235	213	16	𝛽.	𝛽.	NOUN
cana-5235	213	17	moreover	moreover	ADV
cana-5235	213	18	,	,	PUNCT
cana-5235	213	19	there	there	PRON
cana-5235	213	20	is	be	VERB
cana-5235	213	21	a	a	DET
cana-5235	213	22	negligible	negligible	ADJ
cana-5235	213	23	effect	effect	NOUN
cana-5235	213	24	for	for	ADP
cana-5235	213	25	wavenumber	wavenumber	NOUN
cana-5235	213	26	𝑘	𝑘	PRON
cana-5235	213	27	≥	≥	NOUN
cana-5235	213	28	0.01	0.01	NUM
cana-5235	213	29	.	.	PUNCT
cana-5235	214	1	(	(	PUNCT
cana-5235	214	2	a	a	X
cana-5235	214	3	)	)	PUNCT
cana-5235	214	4	(	(	PUNCT
cana-5235	214	5	b	b	X
cana-5235	214	6	)	)	PUNCT
cana-5235	214	7	figure	figure	NOUN
cana-5235	214	8	6	6	NUM
cana-5235	214	9	:	:	PUNCT
cana-5235	214	10	growth	growth	NOUN
cana-5235	214	11	rate	rate	NOUN
cana-5235	214	12	against	against	ADP
cana-5235	214	13	the	the	DET
cana-5235	214	14	reynolds	reynolds	PROPN
cana-5235	214	15	number	number	NOUN
cana-5235	214	16	for	for	ADP
cana-5235	214	17	different	different	ADJ
cana-5235	214	18	values	value	NOUN
cana-5235	214	19	of	of	ADP
cana-5235	214	20	(	(	PUNCT
cana-5235	214	21	a	a	PRON
cana-5235	214	22	)	)	PUNCT
cana-5235	214	23	marangoni	marangoni	NOUN
cana-5235	214	24	number	number	NOUN
cana-5235	214	25	𝑴𝒂	𝑴𝒂	PROPN
cana-5235	214	26	with	with	ADP
cana-5235	214	27	𝒅	𝒅	NOUN
cana-5235	214	28	=	=	SYM
cana-5235	214	29	𝟎.	𝟎.	X
cana-5235	214	30	𝟓	𝟓	NUM
cana-5235	214	31	and	and	CCONJ
cana-5235	214	32	(	(	PUNCT
cana-5235	214	33	b	b	NOUN
cana-5235	214	34	)	)	PUNCT
cana-5235	214	35	interface	interface	NOUN
cana-5235	214	36	position	position	NOUN
cana-5235	214	37	𝒅	𝒅	NOUN
cana-5235	214	38	with	with	ADP
cana-5235	214	39	𝑴𝒂	𝑴𝒂	PROPN
cana-5235	214	40	=	=	SYM
cana-5235	214	41	𝟎.	𝟎.	NOUN
cana-5235	214	42	𝟏	𝟏	NUM
cana-5235	214	43	,	,	PUNCT
cana-5235	214	44	and	and	CCONJ
cana-5235	214	45	other	other	ADJ
cana-5235	214	46	parameters	parameter	NOUN
cana-5235	214	47	are	be	AUX
cana-5235	214	48	𝑪𝒂	𝑪𝒂	PROPN
cana-5235	214	49	=	=	PUNCT
cana-5235	214	50	𝟎.	𝟎.	X
cana-5235	214	51	𝟎𝟐	𝟎𝟐	NUM
cana-5235	214	52	,	,	PUNCT
cana-5235	214	53	𝒎	𝒎	X
cana-5235	214	54	=	=	SYM
cana-5235	214	55	𝟎.	𝟎.	X
cana-5235	214	56	𝟖	𝟖	NUM
cana-5235	214	57	,	,	PUNCT
cana-5235	214	58	𝒅	𝒅	X
cana-5235	214	59	=	=	PRON
cana-5235	214	60	𝟎.	𝟎.	ADJ
cana-5235	214	61	𝟓	𝟓	NUM
cana-5235	214	62	,	,	PUNCT
cana-5235	214	63	𝑴𝒂	𝑴𝒂	PROPN
cana-5235	214	64	=	=	SYM
cana-5235	214	65	𝟎.	𝟎.	PUNCT
cana-5235	214	66	𝟏	𝟏	NUM
cana-5235	214	67	and	and	CCONJ
cana-5235	214	68	𝒓	𝒓	PROPN
cana-5235	214	69	=	=	PUNCT
cana-5235	214	70	𝟎.	𝟎.	PROPN
cana-5235	214	71	𝟔.	𝟔.	X
cana-5235	214	72	(	(	PUNCT
cana-5235	214	73	a	a	NOUN
cana-5235	214	74	)	)	PUNCT
cana-5235	214	75	(	(	PUNCT
cana-5235	214	76	b	b	X
cana-5235	214	77	)	)	PUNCT
cana-5235	214	78	figure	figure	NOUN
cana-5235	214	79	7	7	NUM
cana-5235	214	80	:	:	PUNCT
cana-5235	214	81	growth	growth	NOUN
cana-5235	214	82	rate	rate	NOUN
cana-5235	214	83	against	against	ADP
cana-5235	214	84	the	the	DET
cana-5235	214	85	reynolds	reynolds	PROPN
cana-5235	214	86	number	number	NOUN
cana-5235	214	87	for	for	ADP
cana-5235	214	88	different	different	ADJ
cana-5235	214	89	values	value	NOUN
cana-5235	214	90	of	of	ADP
cana-5235	214	91	(	(	PUNCT
cana-5235	214	92	a	a	X
cana-5235	214	93	)	)	PUNCT
cana-5235	214	94	shear	shear	NOUN
cana-5235	214	95	parameter	parameter	NOUN
cana-5235	214	96	𝝉	𝝉	NOUN
cana-5235	214	97	with	with	ADP
cana-5235	214	98	𝜷	𝜷	NOUN
cana-5235	214	99	=	=	PUNCT
cana-5235	214	100	𝟎.	𝟎.	X
cana-5235	214	101	𝟓	𝟓	NUM
cana-5235	214	102	and	and	CCONJ
cana-5235	214	103	(	(	PUNCT
cana-5235	214	104	b	b	NOUN
cana-5235	214	105	)	)	PUNCT
cana-5235	214	106	slip	slip	NOUN
cana-5235	214	107	parameter	parameter	NOUN
cana-5235	214	108	𝜷	𝜷	NOUN
cana-5235	214	109	with	with	ADP
cana-5235	214	110	𝝉	𝝉	PROPN
cana-5235	214	111	=	=	SYM
cana-5235	214	112	𝟎.	𝟎.	NUM
cana-5235	214	113	𝟔	𝟔	NUM
cana-5235	214	114	,	,	PUNCT
cana-5235	214	115	and	and	CCONJ
cana-5235	214	116	other	other	ADJ
cana-5235	214	117	parameters	parameter	NOUN
cana-5235	214	118	are	be	AUX
cana-5235	214	119	𝑪𝒂	𝑪𝒂	PROPN
cana-5235	214	120	=	=	PUNCT
cana-5235	214	121	𝟎.	𝟎.	X
cana-5235	214	122	𝟎𝟐	𝟎𝟐	NUM
cana-5235	214	123	,	,	PUNCT
cana-5235	214	124	𝒎	𝒎	X
cana-5235	214	125	=	=	SYM
cana-5235	214	126	𝟎.	𝟎.	X
cana-5235	214	127	𝟖	𝟖	NUM
cana-5235	214	128	,	,	PUNCT
cana-5235	214	129	𝒅	𝒅	X
cana-5235	214	130	=	=	PRON
cana-5235	214	131	𝟎.	𝟎.	ADJ
cana-5235	214	132	𝟓	𝟓	NUM
cana-5235	214	133	,	,	PUNCT
cana-5235	214	134	𝑴𝒂	𝑴𝒂	PROPN
cana-5235	214	135	=	=	SYM
cana-5235	214	136	𝟎.	𝟎.	PUNCT
cana-5235	214	137	𝟏	𝟏	NUM
cana-5235	214	138	and	and	CCONJ
cana-5235	214	139	𝒓	𝒓	PROPN
cana-5235	214	140	=	=	PUNCT
cana-5235	215	1	𝟎.	𝟎.	PROPN
cana-5235	215	2	𝟔.	𝟔.	X
cana-5235	215	3	the	the	DET
cana-5235	215	4	inertial	inertial	ADJ
cana-5235	215	5	effect	effect	NOUN
cana-5235	215	6	on	on	ADP
cana-5235	215	7	the	the	DET
cana-5235	215	8	maximum	maximum	ADJ
cana-5235	215	9	growth	growth	NOUN
cana-5235	215	10	rate	rate	NOUN
cana-5235	215	11	is	be	AUX
cana-5235	215	12	plotted	plot	VERB
cana-5235	215	13	for	for	ADP
cana-5235	215	14	the	the	DET
cana-5235	215	15	different	different	ADJ
cana-5235	215	16	values	value	NOUN
cana-5235	215	17	of	of	ADP
cana-5235	215	18	marangoni	marangoni	ADJ
cana-5235	215	19	number	number	NOUN
cana-5235	215	20	(	(	PUNCT
cana-5235	215	21	𝑀𝑎	𝑀𝑎	PROPN
cana-5235	215	22	)	)	PUNCT
cana-5235	215	23	and	and	CCONJ
cana-5235	215	24	interface	interface	NOUN
cana-5235	215	25	position	position	NOUN
cana-5235	215	26	(	(	PUNCT
cana-5235	215	27	𝑑	𝑑	NOUN
cana-5235	215	28	)	)	PUNCT
cana-5235	215	29	in	in	ADP
cana-5235	215	30	figs	fig	NOUN
cana-5235	215	31	.	.	PUNCT
cana-5235	216	1	6(a	6(a	NUM
cana-5235	216	2	)	)	PUNCT
cana-5235	217	1	and	and	CCONJ
cana-5235	217	2	(	(	PUNCT
cana-5235	217	3	b	b	NOUN
cana-5235	217	4	)	)	PUNCT
cana-5235	217	5	,	,	PUNCT
cana-5235	217	6	respectively	respectively	ADV
cana-5235	217	7	.	.	PUNCT
cana-5235	218	1	from	from	ADP
cana-5235	218	2	both	both	DET
cana-5235	218	3	the	the	DET
cana-5235	218	4	figures	figure	NOUN
cana-5235	218	5	,	,	PUNCT
cana-5235	218	6	it	it	PRON
cana-5235	218	7	is	be	AUX
cana-5235	218	8	noticed	notice	VERB
cana-5235	218	9	that	that	SCONJ
cana-5235	218	10	the	the	DET
cana-5235	218	11	growth	growth	NOUN
cana-5235	218	12	rate	rate	NOUN
cana-5235	218	13	increases	increase	NOUN
cana-5235	218	14	and	and	CCONJ
cana-5235	218	15	attains	attain	NOUN
cana-5235	218	16	maximum	maximum	ADJ
cana-5235	218	17	,	,	PUNCT
cana-5235	218	18	then	then	ADV
cana-5235	218	19	decreases	decrease	VERB
cana-5235	218	20	for	for	ADP
cana-5235	218	21	increase	increase	NOUN
cana-5235	218	22	in	in	ADP
cana-5235	218	23	the	the	DET
cana-5235	218	24	values	value	NOUN
cana-5235	218	25	of	of	ADP
cana-5235	218	26	𝑅𝑒1	𝑅𝑒1	NOUN
cana-5235	218	27	.	.	PUNCT
cana-5235	219	1	the	the	DET
cana-5235	219	2	fluid	fluid	ADJ
cana-5235	219	3	flow	flow	NOUN
cana-5235	219	4	becomes	become	VERB
cana-5235	219	5	stable	stable	ADJ
cana-5235	219	6	for	for	ADP
cana-5235	219	7	smaller	small	ADJ
cana-5235	219	8	values	value	NOUN
cana-5235	219	9	of	of	ADP
cana-5235	219	10	𝑅𝑒1	𝑅𝑒1	NOUN
cana-5235	219	11	,	,	PUNCT
cana-5235	219	12	whereas	whereas	SCONJ
cana-5235	219	13	it	it	PRON
cana-5235	219	14	becomes	become	VERB
cana-5235	219	15	unstable	unstable	ADJ
cana-5235	219	16	gradually	gradually	ADV
cana-5235	219	17	for	for	ADP
cana-5235	219	18	larger	large	ADJ
cana-5235	219	19	values	value	NOUN
cana-5235	219	20	of	of	ADP
cana-5235	219	21	𝑅𝑒1	𝑅𝑒1	NOUN
cana-5235	219	22	.	.	PUNCT
cana-5235	220	1	this	this	PRON
cana-5235	220	2	is	be	AUX
cana-5235	220	3	due	due	ADJ
cana-5235	220	4	to	to	ADP
cana-5235	220	5	the	the	DET
cana-5235	220	6	fact	fact	NOUN
cana-5235	220	7	that	that	SCONJ
cana-5235	220	8	the	the	DET
cana-5235	220	9	viscous	viscous	ADJ
cana-5235	220	10	force	force	NOUN
cana-5235	220	11	dominates	dominate	VERB
cana-5235	220	12	the	the	DET
cana-5235	220	13	inertial	inertial	ADJ
cana-5235	220	14	force	force	NOUN
cana-5235	220	15	for	for	ADP
cana-5235	220	16	communications	communication	NOUN
cana-5235	220	17	on	on	ADP
cana-5235	220	18	applied	apply	VERB
cana-5235	220	19	nonlinear	nonlinear	ADJ
cana-5235	220	20	analysis	analysis	NOUN
cana-5235	220	21	issn	issn	NOUN
cana-5235	220	22	:	:	PUNCT
cana-5235	220	23	1074	1074	NUM
cana-5235	220	24	-	-	PUNCT
cana-5235	220	25	133x	133x	NUM
cana-5235	220	26	vol	vol	VERB
cana-5235	220	27	32	32	NUM
cana-5235	220	28	no	no	NOUN
cana-5235	220	29	.	.	PUNCT
cana-5235	221	1	10s	10	NOUN
cana-5235	221	2	(	(	PUNCT
cana-5235	221	3	2025	2025	NUM
cana-5235	221	4	)	)	PUNCT
cana-5235	221	5	1333	1333	NUM
cana-5235	221	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5235	221	7	smaller	small	ADJ
cana-5235	221	8	values	value	NOUN
cana-5235	221	9	of	of	ADP
cana-5235	221	10	𝑅𝑒1	𝑅𝑒1	NOUN
cana-5235	221	11	and	and	CCONJ
cana-5235	221	12	vice	vice	NOUN
cana-5235	221	13	versa	versa	ADV
cana-5235	221	14	.	.	PUNCT
cana-5235	222	1	the	the	DET
cana-5235	222	2	maximum	maximum	ADJ
cana-5235	222	3	value	value	NOUN
cana-5235	222	4	of	of	ADP
cana-5235	222	5	growth	growth	NOUN
cana-5235	222	6	rate	rate	NOUN
cana-5235	222	7	is	be	AUX
cana-5235	222	8	due	due	ADJ
cana-5235	222	9	to	to	ADP
cana-5235	222	10	the	the	DET
cana-5235	222	11	balance	balance	NOUN
cana-5235	222	12	between	between	ADP
cana-5235	222	13	the	the	DET
cana-5235	222	14	inertial	inertial	ADJ
cana-5235	222	15	and	and	CCONJ
cana-5235	222	16	viscous	viscous	ADJ
cana-5235	222	17	force	force	NOUN
cana-5235	222	18	.	.	PUNCT
cana-5235	223	1	moreover	moreover	ADV
cana-5235	223	2	,	,	PUNCT
cana-5235	223	3	the	the	DET
cana-5235	223	4	inertial	inertial	ADJ
cana-5235	223	5	force	force	NOUN
cana-5235	223	6	eventually	eventually	ADV
cana-5235	223	7	overcomes	overcome	VERB
cana-5235	223	8	the	the	DET
cana-5235	223	9	viscous	viscous	ADJ
cana-5235	223	10	force	force	NOUN
cana-5235	223	11	for	for	ADP
cana-5235	223	12	larger	large	ADJ
cana-5235	223	13	values	value	NOUN
cana-5235	223	14	of	of	ADP
cana-5235	223	15	𝑅𝑒1	𝑅𝑒1	NOUN
cana-5235	223	16	.	.	PUNCT
cana-5235	224	1	from	from	ADP
cana-5235	224	2	fig	fig	NOUN
cana-5235	224	3	.	.	PUNCT
cana-5235	225	1	6(a	6(a	NUM
cana-5235	225	2	)	)	PUNCT
cana-5235	225	3	,	,	PUNCT
cana-5235	225	4	it	it	PRON
cana-5235	225	5	is	be	AUX
cana-5235	225	6	observed	observe	VERB
cana-5235	225	7	that	that	SCONJ
cana-5235	225	8	the	the	DET
cana-5235	225	9	growth	growth	NOUN
cana-5235	225	10	rate	rate	NOUN
cana-5235	225	11	decreases	decrease	VERB
cana-5235	225	12	for	for	ADP
cana-5235	225	13	increase	increase	NOUN
cana-5235	225	14	in	in	ADP
cana-5235	225	15	the	the	DET
cana-5235	225	16	concentration	concentration	NOUN
cana-5235	225	17	of	of	ADP
cana-5235	225	18	surfactant	surfactant	NOUN
cana-5235	225	19	.	.	PUNCT
cana-5235	226	1	this	this	PRON
cana-5235	226	2	implies	imply	VERB
cana-5235	226	3	that	that	SCONJ
cana-5235	226	4	the	the	DET
cana-5235	226	5	higher	high	ADJ
cana-5235	226	6	concentration	concentration	NOUN
cana-5235	226	7	of	of	ADP
cana-5235	226	8	surfactant	surfactant	NOUN
cana-5235	226	9	enhances	enhance	VERB
cana-5235	226	10	the	the	DET
cana-5235	226	11	stability	stability	NOUN
cana-5235	226	12	of	of	ADP
cana-5235	226	13	flow	flow	NOUN
cana-5235	226	14	system	system	NOUN
cana-5235	226	15	.	.	PUNCT
cana-5235	227	1	in	in	ADP
cana-5235	227	2	the	the	DET
cana-5235	227	3	case	case	NOUN
cana-5235	227	4	of	of	ADP
cana-5235	227	5	fig	fig	NOUN
cana-5235	227	6	.	.	PUNCT
cana-5235	228	1	6(b	6(b	NUM
cana-5235	228	2	)	)	PUNCT
cana-5235	228	3	,	,	PUNCT
cana-5235	228	4	the	the	DET
cana-5235	228	5	growth	growth	NOUN
cana-5235	228	6	rate	rate	NOUN
cana-5235	228	7	follows	follow	VERB
cana-5235	228	8	reverse	reverse	ADJ
cana-5235	228	9	pattern	pattern	NOUN
cana-5235	228	10	for	for	ADP
cana-5235	228	11	increase	increase	NOUN
cana-5235	228	12	in	in	ADP
cana-5235	228	13	the	the	DET
cana-5235	228	14	values	value	NOUN
cana-5235	228	15	of	of	ADP
cana-5235	228	16	𝑑	𝑑	PRON
cana-5235	228	17	against	against	ADP
cana-5235	228	18	the	the	DET
cana-5235	228	19	reynolds	reynolds	PROPN
cana-5235	228	20	number	number	NOUN
cana-5235	228	21	𝑅𝑒1	𝑅𝑒1	NOUN
cana-5235	228	22	.	.	PUNCT
cana-5235	229	1	this	this	PRON
cana-5235	229	2	is	be	AUX
cana-5235	229	3	due	due	ADJ
cana-5235	229	4	to	to	ADP
cana-5235	229	5	the	the	DET
cana-5235	229	6	fact	fact	NOUN
cana-5235	229	7	that	that	SCONJ
cana-5235	229	8	there	there	PRON
cana-5235	229	9	is	be	VERB
cana-5235	229	10	more	more	ADJ
cana-5235	229	11	instability	instability	NOUN
cana-5235	229	12	as	as	ADP
cana-5235	229	13	the	the	DET
cana-5235	229	14	interface	interface	NOUN
cana-5235	229	15	approach	approach	NOUN
cana-5235	229	16	closer	close	ADV
cana-5235	229	17	to	to	ADP
cana-5235	229	18	the	the	DET
cana-5235	229	19	slippery	slippery	ADJ
cana-5235	229	20	bottom	bottom	NOUN
cana-5235	229	21	.	.	PUNCT
cana-5235	230	1	in	in	ADP
cana-5235	230	2	figs.7(a	figs.7(a	ADJ
cana-5235	230	3	)	)	PUNCT
cana-5235	230	4	and	and	CCONJ
cana-5235	230	5	(	(	PUNCT
cana-5235	230	6	b	b	NOUN
cana-5235	230	7	)	)	PUNCT
cana-5235	230	8	,	,	PUNCT
cana-5235	230	9	the	the	DET
cana-5235	230	10	inertial	inertial	ADJ
cana-5235	230	11	effects	effect	NOUN
cana-5235	230	12	on	on	ADP
cana-5235	230	13	the	the	DET
cana-5235	230	14	maximum	maximum	ADJ
cana-5235	230	15	growth	growth	NOUN
cana-5235	230	16	rate	rate	NOUN
cana-5235	230	17	are	be	AUX
cana-5235	230	18	plotted	plot	VERB
cana-5235	230	19	for	for	ADP
cana-5235	230	20	different	different	ADJ
cana-5235	230	21	values	value	NOUN
cana-5235	230	22	of	of	ADP
cana-5235	230	23	shear	shear	ADJ
cana-5235	230	24	parameter	parameter	NOUN
cana-5235	230	25	(	(	PUNCT
cana-5235	230	26	𝜏	𝜏	NOUN
cana-5235	230	27	)	)	PUNCT
cana-5235	230	28	and	and	CCONJ
cana-5235	230	29	slip	slip	VERB
cana-5235	230	30	parameter	parameter	NOUN
cana-5235	230	31	(	(	PUNCT
cana-5235	230	32	𝛽	𝛽	NOUN
cana-5235	230	33	)	)	PUNCT
cana-5235	230	34	,	,	PUNCT
cana-5235	230	35	respectively	respectively	ADV
cana-5235	230	36	.	.	PUNCT
cana-5235	231	1	the	the	DET
cana-5235	231	2	patterns	pattern	NOUN
cana-5235	231	3	are	be	AUX
cana-5235	231	4	similar	similar	ADJ
cana-5235	231	5	to	to	ADP
cana-5235	231	6	fig	fig	NOUN
cana-5235	231	7	.	.	PUNCT
cana-5235	232	1	6	6	NUM
cana-5235	232	2	.	.	X
cana-5235	233	1	as	as	ADP
cana-5235	233	2	the	the	DET
cana-5235	233	3	value	value	NOUN
cana-5235	233	4	of	of	ADP
cana-5235	233	5	𝜏	𝜏	DET
cana-5235	233	6	increases	increase	NOUN
cana-5235	233	7	,	,	PUNCT
cana-5235	233	8	the	the	DET
cana-5235	233	9	instability	instability	NOUN
cana-5235	233	10	of	of	ADP
cana-5235	233	11	two	two	NUM
cana-5235	233	12	-	-	PUNCT
cana-5235	233	13	layer	layer	NOUN
cana-5235	233	14	fluid	fluid	NOUN
cana-5235	233	15	increases	increase	NOUN
cana-5235	233	16	for	for	ADP
cana-5235	233	17	𝑅𝑒1	𝑅𝑒1	NOUN
cana-5235	233	18	<	<	X
cana-5235	233	19	6	6	NUM
cana-5235	233	20	and	and	CCONJ
cana-5235	233	21	it	it	PRON
cana-5235	233	22	follows	follow	VERB
cana-5235	233	23	a	a	DET
cana-5235	233	24	reverse	reverse	ADJ
cana-5235	233	25	pattern	pattern	NOUN
cana-5235	233	26	for	for	ADP
cana-5235	233	27	𝑅𝑒1	𝑅𝑒1	NOUN
cana-5235	233	28	>	>	X
cana-5235	234	1	6	6	NUM
cana-5235	234	2	.	.	PUNCT
cana-5235	235	1	this	this	PRON
cana-5235	235	2	may	may	AUX
cana-5235	235	3	be	be	AUX
cana-5235	235	4	due	due	ADJ
cana-5235	235	5	to	to	ADP
cana-5235	235	6	the	the	DET
cana-5235	235	7	stabilizing	stabilize	VERB
cana-5235	235	8	effect	effect	NOUN
cana-5235	235	9	of	of	ADP
cana-5235	235	10	shear	shear	NOUN
cana-5235	235	11	stress	stress	NOUN
cana-5235	235	12	for	for	ADP
cana-5235	235	13	increase	increase	NOUN
cana-5235	235	14	in	in	ADP
cana-5235	235	15	the	the	DET
cana-5235	235	16	inertial	inertial	ADJ
cana-5235	235	17	force	force	NOUN
cana-5235	235	18	between	between	ADP
cana-5235	235	19	the	the	DET
cana-5235	235	20	layers	layer	NOUN
cana-5235	235	21	of	of	ADP
cana-5235	235	22	fluid	fluid	NOUN
cana-5235	235	23	.	.	PUNCT
cana-5235	236	1	in	in	ADP
cana-5235	236	2	the	the	DET
cana-5235	236	3	case	case	NOUN
cana-5235	236	4	of	of	ADP
cana-5235	236	5	fig	fig	NOUN
cana-5235	236	6	.	.	PUNCT
cana-5235	237	1	7(b	7(b	X
cana-5235	237	2	)	)	PUNCT
cana-5235	237	3	,	,	PUNCT
cana-5235	237	4	the	the	DET
cana-5235	237	5	instability	instability	NOUN
cana-5235	237	6	of	of	ADP
cana-5235	237	7	fluid	fluid	ADJ
cana-5235	237	8	flow	flow	NOUN
cana-5235	237	9	increases	increase	NOUN
cana-5235	237	10	due	due	ADJ
cana-5235	237	11	to	to	PART
cana-5235	237	12	increase	increase	VERB
cana-5235	237	13	in	in	ADP
cana-5235	237	14	the	the	DET
cana-5235	237	15	velocity	velocity	NOUN
cana-5235	237	16	gradient	gradient	NOUN
cana-5235	237	17	at	at	ADP
cana-5235	237	18	the	the	DET
cana-5235	237	19	bottom	bottom	NOUN
cana-5235	237	20	for	for	ADP
cana-5235	237	21	larger	large	ADJ
cana-5235	237	22	values	value	NOUN
cana-5235	237	23	of	of	ADP
cana-5235	237	24	𝛽.	𝛽.	NOUN
cana-5235	237	25	(	(	PUNCT
cana-5235	237	26	a	a	NOUN
cana-5235	237	27	)	)	PUNCT
cana-5235	237	28	(	(	PUNCT
cana-5235	237	29	b	b	X
cana-5235	237	30	)	)	PUNCT
cana-5235	237	31	figure	figure	NOUN
cana-5235	237	32	8	8	NUM
cana-5235	237	33	:	:	PUNCT
cana-5235	237	34	contours	contours	NOUN
cana-5235	237	35	of	of	ADP
cana-5235	237	36	growth	growth	NOUN
cana-5235	237	37	rate	rate	NOUN
cana-5235	237	38	for	for	ADP
cana-5235	237	39	different	different	ADJ
cana-5235	237	40	values	value	NOUN
cana-5235	237	41	of	of	ADP
cana-5235	237	42	(	(	PUNCT
cana-5235	237	43	a	a	X
cana-5235	237	44	)	)	PUNCT
cana-5235	237	45	shear	shear	NOUN
cana-5235	237	46	parameter	parameter	NOUN
cana-5235	237	47	𝝉	𝝉	NOUN
cana-5235	237	48	with	with	ADP
cana-5235	237	49	𝜷	𝜷	NOUN
cana-5235	237	50	=	=	PUNCT
cana-5235	237	51	𝟎.	𝟎.	X
cana-5235	237	52	𝟓	𝟓	NUM
cana-5235	237	53	and	and	CCONJ
cana-5235	237	54	(	(	PUNCT
cana-5235	237	55	b	b	NOUN
cana-5235	237	56	)	)	PUNCT
cana-5235	237	57	slip	slip	NOUN
cana-5235	237	58	parameter	parameter	NOUN
cana-5235	237	59	𝜷	𝜷	NOUN
cana-5235	237	60	with	with	ADP
cana-5235	237	61	𝝉	𝝉	PROPN
cana-5235	237	62	=	=	PUNCT
cana-5235	237	63	𝟎.	𝟎.	NUM
cana-5235	237	64	𝟔	𝟔	NUM
cana-5235	237	65	,	,	PUNCT
cana-5235	237	66	against	against	ADP
cana-5235	237	67	the	the	DET
cana-5235	237	68	reynolds	reynolds	PROPN
cana-5235	237	69	number	number	NOUN
cana-5235	237	70	𝑹𝒆𝟏	𝑹𝒆𝟏	NOUN
cana-5235	237	71	,	,	PUNCT
cana-5235	237	72	and	and	CCONJ
cana-5235	237	73	other	other	ADJ
cana-5235	237	74	parameters	parameter	NOUN
cana-5235	237	75	are	be	AUX
cana-5235	237	76	𝑪𝒂	𝑪𝒂	PROPN
cana-5235	237	77	=	=	PUNCT
cana-5235	237	78	𝟎.	𝟎.	X
cana-5235	237	79	𝟎𝟐	𝟎𝟐	NUM
cana-5235	237	80	,	,	PUNCT
cana-5235	237	81	𝒎	𝒎	X
cana-5235	237	82	=	=	SYM
cana-5235	237	83	𝟎.	𝟎.	X
cana-5235	237	84	𝟖	𝟖	NUM
cana-5235	237	85	,	,	PUNCT
cana-5235	237	86	𝒅	𝒅	X
cana-5235	237	87	=	=	PRON
cana-5235	237	88	𝟎.	𝟎.	ADJ
cana-5235	237	89	𝟓	𝟓	NUM
cana-5235	237	90	,	,	PUNCT
cana-5235	237	91	𝑴𝒂	𝑴𝒂	PROPN
cana-5235	237	92	=	=	SYM
cana-5235	237	93	𝟎.	𝟎.	PUNCT
cana-5235	237	94	𝟏	𝟏	NUM
cana-5235	237	95	and	and	CCONJ
cana-5235	237	96	𝒓	𝒓	PROPN
cana-5235	237	97	=	=	AUX
cana-5235	237	98	𝟎.	𝟎.	PROPN
cana-5235	237	99	𝟔.	𝟔.	NOUN
cana-5235	237	100	figs	fig	NOUN
cana-5235	237	101	.	.	PUNCT
cana-5235	238	1	8(a	8(a	NUM
cana-5235	238	2	)	)	PUNCT
cana-5235	238	3	and	and	CCONJ
cana-5235	238	4	(	(	PUNCT
cana-5235	238	5	b	b	X
cana-5235	238	6	)	)	PUNCT
cana-5235	238	7	depict	depict	VERB
cana-5235	238	8	the	the	DET
cana-5235	238	9	contours	contours	NOUN
cana-5235	238	10	of	of	ADP
cana-5235	238	11	growth	growth	NOUN
cana-5235	238	12	rate	rate	NOUN
cana-5235	238	13	for	for	ADP
cana-5235	238	14	different	different	ADJ
cana-5235	238	15	values	value	NOUN
cana-5235	238	16	of	of	ADP
cana-5235	238	17	shear	shear	ADJ
cana-5235	238	18	parameter	parameter	NOUN
cana-5235	238	19	(	(	PUNCT
cana-5235	238	20	𝜏	𝜏	NOUN
cana-5235	238	21	)	)	PUNCT
cana-5235	238	22	and	and	CCONJ
cana-5235	238	23	slip	slip	VERB
cana-5235	238	24	parameter	parameter	NOUN
cana-5235	238	25	(	(	PUNCT
cana-5235	238	26	𝛽	𝛽	NOUN
cana-5235	238	27	)	)	PUNCT
cana-5235	238	28	as	as	ADP
cana-5235	238	29	a	a	DET
cana-5235	238	30	function	function	NOUN
cana-5235	238	31	of	of	ADP
cana-5235	238	32	𝑅𝑒1	𝑅𝑒1	NOUN
cana-5235	238	33	,	,	PUNCT
cana-5235	238	34	respectively	respectively	ADV
cana-5235	238	35	.	.	PUNCT
cana-5235	239	1	in	in	ADP
cana-5235	239	2	both	both	CCONJ
cana-5235	239	3	the	the	DET
cana-5235	239	4	figures	figure	NOUN
cana-5235	239	5	,	,	PUNCT
cana-5235	239	6	the	the	DET
cana-5235	239	7	stokes	stoke	NOUN
cana-5235	239	8	flow	flow	NOUN
cana-5235	239	9	is	be	AUX
cana-5235	239	10	validated	validate	VERB
cana-5235	239	11	as	as	ADP
cana-5235	239	12	𝑅𝑒1	𝑅𝑒1	NOUN
cana-5235	239	13	→	→	SYM
cana-5235	239	14	0	0	NUM
cana-5235	239	15	,	,	PUNCT
cana-5235	239	16	where	where	SCONJ
cana-5235	239	17	the	the	DET
cana-5235	239	18	flow	flow	NOUN
cana-5235	239	19	is	be	AUX
cana-5235	239	20	completely	completely	ADV
cana-5235	239	21	stabilized	stabilize	VERB
cana-5235	239	22	.	.	PUNCT
cana-5235	240	1	as	as	ADP
cana-5235	240	2	the	the	DET
cana-5235	240	3	𝑅𝑒1	𝑅𝑒1	NOUN
cana-5235	240	4	increases	increase	NOUN
cana-5235	240	5	,	,	PUNCT
cana-5235	240	6	the	the	DET
cana-5235	240	7	growth	growth	NOUN
cana-5235	240	8	rate	rate	NOUN
cana-5235	240	9	increases	increase	NOUN
cana-5235	240	10	and	and	CCONJ
cana-5235	240	11	destabilizes	destabilize	VERB
cana-5235	240	12	the	the	DET
cana-5235	240	13	flow	flow	NOUN
cana-5235	240	14	due	due	ADP
cana-5235	240	15	to	to	ADP
cana-5235	240	16	the	the	DET
cana-5235	240	17	increase	increase	NOUN
cana-5235	240	18	in	in	ADP
cana-5235	240	19	the	the	DET
cana-5235	240	20	inertial	inertial	ADJ
cana-5235	240	21	effect	effect	NOUN
cana-5235	240	22	.	.	PUNCT
cana-5235	241	1	in	in	ADP
cana-5235	241	2	the	the	DET
cana-5235	241	3	case	case	NOUN
cana-5235	241	4	of	of	ADP
cana-5235	241	5	fig	fig	NOUN
cana-5235	241	6	.	.	PUNCT
cana-5235	242	1	8(a	8(a	NUM
cana-5235	242	2	)	)	PUNCT
cana-5235	242	3	,	,	PUNCT
cana-5235	242	4	the	the	DET
cana-5235	242	5	shear	shear	NOUN
cana-5235	242	6	imposed	impose	VERB
cana-5235	242	7	marangoni	marangoni	NOUN
cana-5235	242	8	instability	instability	NOUN
cana-5235	242	9	increases	increase	NOUN
cana-5235	242	10	as	as	ADP
cana-5235	242	11	the	the	DET
cana-5235	242	12	value	value	NOUN
cana-5235	242	13	of	of	ADP
cana-5235	242	14	𝜏	𝜏	DET
cana-5235	242	15	increases	increase	NOUN
cana-5235	242	16	.	.	PUNCT
cana-5235	243	1	however	however	ADV
cana-5235	243	2	,	,	PUNCT
cana-5235	243	3	the	the	DET
cana-5235	243	4	variation	variation	NOUN
cana-5235	243	5	of	of	ADP
cana-5235	243	6	slip	slip	NOUN
cana-5235	243	7	parameters	parameter	NOUN
cana-5235	243	8	(	(	PUNCT
cana-5235	243	9	fig	fig	NOUN
cana-5235	243	10	.	.	PUNCT
cana-5235	243	11	8(b	8(b	NUM
cana-5235	243	12	)	)	PUNCT
cana-5235	243	13	)	)	PUNCT
cana-5235	243	14	destabilizes	destabilize	VERB
cana-5235	243	15	the	the	DET
cana-5235	243	16	fluid	fluid	NOUN
cana-5235	243	17	and	and	CCONJ
cana-5235	243	18	it	it	PRON
cana-5235	243	19	decreases	decrease	VERB
cana-5235	243	20	gradually	gradually	ADV
cana-5235	243	21	for	for	ADP
cana-5235	243	22	the	the	DET
cana-5235	243	23	larger	large	ADJ
cana-5235	243	24	values	value	NOUN
cana-5235	243	25	of	of	ADP
cana-5235	243	26	𝑅𝑒1	𝑅𝑒1	NOUN
cana-5235	243	27	.	.	PUNCT
cana-5235	244	1	in	in	ADP
cana-5235	244	2	figs	fig	NOUN
cana-5235	244	3	.	.	PUNCT
cana-5235	245	1	9(a	9(a	X
cana-5235	245	2	)	)	PUNCT
cana-5235	245	3	,	,	PUNCT
cana-5235	245	4	(	(	PUNCT
cana-5235	245	5	b	b	X
cana-5235	245	6	)	)	PUNCT
cana-5235	245	7	and	and	CCONJ
cana-5235	245	8	(	(	PUNCT
cana-5235	245	9	c	c	X
cana-5235	245	10	)	)	PUNCT
cana-5235	245	11	depict	depict	VERB
cana-5235	245	12	the	the	DET
cana-5235	245	13	marginal	marginal	ADJ
cana-5235	245	14	stability	stability	NOUN
cana-5235	245	15	curve	curve	NOUN
cana-5235	245	16	for	for	ADP
cana-5235	245	17	different	different	ADJ
cana-5235	245	18	values	value	NOUN
cana-5235	245	19	of	of	ADP
cana-5235	245	20	shear	shear	NOUN
cana-5235	245	21	parameter	parameter	NOUN
cana-5235	245	22	,	,	PUNCT
cana-5235	245	23	slip	slip	VERB
cana-5235	245	24	parameter	parameter	NOUN
cana-5235	245	25	and	and	CCONJ
cana-5235	245	26	marangoni	marangoni	ADJ
cana-5235	245	27	number	number	NOUN
cana-5235	245	28	,	,	PUNCT
cana-5235	245	29	respectively	respectively	ADV
cana-5235	245	30	.	.	PUNCT
cana-5235	246	1	communications	communication	NOUN
cana-5235	246	2	on	on	ADP
cana-5235	246	3	applied	apply	VERB
cana-5235	246	4	nonlinear	nonlinear	ADJ
cana-5235	246	5	analysis	analysis	NOUN
cana-5235	246	6	issn	issn	NOUN
cana-5235	246	7	:	:	PUNCT
cana-5235	246	8	1074	1074	NUM
cana-5235	246	9	-	-	PUNCT
cana-5235	246	10	133x	133x	NUM
cana-5235	246	11	vol	vol	VERB
cana-5235	246	12	32	32	NUM
cana-5235	246	13	no	no	NOUN
cana-5235	246	14	.	.	PUNCT
cana-5235	247	1	10s	10	NOUN
cana-5235	247	2	(	(	PUNCT
cana-5235	247	3	2025	2025	NUM
cana-5235	247	4	)	)	PUNCT
cana-5235	247	5	1334	1334	NUM
cana-5235	247	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5235	247	7	(	(	PUNCT
cana-5235	247	8	a	a	NOUN
cana-5235	247	9	)	)	PUNCT
cana-5235	247	10	(	(	PUNCT
cana-5235	247	11	b	b	X
cana-5235	247	12	)	)	PUNCT
cana-5235	247	13	(	(	PUNCT
cana-5235	247	14	c	c	X
cana-5235	247	15	)	)	PUNCT
cana-5235	247	16	figure	figure	NOUN
cana-5235	247	17	9	9	NUM
cana-5235	247	18	:	:	PUNCT
cana-5235	247	19	neutral	neutral	ADJ
cana-5235	247	20	stability	stability	NOUN
cana-5235	247	21	curve	curve	NOUN
cana-5235	247	22	for	for	ADP
cana-5235	247	23	different	different	ADJ
cana-5235	247	24	values	value	NOUN
cana-5235	247	25	of	of	ADP
cana-5235	247	26	(	(	PUNCT
cana-5235	247	27	a	a	X
cana-5235	247	28	)	)	PUNCT
cana-5235	247	29	shear	shear	NOUN
cana-5235	247	30	parameter	parameter	NOUN
cana-5235	247	31	𝝉	𝝉	NOUN
cana-5235	247	32	with	with	ADP
cana-5235	247	33	𝜷	𝜷	NOUN
cana-5235	247	34	=	=	PUNCT
cana-5235	247	35	𝟎.	𝟎.	X
cana-5235	247	36	𝟓	𝟓	NUM
cana-5235	247	37	and	and	CCONJ
cana-5235	247	38	𝑴𝒂	𝑴𝒂	PROPN
cana-5235	247	39	=	=	SYM
cana-5235	247	40	𝟎.	𝟎.	NOUN
cana-5235	247	41	𝟏	𝟏	NUM
cana-5235	247	42	,	,	PUNCT
cana-5235	247	43	(	(	PUNCT
cana-5235	247	44	b	b	X
cana-5235	247	45	)	)	PUNCT
cana-5235	247	46	slip	slip	NOUN
cana-5235	247	47	parameter	parameter	NOUN
cana-5235	247	48	𝜷	𝜷	NOUN
cana-5235	247	49	with	with	ADP
cana-5235	247	50	𝝉	𝝉	X
cana-5235	247	51	=	=	PUNCT
cana-5235	247	52	𝟎.	𝟎.	X
cana-5235	247	53	𝟔	𝟔	NUM
cana-5235	247	54	and	and	CCONJ
cana-5235	247	55	𝑴𝒂	𝑴𝒂	PROPN
cana-5235	247	56	=	=	SYM
cana-5235	247	57	𝟎.	𝟎.	PRON
cana-5235	247	58	𝟏	𝟏	NUM
cana-5235	247	59	and	and	CCONJ
cana-5235	247	60	(	(	PUNCT
cana-5235	247	61	c	c	NOUN
cana-5235	247	62	)	)	PUNCT
cana-5235	247	63	marangoni	marangoni	NOUN
cana-5235	247	64	number	number	NOUN
cana-5235	247	65	𝑴𝒂	𝑴𝒂	PROPN
cana-5235	247	66	with	with	ADP
cana-5235	247	67	𝜷	𝜷	NOUN
cana-5235	247	68	=	=	PUNCT
cana-5235	247	69	𝟎.	𝟎.	X
cana-5235	247	70	𝟓	𝟓	NUM
cana-5235	247	71	and	and	CCONJ
cana-5235	247	72	𝝉	𝝉	X
cana-5235	247	73	=	=	PUNCT
cana-5235	247	74	𝟎.	𝟎.	NUM
cana-5235	247	75	𝟔	𝟔	NUM
cana-5235	247	76	,	,	PUNCT
cana-5235	247	77	and	and	CCONJ
cana-5235	247	78	other	other	ADJ
cana-5235	247	79	parameters	parameter	NOUN
cana-5235	247	80	are	be	AUX
cana-5235	247	81	𝑪𝒂	𝑪𝒂	PROPN
cana-5235	247	82	=	=	PUNCT
cana-5235	247	83	𝟎.	𝟎.	X
cana-5235	247	84	𝟎𝟐	𝟎𝟐	NUM
cana-5235	247	85	,	,	PUNCT
cana-5235	247	86	𝒎	𝒎	X
cana-5235	247	87	=	=	SYM
cana-5235	247	88	𝟎.	𝟎.	X
cana-5235	247	89	𝟖	𝟖	NUM
cana-5235	247	90	,	,	PUNCT
cana-5235	247	91	𝒅	𝒅	X
cana-5235	247	92	=	=	NOUN
cana-5235	247	93	𝟎.	𝟎.	X
cana-5235	247	94	𝟓	𝟓	NUM
cana-5235	247	95	and	and	CCONJ
cana-5235	247	96	𝒓	𝒓	PROPN
cana-5235	247	97	=	=	PUNCT
cana-5235	247	98	𝟎.	𝟎.	PROPN
cana-5235	247	99	𝟔.	𝟔.	AUX
cana-5235	247	100	in	in	ADP
cana-5235	247	101	all	all	DET
cana-5235	247	102	figures	figure	NOUN
cana-5235	247	103	,	,	PUNCT
cana-5235	247	104	it	it	PRON
cana-5235	247	105	is	be	AUX
cana-5235	247	106	noticed	notice	VERB
cana-5235	247	107	that	that	SCONJ
cana-5235	247	108	the	the	DET
cana-5235	247	109	right	right	ADJ
cana-5235	247	110	hand	hand	NOUN
cana-5235	247	111	side	side	NOUN
cana-5235	247	112	of	of	ADP
cana-5235	247	113	each	each	DET
cana-5235	247	114	curve	curve	NOUN
cana-5235	247	115	is	be	AUX
cana-5235	247	116	known	know	VERB
cana-5235	247	117	as	as	ADP
cana-5235	247	118	unstable	unstable	ADJ
cana-5235	247	119	mode	mode	NOUN
cana-5235	247	120	bandwidth	bandwidth	NOUN
cana-5235	247	121	,	,	PUNCT
cana-5235	247	122	while	while	SCONJ
cana-5235	247	123	the	the	DET
cana-5235	247	124	left	left	ADJ
cana-5235	247	125	hand	hand	NOUN
cana-5235	247	126	side	side	NOUN
cana-5235	247	127	is	be	AUX
cana-5235	247	128	known	know	VERB
cana-5235	247	129	as	as	ADP
cana-5235	247	130	stable	stable	ADJ
cana-5235	247	131	mode	mode	NOUN
cana-5235	247	132	bandwidth	bandwidth	NOUN
cana-5235	247	133	.	.	PUNCT
cana-5235	248	1	the	the	DET
cana-5235	248	2	unstable	unstable	ADJ
cana-5235	248	3	mode	mode	NOUN
cana-5235	248	4	bandwidth	bandwidth	NOUN
cana-5235	248	5	known	know	VERB
cana-5235	248	6	as	as	ADP
cana-5235	248	7	shear	shear	NOUN
cana-5235	248	8	mode	mode	NOUN
cana-5235	248	9	,	,	PUNCT
cana-5235	248	10	which	which	PRON
cana-5235	248	11	increases	increase	VERB
cana-5235	248	12	for	for	ADP
cana-5235	248	13	increase	increase	NOUN
cana-5235	248	14	in	in	ADP
cana-5235	248	15	the	the	DET
cana-5235	248	16	values	value	NOUN
cana-5235	248	17	of	of	ADP
cana-5235	248	18	shear	shear	NOUN
cana-5235	248	19	parameters	parameter	NOUN
cana-5235	248	20	and	and	CCONJ
cana-5235	248	21	slip	slip	VERB
cana-5235	248	22	parameters	parameter	NOUN
cana-5235	248	23	as	as	ADP
cana-5235	248	24	in	in	ADP
cana-5235	248	25	figs	fig	NOUN
cana-5235	248	26	.	.	PUNCT
cana-5235	249	1	9(a	9(a	X
cana-5235	249	2	)	)	PUNCT
cana-5235	249	3	,	,	PUNCT
cana-5235	249	4	(	(	PUNCT
cana-5235	249	5	b	b	X
cana-5235	249	6	)	)	PUNCT
cana-5235	249	7	and	and	CCONJ
cana-5235	249	8	(	(	PUNCT
cana-5235	249	9	c	c	NOUN
cana-5235	249	10	)	)	PUNCT
cana-5235	249	11	,	,	PUNCT
cana-5235	249	12	respectively	respectively	ADV
cana-5235	249	13	.	.	PUNCT
cana-5235	250	1	further	far	ADV
cana-5235	250	2	,	,	PUNCT
cana-5235	250	3	the	the	DET
cana-5235	250	4	critical	critical	ADJ
cana-5235	250	5	reynolds	reynold	NOUN
cana-5235	250	6	number	number	NOUN
cana-5235	250	7	shift	shift	NOUN
cana-5235	250	8	towards	towards	ADP
cana-5235	250	9	left	leave	VERB
cana-5235	250	10	for	for	ADP
cana-5235	250	11	larger	large	ADJ
cana-5235	250	12	values	value	NOUN
cana-5235	250	13	of	of	ADP
cana-5235	250	14	𝜏	𝜏	NOUN
cana-5235	250	15	and	and	CCONJ
cana-5235	250	16	𝛽.	𝛽.	NOUN
cana-5235	250	17	this	this	DET
cana-5235	250	18	increases	increase	VERB
cana-5235	250	19	the	the	DET
cana-5235	250	20	unstable	unstable	ADJ
cana-5235	250	21	shear	shear	NOUN
cana-5235	250	22	mode	mode	NOUN
cana-5235	250	23	,	,	PUNCT
cana-5235	250	24	which	which	PRON
cana-5235	250	25	destabilizes	destabilize	VERB
cana-5235	250	26	the	the	DET
cana-5235	250	27	fluid	fluid	ADJ
cana-5235	250	28	flow	flow	NOUN
cana-5235	250	29	.	.	PUNCT
cana-5235	251	1	on	on	ADP
cana-5235	251	2	the	the	DET
cana-5235	251	3	other	other	ADJ
cana-5235	251	4	hand	hand	NOUN
cana-5235	251	5	,	,	PUNCT
cana-5235	251	6	the	the	DET
cana-5235	251	7	unstable	unstable	ADJ
cana-5235	251	8	mode	mode	NOUN
cana-5235	251	9	bandwidth	bandwidth	NOUN
cana-5235	251	10	decreases	decrease	VERB
cana-5235	251	11	for	for	ADP
cana-5235	251	12	increase	increase	NOUN
cana-5235	251	13	in	in	ADP
cana-5235	251	14	the	the	DET
cana-5235	251	15	values	value	NOUN
cana-5235	251	16	of	of	ADP
cana-5235	251	17	𝑀𝑎.	𝑀𝑎.	PROPN
cana-5235	251	18	as	as	ADP
cana-5235	251	19	a	a	DET
cana-5235	251	20	consequence	consequence	NOUN
cana-5235	251	21	,	,	PUNCT
cana-5235	251	22	the	the	DET
cana-5235	251	23	presence	presence	NOUN
cana-5235	251	24	of	of	ADP
cana-5235	251	25	insoluble	insoluble	ADJ
cana-5235	251	26	surfactant	surfactant	NOUN
cana-5235	251	27	stabilizes	stabilize	VERB
cana-5235	251	28	the	the	DET
cana-5235	251	29	fluid	fluid	ADJ
cana-5235	251	30	flow	flow	NOUN
cana-5235	251	31	with	with	ADP
cana-5235	251	32	increase	increase	NOUN
cana-5235	251	33	in	in	ADP
cana-5235	251	34	its	its	PRON
cana-5235	251	35	concentration	concentration	NOUN
cana-5235	251	36	,	,	PUNCT
cana-5235	251	37	which	which	PRON
cana-5235	251	38	is	be	AUX
cana-5235	251	39	evident	evident	ADJ
cana-5235	251	40	from	from	ADP
cana-5235	251	41	fig	fig	NOUN
cana-5235	251	42	.	.	PUNCT
cana-5235	252	1	9(c	9(c	NUM
cana-5235	252	2	)	)	PUNCT
cana-5235	252	3	.	.	PUNCT
cana-5235	253	1	hence	hence	ADV
cana-5235	253	2	,	,	PUNCT
cana-5235	253	3	the	the	DET
cana-5235	253	4	insoluble	insoluble	ADJ
cana-5235	253	5	surfactant	surfactant	NOUN
cana-5235	253	6	present	present	NOUN
cana-5235	253	7	on	on	ADP
cana-5235	253	8	the	the	DET
cana-5235	253	9	heterogeneous	heterogeneous	ADJ
cana-5235	253	10	fluid	fluid	NOUN
cana-5235	253	11	,	,	PUNCT
cana-5235	253	12	stabilizes	stabilize	VERB
cana-5235	253	13	the	the	DET
cana-5235	253	14	uniform	uniform	ADJ
cana-5235	253	15	external	external	ADJ
cana-5235	253	16	shear	shear	NOUN
cana-5235	253	17	-	-	PUNCT
cana-5235	253	18	imposed	impose	VERB
cana-5235	253	19	flow	flow	NOUN
cana-5235	253	20	.	.	PUNCT
cana-5235	254	1	4	4	NUM
cana-5235	254	2	conclusion	conclusion	NOUN
cana-5235	254	3	the	the	DET
cana-5235	254	4	present	present	ADJ
cana-5235	254	5	study	study	NOUN
cana-5235	254	6	deals	deal	NOUN
cana-5235	254	7	with	with	ADP
cana-5235	254	8	the	the	DET
cana-5235	254	9	effect	effect	NOUN
cana-5235	254	10	of	of	ADP
cana-5235	254	11	insoluble	insoluble	ADJ
cana-5235	254	12	surfactant	surfactant	NOUN
cana-5235	254	13	on	on	ADP
cana-5235	254	14	the	the	DET
cana-5235	254	15	shear	shear	NOUN
cana-5235	254	16	-	-	PUNCT
cana-5235	254	17	imposed	impose	VERB
cana-5235	254	18	fluid	fluid	NOUN
cana-5235	254	19	flow	flow	NOUN
cana-5235	254	20	having	have	VERB
cana-5235	254	21	the	the	DET
cana-5235	254	22	slippery	slippery	ADJ
cana-5235	254	23	bottom	bottom	NOUN
cana-5235	254	24	using	use	VERB
cana-5235	254	25	normal	normal	ADJ
cana-5235	254	26	mode	mode	NOUN
cana-5235	254	27	analysis	analysis	NOUN
cana-5235	254	28	.	.	PUNCT
cana-5235	255	1	the	the	DET
cana-5235	255	2	resultant	resultant	PROPN
cana-5235	255	3	orr	orr	PROPN
cana-5235	255	4	-	-	PUNCT
cana-5235	255	5	sommerfeld	sommerfeld	ADJ
cana-5235	255	6	system	system	NOUN
cana-5235	255	7	is	be	AUX
cana-5235	255	8	derived	derive	VERB
cana-5235	255	9	and	and	CCONJ
cana-5235	255	10	solved	solve	VERB
cana-5235	255	11	by	by	ADP
cana-5235	255	12	using	use	VERB
cana-5235	255	13	the	the	DET
cana-5235	255	14	spectral	spectral	ADJ
cana-5235	255	15	collocation	collocation	NOUN
cana-5235	255	16	method	method	NOUN
cana-5235	255	17	,	,	PUNCT
cana-5235	255	18	where	where	SCONJ
cana-5235	255	19	the	the	DET
cana-5235	255	20	domain	domain	NOUN
cana-5235	255	21	is	be	AUX
cana-5235	255	22	discritized	discritize	VERB
cana-5235	255	23	by	by	ADP
cana-5235	255	24	chebyshev	chebyshev	NOUN
cana-5235	255	25	collocation	collocation	NOUN
cana-5235	255	26	points	point	NOUN
cana-5235	255	27	.	.	PUNCT
cana-5235	256	1	the	the	DET
cana-5235	256	2	effect	effect	NOUN
cana-5235	256	3	of	of	ADP
cana-5235	256	4	surfactant	surfactant	ADJ
cana-5235	256	5	concentration	concentration	NOUN
cana-5235	256	6	,	,	PUNCT
cana-5235	256	7	shear	shear	NOUN
cana-5235	256	8	and	and	CCONJ
cana-5235	256	9	slip	slip	VERB
cana-5235	256	10	parameters	parameter	NOUN
cana-5235	256	11	on	on	ADP
cana-5235	256	12	the	the	DET
cana-5235	256	13	spatiotemporal	spatiotemporal	ADJ
cana-5235	256	14	growth	growth	NOUN
cana-5235	256	15	rate	rate	NOUN
cana-5235	256	16	are	be	AUX
cana-5235	256	17	analyzed	analyze	VERB
cana-5235	256	18	for	for	ADP
cana-5235	256	19	smaller	small	ADJ
cana-5235	256	20	reynolds	reynold	NOUN
cana-5235	256	21	number	number	NOUN
cana-5235	256	22	.	.	PUNCT
cana-5235	257	1	the	the	DET
cana-5235	257	2	dispersion	dispersion	NOUN
cana-5235	257	3	curves	curve	NOUN
cana-5235	257	4	shows	show	VERB
cana-5235	257	5	that	that	SCONJ
cana-5235	257	6	the	the	DET
cana-5235	257	7	communications	communication	NOUN
cana-5235	257	8	on	on	ADP
cana-5235	257	9	applied	apply	VERB
cana-5235	257	10	nonlinear	nonlinear	ADJ
cana-5235	257	11	analysis	analysis	NOUN
cana-5235	257	12	issn	issn	NOUN
cana-5235	257	13	:	:	PUNCT
cana-5235	257	14	1074	1074	NUM
cana-5235	257	15	-	-	PUNCT
cana-5235	257	16	133x	133x	NUM
cana-5235	257	17	vol	vol	VERB
cana-5235	257	18	32	32	NUM
cana-5235	257	19	no	no	NOUN
cana-5235	257	20	.	.	PUNCT
cana-5235	258	1	10s	10	NOUN
cana-5235	258	2	(	(	PUNCT
cana-5235	258	3	2025	2025	NUM
cana-5235	258	4	)	)	PUNCT
cana-5235	258	5	1335	1335	NUM
cana-5235	258	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5235	258	7	instability	instability	NOUN
cana-5235	258	8	enhances	enhance	VERB
cana-5235	258	9	for	for	ADP
cana-5235	258	10	the	the	DET
cana-5235	258	11	larger	large	ADJ
cana-5235	258	12	values	value	NOUN
cana-5235	258	13	of	of	ADP
cana-5235	258	14	shear	shear	NOUN
cana-5235	258	15	parameters	parameter	NOUN
cana-5235	258	16	,	,	PUNCT
cana-5235	258	17	whereas	whereas	SCONJ
cana-5235	258	18	it	it	PRON
cana-5235	258	19	decreases	decrease	VERB
cana-5235	258	20	for	for	ADP
cana-5235	258	21	the	the	DET
cana-5235	258	22	larger	large	ADJ
cana-5235	258	23	surfactant	surfactant	ADJ
cana-5235	258	24	concentration	concentration	NOUN
cana-5235	258	25	.	.	PUNCT
cana-5235	259	1	also	also	ADV
cana-5235	259	2	,	,	PUNCT
cana-5235	259	3	the	the	DET
cana-5235	259	4	instability	instability	NOUN
cana-5235	259	5	increases	increase	VERB
cana-5235	259	6	when	when	SCONJ
cana-5235	259	7	the	the	DET
cana-5235	259	8	interface	interface	NOUN
cana-5235	259	9	is	be	AUX
cana-5235	259	10	closer	close	ADJ
cana-5235	259	11	to	to	ADP
cana-5235	259	12	the	the	DET
cana-5235	259	13	slippery	slippery	ADJ
cana-5235	259	14	bottom	bottom	NOUN
cana-5235	259	15	and	and	CCONJ
cana-5235	259	16	the	the	DET
cana-5235	259	17	presence	presence	NOUN
cana-5235	259	18	of	of	ADP
cana-5235	259	19	high	high	ADJ
cana-5235	259	20	viscous	viscous	ADJ
cana-5235	259	21	fluid	fluid	NOUN
cana-5235	259	22	on	on	ADP
cana-5235	259	23	the	the	DET
cana-5235	259	24	upper	upper	ADJ
cana-5235	259	25	layer	layer	NOUN
cana-5235	259	26	.	.	PUNCT
cana-5235	260	1	further	far	ADV
cana-5235	260	2	,	,	PUNCT
cana-5235	260	3	the	the	DET
cana-5235	260	4	shear	shear	NOUN
cana-5235	260	5	-	-	PUNCT
cana-5235	260	6	imposed	impose	VERB
cana-5235	260	7	instability	instability	NOUN
cana-5235	260	8	decreases	decrease	VERB
cana-5235	260	9	as	as	ADP
cana-5235	260	10	a	a	DET
cana-5235	260	11	consequence	consequence	NOUN
cana-5235	260	12	of	of	ADP
cana-5235	260	13	insoluble	insoluble	ADJ
cana-5235	260	14	surfactant	surfactant	NOUN
cana-5235	260	15	.	.	PUNCT
cana-5235	261	1	it	it	PRON
cana-5235	261	2	is	be	AUX
cana-5235	261	3	concluded	conclude	VERB
cana-5235	261	4	that	that	SCONJ
cana-5235	261	5	the	the	DET
cana-5235	261	6	presence	presence	NOUN
cana-5235	261	7	of	of	ADP
cana-5235	261	8	surfactant	surfactant	NOUN
cana-5235	261	9	stabilizes	stabilize	VERB
cana-5235	261	10	the	the	DET
cana-5235	261	11	both	both	CCONJ
cana-5235	261	12	the	the	DET
cana-5235	261	13	gravity	gravity	NOUN
cana-5235	261	14	-	-	PUNCT
cana-5235	261	15	driven	drive	VERB
cana-5235	261	16	and	and	CCONJ
cana-5235	261	17	shear	shear	NOUN
cana-5235	261	18	-	-	PUNCT
cana-5235	261	19	driven	drive	VERB
cana-5235	261	20	heterogeneous	heterogeneous	ADJ
cana-5235	261	21	flows	flow	NOUN
cana-5235	261	22	.	.	PUNCT
cana-5235	262	1	this	this	DET
cana-5235	262	2	study	study	NOUN
cana-5235	262	3	can	can	AUX
cana-5235	262	4	be	be	AUX
cana-5235	262	5	helpful	helpful	ADJ
cana-5235	262	6	in	in	ADP
cana-5235	262	7	understanding	understand	VERB
cana-5235	262	8	the	the	DET
cana-5235	262	9	instabilities	instability	NOUN
cana-5235	262	10	occurred	occur	VERB
cana-5235	262	11	due	due	ADP
cana-5235	262	12	to	to	ADP
cana-5235	262	13	the	the	DET
cana-5235	262	14	shear	shear	NOUN
cana-5235	262	15	imposed	impose	VERB
cana-5235	262	16	on	on	ADP
cana-5235	262	17	the	the	DET
cana-5235	262	18	respiratory	respiratory	ADJ
cana-5235	262	19	airways	airway	NOUN
cana-5235	262	20	.	.	PUNCT
cana-5235	263	1	references	reference	NOUN
cana-5235	263	2	[	[	X
cana-5235	263	3	1	1	NUM
cana-5235	263	4	]	]	PUNCT
cana-5235	263	5	a.	a.	NOUN
cana-5235	263	6	anjalaiah	anjalaiah	PROPN
cana-5235	263	7	,	,	PUNCT
cana-5235	263	8	r.	r.	PROPN
cana-5235	263	9	usha	usha	PROPN
cana-5235	263	10	,	,	PUNCT
cana-5235	263	11	s.	s.	PROPN
cana-5235	263	12	millet	millet	PROPN
cana-5235	263	13	,	,	PUNCT
cana-5235	263	14	thin	thin	ADJ
cana-5235	263	15	film	film	NOUN
cana-5235	263	16	flow	flow	VERB
cana-5235	263	17	down	down	ADP
cana-5235	263	18	a	a	DET
cana-5235	263	19	porous	porous	ADJ
cana-5235	263	20	substrate	substrate	NOUN
cana-5235	263	21	in	in	ADP
cana-5235	263	22	the	the	DET
cana-5235	263	23	presence	presence	NOUN
cana-5235	263	24	of	of	ADP
cana-5235	263	25	an	an	DET
cana-5235	263	26	insoluble	insoluble	ADJ
cana-5235	263	27	surfactant	surfactant	NOUN
cana-5235	263	28	:	:	PUNCT
cana-5235	263	29	stability	stability	NOUN
cana-5235	263	30	analysis	analysis	NOUN
cana-5235	263	31	,	,	PUNCT
cana-5235	263	32	phys	phy	NOUN
cana-5235	263	33	.	.	PUNCT
cana-5235	264	1	fluids	fluid	NOUN
cana-5235	264	2	.	.	PUNCT
cana-5235	264	3	,	,	PUNCT
cana-5235	264	4	25.2(2013	25.2(2013	NUM
cana-5235	264	5	)	)	PUNCT
cana-5235	264	6	.	.	PUNCT
cana-5235	265	1	[	[	X
cana-5235	265	2	2	2	NUM
cana-5235	265	3	]	]	X
cana-5235	265	4	f.a	f.a	PROPN
cana-5235	265	5	.	.	PROPN
cana-5235	265	6	bhat	bhat	PROPN
cana-5235	265	7	,	,	PUNCT
cana-5235	265	8	a.	a.	PROPN
cana-5235	265	9	samanta	samanta	PROPN
cana-5235	265	10	,	,	PUNCT
cana-5235	265	11	linear	linear	VERB
cana-5235	265	12	stability	stability	NOUN
cana-5235	265	13	analysis	analysis	NOUN
cana-5235	265	14	of	of	ADP
cana-5235	265	15	a	a	DET
cana-5235	265	16	surfactant	surfactant	NOUN
cana-5235	265	17	-	-	PUNCT
cana-5235	265	18	laden	laden	NOUN
cana-5235	265	19	shear	shear	NOUN
cana-5235	265	20	-	-	PUNCT
cana-5235	265	21	imposed	impose	VERB
cana-5235	265	22	falling	fall	VERB
cana-5235	265	23	film	film	NOUN
cana-5235	265	24	,	,	PUNCT
cana-5235	265	25	phys	phy	NOUN
cana-5235	265	26	.	.	PUNCT
cana-5235	266	1	fluids	fluid	NOUN
cana-5235	266	2	.	.	PROPN
cana-5235	266	3	,	,	PUNCT
cana-5235	266	4	31.5(2019	31.5(2019	NUM
cana-5235	266	5	)	)	PUNCT
cana-5235	266	6	.	.	PUNCT
cana-5235	267	1	[	[	X
cana-5235	267	2	3	3	X
cana-5235	267	3	]	]	X
cana-5235	267	4	f.a	f.a	PROPN
cana-5235	267	5	.	.	PROPN
cana-5235	267	6	bhat	bhat	PROPN
cana-5235	267	7	,	,	PUNCT
cana-5235	267	8	a.	a.	PROPN
cana-5235	267	9	samanta	samanta	PROPN
cana-5235	267	10	,	,	PUNCT
cana-5235	267	11	linear	linear	ADJ
cana-5235	267	12	stability	stability	NOUN
cana-5235	267	13	for	for	ADP
cana-5235	267	14	surfactant	surfactant	NOUN
cana-5235	267	15	-	-	PUNCT
cana-5235	267	16	laden	laden	ADJ
cana-5235	267	17	two	two	NUM
cana-5235	267	18	-	-	PUNCT
cana-5235	267	19	layer	layer	NOUN
cana-5235	267	20	film	film	NOUN
cana-5235	267	21	flows	flow	VERB
cana-5235	267	22	down	down	ADP
cana-5235	267	23	a	a	DET
cana-5235	267	24	slippery	slippery	ADJ
cana-5235	267	25	inclined	inclined	ADJ
cana-5235	267	26	plane	plane	NOUN
cana-5235	267	27	,	,	PUNCT
cana-5235	267	28	chem	chem	NOUN
cana-5235	267	29	.	.	PUNCT
cana-5235	268	1	eng	eng	PROPN
cana-5235	268	2	.	.	PUNCT
cana-5235	269	1	sci	sci	PROPN
cana-5235	269	2	.	.	PROPN
cana-5235	269	3	,	,	PUNCT
cana-5235	269	4	220(2020	220(2020	NUM
cana-5235	269	5	)	)	PUNCT
cana-5235	269	6	,	,	PUNCT
cana-5235	269	7	115611	115611	NUM
cana-5235	269	8	.	.	PUNCT
cana-5235	270	1	[	[	X
cana-5235	270	2	4	4	NUM
cana-5235	270	3	]	]	X
cana-5235	270	4	m.g	m.g	PROPN
cana-5235	270	5	.	.	PROPN
cana-5235	270	6	blyth	blyth	PROPN
cana-5235	270	7	,	,	PUNCT
cana-5235	270	8	c.	c.	PROPN
cana-5235	270	9	pozrikidis	pozrikidis	PROPN
cana-5235	270	10	,	,	PUNCT
cana-5235	270	11	effect	effect	NOUN
cana-5235	270	12	of	of	ADP
cana-5235	270	13	surfactant	surfactant	NOUN
cana-5235	270	14	on	on	ADP
cana-5235	270	15	the	the	DET
cana-5235	270	16	stability	stability	NOUN
cana-5235	270	17	of	of	ADP
cana-5235	270	18	film	film	NOUN
cana-5235	270	19	flow	flow	VERB
cana-5235	270	20	down	down	ADP
cana-5235	270	21	an	an	DET
cana-5235	270	22	inclined	inclined	ADJ
cana-5235	270	23	plane	plane	NOUN
cana-5235	270	24	,	,	PUNCT
cana-5235	270	25	j.	j.	PROPN
cana-5235	270	26	fluid	fluid	PROPN
cana-5235	270	27	.	.	PUNCT
cana-5235	270	28	mech	mech	PROPN
cana-5235	270	29	.	.	PROPN
cana-5235	270	30	,	,	PUNCT
cana-5235	270	31	521(2004	521(2004	NOUN
cana-5235	270	32	)	)	PUNCT
cana-5235	270	33	,	,	PUNCT
cana-5235	270	34	241	241	NUM
cana-5235	270	35	-	-	SYM
cana-5235	270	36	250	250	NUM
cana-5235	270	37	.	.	PUNCT
cana-5235	271	1	[	[	X
cana-5235	271	2	5	5	NUM
cana-5235	271	3	]	]	SYM
cana-5235	271	4	k.p	k.p	PROPN
cana-5235	271	5	.	.	PROPN
cana-5235	271	6	chen	chen	PROPN
cana-5235	271	7	,	,	PUNCT
cana-5235	271	8	wave	wave	VERB
cana-5235	271	9	formation	formation	NOUN
cana-5235	271	10	in	in	ADP
cana-5235	271	11	the	the	DET
cana-5235	271	12	gravity	gravity	NOUN
cana-5235	271	13	driven	drive	VERB
cana-5235	271	14	lower	low	ADJ
cana-5235	271	15	reynolds	reynold	NOUN
cana-5235	271	16	number	number	NOUN
cana-5235	271	17	flow	flow	NOUN
cana-5235	271	18	of	of	ADP
cana-5235	271	19	two	two	NUM
cana-5235	271	20	liquid	liquid	ADJ
cana-5235	271	21	films	film	NOUN
cana-5235	271	22	down	down	ADP
cana-5235	271	23	an	an	DET
cana-5235	271	24	inclined	inclined	ADJ
cana-5235	271	25	plane	plane	NOUN
cana-5235	271	26	,	,	PUNCT
cana-5235	271	27	phys	phy	NOUN
cana-5235	271	28	.	.	PUNCT
cana-5235	272	1	fluids	fluid	NOUN
cana-5235	272	2	a	a	DET
cana-5235	272	3	:	:	PUNCT
cana-5235	272	4	fluid	fluid	ADJ
cana-5235	272	5	dyn	dyn	NOUN
cana-5235	272	6	.	.	PUNCT
cana-5235	272	7	,	,	PUNCT
cana-5235	272	8	5.12(1993	5.12(1993	NUM
cana-5235	272	9	)	)	PUNCT
cana-5235	272	10	,	,	PUNCT
cana-5235	272	11	3038	3038	NUM
cana-5235	272	12	-	-	SYM
cana-5235	272	13	3048	3048	NUM
cana-5235	272	14	.	.	PUNCT
cana-5235	273	1	[	[	X
cana-5235	273	2	6	6	NUM
cana-5235	273	3	]	]	X
cana-5235	273	4	p.g	p.g	PROPN
cana-5235	273	5	.	.	PROPN
cana-5235	273	6	drazin	drazin	PROPN
cana-5235	273	7	,	,	PUNCT
cana-5235	273	8	introduction	introduction	NOUN
cana-5235	273	9	to	to	ADP
cana-5235	273	10	hydrodynamic	hydrodynamic	ADJ
cana-5235	273	11	stability	stability	NOUN
cana-5235	273	12	,	,	PUNCT
cana-5235	273	13	cambridge	cambridge	PROPN
cana-5235	273	14	university	university	PROPN
cana-5235	273	15	press	press	NOUN
cana-5235	273	16	,	,	PUNCT
cana-5235	273	17	32	32	NUM
cana-5235	273	18	(	(	PUNCT
cana-5235	273	19	2002	2002	NUM
cana-5235	273	20	)	)	PUNCT
cana-5235	273	21	.	.	PUNCT
cana-5235	274	1	[	[	X
cana-5235	274	2	7	7	X
cana-5235	274	3	]	]	X
cana-5235	274	4	f.f	f.f	PROPN
cana-5235	274	5	.	.	PROPN
cana-5235	274	6	espinosa	espinosa	PROPN
cana-5235	274	7	,	,	PUNCT
cana-5235	274	8	r.d	r.d	PROPN
cana-5235	274	9	.	.	PROPN
cana-5235	274	10	kamm	kamm	PROPN
cana-5235	274	11	,	,	PUNCT
cana-5235	274	12	bolus	bolus	ADJ
cana-5235	274	13	dispersal	dispersal	NOUN
cana-5235	274	14	through	through	ADP
cana-5235	274	15	the	the	DET
cana-5235	274	16	lungs	lung	NOUN
cana-5235	274	17	in	in	ADP
cana-5235	274	18	surfactant	surfactant	ADJ
cana-5235	274	19	replacement	replacement	NOUN
cana-5235	274	20	therapy	therapy	NOUN
cana-5235	274	21	,	,	PUNCT
cana-5235	274	22	j.	j.	PROPN
cana-5235	274	23	appl	appl	PROPN
cana-5235	274	24	.	.	PUNCT
cana-5235	275	1	phys	phy	NOUN
cana-5235	275	2	.	.	PUNCT
cana-5235	275	3	,	,	PUNCT
cana-5235	275	4	86.1(1999	86.1(1999	NUM
cana-5235	275	5	)	)	PUNCT
cana-5235	275	6	,	,	PUNCT
cana-5235	275	7	391	391	NUM
cana-5235	275	8	-	-	SYM
cana-5235	275	9	410	410	NUM
cana-5235	275	10	.	.	PUNCT
cana-5235	276	1	[	[	X
cana-5235	276	2	8	8	NUM
cana-5235	276	3	]	]	X
cana-5235	276	4	a.e	a.e	PROPN
cana-5235	276	5	.	.	PROPN
cana-5235	276	6	hosoi	hosoi	PROPN
cana-5235	276	7	,	,	PUNCT
cana-5235	276	8	l.	l.	PROPN
cana-5235	276	9	mahadevan	mahadevan	PROPN
cana-5235	276	10	,	,	PUNCT
cana-5235	276	11	peeling	peel	VERB
cana-5235	276	12	,	,	PUNCT
cana-5235	276	13	healing	healing	NOUN
cana-5235	276	14	,	,	PUNCT
cana-5235	276	15	and	and	CCONJ
cana-5235	276	16	bursting	burst	VERB
cana-5235	276	17	in	in	ADP
cana-5235	276	18	a	a	DET
cana-5235	276	19	lubricated	lubricated	ADJ
cana-5235	276	20	elastic	elastic	ADJ
cana-5235	276	21	sheet	sheet	NOUN
cana-5235	276	22	,	,	PUNCT
cana-5235	276	23	physical	physical	ADJ
cana-5235	276	24	review	review	NOUN
cana-5235	276	25	letters	letter	NOUN
cana-5235	276	26	,	,	PUNCT
cana-5235	276	27	93.13(2004	93.13(2004	NUM
cana-5235	276	28	)	)	PUNCT
cana-5235	276	29	,	,	PUNCT
cana-5235	276	30	137802	137802	NUM
cana-5235	276	31	.	.	PUNCT
cana-5235	277	1	[	[	X
cana-5235	277	2	9	9	NUM
cana-5235	277	3	]	]	X
cana-5235	277	4	m.m	m.m	PROPN
cana-5235	277	5	.	.	PROPN
cana-5235	277	6	hossain	hossain	PROPN
cana-5235	277	7	,	,	PUNCT
cana-5235	277	8	s.	s.	PROPN
cana-5235	277	9	ghosh	ghosh	PROPN
cana-5235	277	10	,	,	PUNCT
cana-5235	277	11	h.	h.	PROPN
cana-5235	277	12	behera	behera	PROPN
cana-5235	277	13	,	,	PUNCT
cana-5235	277	14	linear	linear	ADJ
cana-5235	277	15	instability	instability	NOUN
cana-5235	277	16	of	of	ADP
cana-5235	277	17	a	a	DET
cana-5235	277	18	surfactant	surfactant	NOUN
cana-5235	277	19	-	-	PUNCT
cana-5235	277	20	laden	laden	NOUN
cana-5235	277	21	shear	shear	NOUN
cana-5235	277	22	imposed	impose	VERB
cana-5235	277	23	falling	fall	VERB
cana-5235	277	24	film	film	NOUN
cana-5235	277	25	over	over	ADP
cana-5235	277	26	an	an	DET
cana-5235	277	27	inclined	inclined	ADJ
cana-5235	277	28	porous	porous	ADJ
cana-5235	277	29	bed	bed	NOUN
cana-5235	277	30	,	,	PUNCT
cana-5235	277	31	physics	physics	NOUN
cana-5235	277	32	of	of	ADP
cana-5235	277	33	fluids	fluid	NOUN
cana-5235	277	34	.	.	PUNCT
cana-5235	277	35	,	,	PUNCT
cana-5235	277	36	34.8	34.8	NUM
cana-5235	277	37	(	(	PUNCT
cana-5235	277	38	2022	2022	NUM
cana-5235	277	39	)	)	PUNCT
cana-5235	277	40	.	.	PUNCT
cana-5235	278	1	[	[	X
cana-5235	278	2	10	10	NUM
cana-5235	278	3	]	]	PUNCT
cana-5235	278	4	m.	m.	PROPN
cana-5235	278	5	sani	sani	PROPN
cana-5235	278	6	,	,	PUNCT
cana-5235	278	7	sa	sa	PROPN
cana-5235	278	8	selvan	selvan	PROPN
cana-5235	278	9	,	,	PUNCT
cana-5235	278	10	s.	s.	PROPN
cana-5235	278	11	ghosh	ghosh	PROPN
cana-5235	278	12	,	,	PUNCT
cana-5235	278	13	h.	h.	PROPN
cana-5235	278	14	behera	behera	PROPN
cana-5235	278	15	effect	effect	NOUN
cana-5235	278	16	of	of	ADP
cana-5235	278	17	imposed	impose	VERB
cana-5235	278	18	shear	shear	NOUN
cana-5235	278	19	on	on	ADP
cana-5235	278	20	the	the	DET
cana-5235	278	21	dynamics	dynamic	NOUN
cana-5235	278	22	of	of	ADP
cana-5235	278	23	a	a	DET
cana-5235	278	24	contaminated	contaminate	VERB
cana-5235	278	25	two	two	NUM
cana-5235	278	26	-	-	PUNCT
cana-5235	278	27	layer	layer	NOUN
cana-5235	278	28	film	film	NOUN
cana-5235	278	29	flow	flow	VERB
cana-5235	278	30	down	down	ADP
cana-5235	278	31	a	a	DET
cana-5235	278	32	slippery	slippery	ADJ
cana-5235	278	33	inclined	incline	VERB
cana-5235	278	34	.	.	PUNCT
cana-5235	279	1	physics	physics	PROPN
cana-5235	279	2	of	of	ADP
cana-5235	279	3	fluids	fluid	NOUN
cana-5235	279	4	(	(	PUNCT
cana-5235	279	5	2020	2020	NUM
cana-5235	279	6	)	)	PUNCT
cana-5235	279	7	,	,	PUNCT
cana-5235	279	8	32(10	32(10	NUM
cana-5235	279	9	)	)	PUNCT
cana-5235	279	10	.	.	PUNCT
cana-5235	280	1	[	[	X
cana-5235	280	2	11	11	NUM
cana-5235	280	3	]	]	X
cana-5235	280	4	t.w	t.w	PROPN
cana-5235	280	5	.	.	PROPN
cana-5235	280	6	kao	kao	PROPN
cana-5235	280	7	,	,	PUNCT
cana-5235	280	8	role	role	NOUN
cana-5235	280	9	of	of	ADP
cana-5235	280	10	the	the	DET
cana-5235	280	11	interface	interface	NOUN
cana-5235	280	12	in	in	ADP
cana-5235	280	13	the	the	DET
cana-5235	280	14	stability	stability	NOUN
cana-5235	280	15	of	of	ADP
cana-5235	280	16	stratified	stratified	ADJ
cana-5235	280	17	flow	flow	NOUN
cana-5235	280	18	down	down	ADP
cana-5235	280	19	an	an	DET
cana-5235	280	20	inclined	inclined	ADJ
cana-5235	280	21	plane	plane	NOUN
cana-5235	280	22	,	,	PUNCT
cana-5235	280	23	phys	phy	NOUN
cana-5235	280	24	.	.	PUNCT
cana-5235	281	1	fluid	fluid	NOUN
cana-5235	281	2	.	.	PUNCT
cana-5235	281	3	,	,	PUNCT
cana-5235	281	4	8.12(1965	8.12(1965	NUM
cana-5235	281	5	)	)	PUNCT
cana-5235	281	6	,	,	PUNCT
cana-5235	281	7	2190	2190	NUM
cana-5235	281	8	-	-	SYM
cana-5235	281	9	2194	2194	NUM
cana-5235	281	10	.	.	PUNCT
cana-5235	282	1	[	[	X
cana-5235	282	2	12	12	NUM
cana-5235	282	3	]	]	X
cana-5235	282	4	t.w	t.w	PROPN
cana-5235	282	5	.	.	PROPN
cana-5235	282	6	kao	kao	PROPN
cana-5235	282	7	,	,	PUNCT
cana-5235	282	8	role	role	NOUN
cana-5235	282	9	of	of	ADP
cana-5235	282	10	viscosity	viscosity	NOUN
cana-5235	282	11	stratification	stratification	NOUN
cana-5235	282	12	in	in	ADP
cana-5235	282	13	the	the	DET
cana-5235	282	14	stability	stability	NOUN
cana-5235	282	15	of	of	ADP
cana-5235	282	16	two	two	NUM
cana-5235	282	17	-	-	PUNCT
cana-5235	282	18	layer	layer	NOUN
cana-5235	282	19	flow	flow	NOUN
cana-5235	282	20	down	down	ADP
cana-5235	282	21	an	an	DET
cana-5235	282	22	incline	incline	NOUN
cana-5235	282	23	,	,	PUNCT
cana-5235	282	24	j.	j.	PROPN
cana-5235	282	25	fluid	fluid	PROPN
cana-5235	282	26	.	.	PUNCT
cana-5235	282	27	mech	mech	PROPN
cana-5235	282	28	.	.	PROPN
cana-5235	282	29	,	,	PUNCT
cana-5235	282	30	33.3(1968	33.3(1968	NUM
cana-5235	282	31	)	)	PUNCT
cana-5235	282	32	,	,	PUNCT
cana-5235	282	33	561	561	NUM
cana-5235	282	34	-	-	SYM
cana-5235	282	35	572	572	NUM
cana-5235	282	36	.	.	PUNCT
cana-5235	283	1	[	[	X
cana-5235	283	2	13	13	NUM
cana-5235	283	3	]	]	X
cana-5235	283	4	t.w	t.w	PROPN
cana-5235	283	5	.	.	PROPN
cana-5235	283	6	kao	kao	PROPN
cana-5235	283	7	,	,	PUNCT
cana-5235	283	8	stability	stability	NOUN
cana-5235	283	9	of	of	ADP
cana-5235	283	10	two	two	NUM
cana-5235	283	11	-	-	PUNCT
cana-5235	283	12	layer	layer	NOUN
cana-5235	283	13	viscous	viscous	ADJ
cana-5235	283	14	stratified	stratify	VERB
cana-5235	283	15	flow	flow	NOUN
cana-5235	283	16	down	down	ADP
cana-5235	283	17	an	an	DET
cana-5235	283	18	inclined	inclined	ADJ
cana-5235	283	19	plane	plane	NOUN
cana-5235	283	20	,	,	PUNCT
cana-5235	283	21	technical	technical	ADJ
cana-5235	283	22	report	report	NOUN
cana-5235	283	23	,	,	PUNCT
cana-5235	283	24	nasa	nasa	PROPN
cana-5235	283	25	-	-	PUNCT
cana-5235	283	26	cr-57878	cr-57878	PROPN
cana-5235	283	27	,	,	PUNCT
cana-5235	283	28	(	(	PUNCT
cana-5235	283	29	1964	1964	NUM
cana-5235	283	30	)	)	PUNCT
cana-5235	283	31	.	.	PUNCT
cana-5235	284	1	[	[	X
cana-5235	284	2	14	14	NUM
cana-5235	284	3	]	]	PUNCT
cana-5235	284	4	p.	p.	PROPN
cana-5235	284	5	gao	gao	PROPN
cana-5235	284	6	,	,	PUNCT
cana-5235	284	7	x.y	x.y	PROPN
cana-5235	284	8	.	.	PROPN
cana-5235	284	9	lu	lu	PROPN
cana-5235	284	10	,	,	PUNCT
cana-5235	284	11	effect	effect	NOUN
cana-5235	284	12	of	of	ADP
cana-5235	284	13	surfactants	surfactant	NOUN
cana-5235	284	14	on	on	ADP
cana-5235	284	15	the	the	DET
cana-5235	284	16	inertialess	inertialess	NOUN
cana-5235	284	17	instability	instability	NOUN
cana-5235	284	18	of	of	ADP
cana-5235	284	19	a	a	DET
cana-5235	284	20	two	two	NUM
cana-5235	284	21	-	-	PUNCT
cana-5235	284	22	layer	layer	NOUN
cana-5235	284	23	film	film	NOUN
cana-5235	284	24	flow	flow	NOUN
cana-5235	284	25	,	,	PUNCT
cana-5235	284	26	j.	j.	PROPN
cana-5235	284	27	fluid	fluid	PROPN
cana-5235	284	28	,	,	PUNCT
cana-5235	284	29	mech	mech	NOUN
cana-5235	284	30	.	.	PUNCT
cana-5235	284	31	,	,	PUNCT
cana-5235	284	32	591(2007	591(2007	NUM
cana-5235	284	33	)	)	PUNCT
cana-5235	284	34	,	,	PUNCT
cana-5235	284	35	495	495	NUM
cana-5235	284	36	-	-	SYM
cana-5235	284	37	507	507	NUM
cana-5235	284	38	.	.	PUNCT
cana-5235	285	1	[	[	X
cana-5235	285	2	15	15	NUM
cana-5235	285	3	]	]	X
cana-5235	285	4	n.a	n.a	PROPN
cana-5235	285	5	.	.	PROPN
cana-5235	285	6	malamataris	malamataris	PROPN
cana-5235	285	7	,	,	PUNCT
cana-5235	285	8	m.	m.	NOUN
cana-5235	285	9	vlachogiannis	vlachogiannis	PROPN
cana-5235	285	10	,	,	PUNCT
cana-5235	285	11	v.	v.	ADP
cana-5235	285	12	bontozoglou	bontozoglou	ADJ
cana-5235	285	13	,	,	PUNCT
cana-5235	285	14	solitary	solitary	ADJ
cana-5235	285	15	waves	wave	NOUN
cana-5235	285	16	on	on	ADP
cana-5235	285	17	inclined	inclined	ADJ
cana-5235	285	18	films	film	NOUN
cana-5235	285	19	:	:	PUNCT
cana-5235	285	20	communications	communication	NOUN
cana-5235	285	21	on	on	ADP
cana-5235	285	22	applied	apply	VERB
cana-5235	285	23	nonlinear	nonlinear	ADJ
cana-5235	285	24	analysis	analysis	NOUN
cana-5235	285	25	issn	issn	NOUN
cana-5235	285	26	:	:	PUNCT
cana-5235	285	27	1074	1074	NUM
cana-5235	285	28	-	-	PUNCT
cana-5235	285	29	133x	133x	NUM
cana-5235	285	30	vol	vol	VERB
cana-5235	285	31	32	32	NUM
cana-5235	285	32	no	no	NOUN
cana-5235	285	33	.	.	PUNCT
cana-5235	285	34	10s	10	NOUN
cana-5235	285	35	(	(	PUNCT
cana-5235	285	36	2025	2025	NUM
cana-5235	285	37	)	)	PUNCT
cana-5235	285	38	1336	1336	NUM
cana-5235	286	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5235	286	2	flow	flow	NOUN
cana-5235	286	3	structure	structure	NOUN
cana-5235	286	4	and	and	CCONJ
cana-5235	286	5	binary	binary	ADJ
cana-5235	286	6	interactions	interaction	NOUN
cana-5235	286	7	,	,	PUNCT
cana-5235	286	8	phys	phy	NOUN
cana-5235	286	9	.	.	PUNCT
cana-5235	287	1	fluids	fluid	NOUN
cana-5235	287	2	.	.	PUNCT
cana-5235	287	3	,	,	PUNCT
cana-5235	287	4	14.3(2002	14.3(2002	NUM
cana-5235	287	5	)	)	PUNCT
cana-5235	287	6	,	,	PUNCT
cana-5235	287	7	1082	1082	NUM
cana-5235	287	8	-	-	SYM
cana-5235	287	9	1094	1094	NUM
cana-5235	287	10	.	.	PUNCT
cana-5235	288	1	[	[	X
cana-5235	288	2	16	16	NUM
cana-5235	288	3	]	]	X
cana-5235	288	4	d.r	d.r	PROPN
cana-5235	288	5	.	.	PROPN
cana-5235	288	6	otis	otis	PROPN
cana-5235	288	7	,	,	PUNCT
cana-5235	288	8	m.	m.	PROPN
cana-5235	288	9	johnson	johnson	PROPN
cana-5235	288	10	,	,	PUNCT
cana-5235	288	11	t.j	t.j	PROPN
cana-5235	288	12	.	.	PROPN
cana-5235	288	13	pedley	pedley	PROPN
cana-5235	288	14	,	,	PUNCT
cana-5235	288	15	r.d	r.d	PROPN
cana-5235	288	16	.	.	PROPN
cana-5235	288	17	kamm	kamm	PROPN
cana-5235	288	18	,	,	PUNCT
cana-5235	288	19	role	role	NOUN
cana-5235	288	20	of	of	ADP
cana-5235	288	21	pulmonary	pulmonary	ADJ
cana-5235	288	22	surfactant	surfactant	NOUN
cana-5235	288	23	in	in	ADP
cana-5235	288	24	airway	airway	NOUN
cana-5235	288	25	closure	closure	NOUN
cana-5235	288	26	:	:	PUNCT
cana-5235	288	27	a	a	DET
cana-5235	288	28	computational	computational	ADJ
cana-5235	288	29	study	study	NOUN
cana-5235	288	30	,	,	PUNCT
cana-5235	288	31	j.	j.	PROPN
cana-5235	288	32	appl	appl	PROPN
cana-5235	288	33	.	.	PUNCT
cana-5235	289	1	phys	phy	NOUN
cana-5235	289	2	.	.	PUNCT
cana-5235	289	3	,	,	PUNCT
cana-5235	289	4	75.3(1993	75.3(1993	NUM
cana-5235	289	5	)	)	PUNCT
cana-5235	289	6	,	,	PUNCT
cana-5235	289	7	1323	1323	NUM
cana-5235	289	8	-	-	SYM
cana-5235	289	9	1333	1333	NUM
cana-5235	289	10	.	.	PUNCT
cana-5235	290	1	[	[	X
cana-5235	290	2	17	17	NUM
cana-5235	290	3	]	]	PUNCT
cana-5235	290	4	x.	x.	NOUN
cana-5235	290	5	li	li	PROPN
cana-5235	290	6	,	,	PUNCT
cana-5235	290	7	c.	c.	PROPN
cana-5235	290	8	pozrikidis	pozrikidis	PROPN
cana-5235	290	9	,	,	PUNCT
cana-5235	290	10	the	the	DET
cana-5235	290	11	effect	effect	NOUN
cana-5235	290	12	of	of	ADP
cana-5235	290	13	surfactants	surfactant	NOUN
cana-5235	290	14	on	on	ADP
cana-5235	290	15	drop	drop	NOUN
cana-5235	290	16	deformation	deformation	NOUN
cana-5235	290	17	and	and	CCONJ
cana-5235	290	18	on	on	ADP
cana-5235	290	19	the	the	DET
cana-5235	290	20	rheology	rheology	NOUN
cana-5235	290	21	of	of	ADP
cana-5235	290	22	dilute	dilute	ADJ
cana-5235	290	23	emulsions	emulsion	NOUN
cana-5235	290	24	in	in	ADP
cana-5235	290	25	stokes	stoke	NOUN
cana-5235	290	26	flow	flow	NOUN
cana-5235	290	27	,	,	PUNCT
cana-5235	290	28	j.	j.	PROPN
cana-5235	290	29	fluid	fluid	PROPN
cana-5235	290	30	.	.	PUNCT
cana-5235	290	31	mech	mech	PROPN
cana-5235	290	32	.	.	PUNCT
cana-5235	290	33	,	,	PUNCT
cana-5235	290	34	341(1997	341(1997	NUM
cana-5235	290	35	)	)	PUNCT
cana-5235	290	36	,	,	PUNCT
cana-5235	290	37	165	165	NUM
cana-5235	290	38	-	-	SYM
cana-5235	290	39	194	194	NUM
cana-5235	290	40	.	.	PUNCT
cana-5235	291	1	[	[	X
cana-5235	291	2	18	18	NUM
cana-5235	291	3	]	]	X
cana-5235	291	4	i.	i.	PROPN
cana-5235	291	5	sadiq	sadiq	PROPN
cana-5235	291	6	,	,	PUNCT
cana-5235	291	7	r.	r.	PROPN
cana-5235	291	8	usha	usha	PROPN
cana-5235	291	9	,	,	PUNCT
cana-5235	291	10	thin	thin	ADJ
cana-5235	291	11	newtonian	newtonian	ADJ
cana-5235	291	12	film	film	NOUN
cana-5235	291	13	flow	flow	VERB
cana-5235	291	14	down	down	ADP
cana-5235	291	15	a	a	DET
cana-5235	291	16	porous	porous	ADJ
cana-5235	291	17	inclined	inclined	ADJ
cana-5235	291	18	plane	plane	NOUN
cana-5235	291	19	:	:	PUNCT
cana-5235	291	20	stability	stability	NOUN
cana-5235	291	21	analysis	analysis	NOUN
cana-5235	291	22	,	,	PUNCT
cana-5235	291	23	phys	phy	NOUN
cana-5235	291	24	.	.	PUNCT
cana-5235	292	1	fluids	fluid	NOUN
cana-5235	292	2	.	.	PROPN
cana-5235	292	3	,	,	PUNCT
cana-5235	292	4	20.2(2008	20.2(2008	NUM
cana-5235	292	5	)	)	PUNCT
cana-5235	292	6	.	.	PUNCT
cana-5235	293	1	[	[	X
cana-5235	293	2	19	19	NUM
cana-5235	293	3	]	]	PUNCT
cana-5235	293	4	a.	a.	NOUN
cana-5235	293	5	samanta	samanta	PROPN
cana-5235	293	6	,	,	PUNCT
cana-5235	293	7	effect	effect	NOUN
cana-5235	293	8	of	of	ADP
cana-5235	293	9	surfactants	surfactant	NOUN
cana-5235	293	10	on	on	ADP
cana-5235	293	11	the	the	DET
cana-5235	293	12	instability	instability	NOUN
cana-5235	293	13	of	of	ADP
cana-5235	293	14	a	a	DET
cana-5235	293	15	two	two	NUM
cana-5235	293	16	-	-	PUNCT
cana-5235	293	17	layer	layer	NOUN
cana-5235	293	18	film	film	NOUN
cana-5235	293	19	flow	flow	VERB
cana-5235	293	20	down	down	ADP
cana-5235	293	21	an	an	DET
cana-5235	293	22	inclined	inclined	ADJ
cana-5235	293	23	plane	plane	NOUN
cana-5235	293	24	,	,	PUNCT
cana-5235	293	25	phys	phy	NOUN
cana-5235	293	26	.	.	PUNCT
cana-5235	294	1	fluids	fluid	NOUN
cana-5235	294	2	.	.	PUNCT
cana-5235	294	3	,	,	PUNCT
cana-5235	294	4	26.9	26.9	NUM
cana-5235	294	5	(	(	PUNCT
cana-5235	294	6	2014	2014	NUM
cana-5235	294	7	)	)	PUNCT
cana-5235	294	8	.	.	PUNCT
cana-5235	295	1	[	[	X
cana-5235	295	2	20	20	NUM
cana-5235	295	3	]	]	PUNCT
cana-5235	295	4	a.	a.	NOUN
cana-5235	295	5	samanta	samanta	PROPN
cana-5235	295	6	,	,	PUNCT
cana-5235	295	7	shear	shear	NOUN
cana-5235	295	8	-	-	PUNCT
cana-5235	295	9	imposed	impose	VERB
cana-5235	295	10	falling	fall	VERB
cana-5235	295	11	film	film	NOUN
cana-5235	295	12	,	,	PUNCT
cana-5235	295	13	j.	j.	PROPN
cana-5235	295	14	fluid	fluid	PROPN
cana-5235	295	15	.	.	PUNCT
cana-5235	296	1	mach	mach	PROPN
cana-5235	296	2	.	.	PUNCT
cana-5235	296	3	,	,	PUNCT
cana-5235	296	4	753(2014	753(2014	NUM
cana-5235	296	5	)	)	PUNCT
cana-5235	296	6	,	,	PUNCT
cana-5235	296	7	131	131	NUM
cana-5235	296	8	-	-	SYM
cana-5235	296	9	149	149	NUM
cana-5235	296	10	.	.	PUNCT
cana-5235	297	1	[	[	X
cana-5235	297	2	21	21	NUM
cana-5235	297	3	]	]	PUNCT
cana-5235	297	4	a.	a.	NOUN
cana-5235	297	5	samanta	samanta	PROPN
cana-5235	297	6	,	,	PUNCT
cana-5235	297	7	linear	linear	ADJ
cana-5235	297	8	stability	stability	NOUN
cana-5235	297	9	of	of	ADP
cana-5235	297	10	a	a	DET
cana-5235	297	11	plane	plane	NOUN
cana-5235	297	12	couette–poiseuille	couette–poiseuille	PROPN
cana-5235	297	13	flow	flow	NOUN
cana-5235	297	14	overlying	overlie	VERB
cana-5235	297	15	a	a	DET
cana-5235	297	16	porous	porous	ADJ
cana-5235	297	17	layer	layer	NOUN
cana-5235	297	18	,	,	PUNCT
cana-5235	297	19	int	int	NOUN
cana-5235	297	20	.	.	PUNCT
cana-5235	298	1	j.	j.	PROPN
cana-5235	298	2	multi	multi	PROPN
cana-5235	298	3	.	.	PUNCT
cana-5235	299	1	flow	flow	PROPN
cana-5235	299	2	.	.	PUNCT
cana-5235	299	3	,	,	PUNCT
cana-5235	299	4	123(2020	123(2020	NUM
cana-5235	299	5	)	)	PUNCT
cana-5235	299	6	,	,	PUNCT
cana-5235	299	7	103160	103160	NUM
cana-5235	299	8	.	.	PUNCT
cana-5235	300	1	[	[	X
cana-5235	300	2	22	22	NUM
cana-5235	300	3	]	]	PUNCT
cana-5235	300	4	a.	a.	NOUN
cana-5235	300	5	samanta	samanta	PROPN
cana-5235	300	6	,	,	PUNCT
cana-5235	300	7	effect	effect	NOUN
cana-5235	300	8	of	of	ADP
cana-5235	300	9	surfactant	surfactant	NOUN
cana-5235	300	10	on	on	ADP
cana-5235	300	11	the	the	DET
cana-5235	300	12	linear	linear	ADJ
cana-5235	300	13	stability	stability	NOUN
cana-5235	300	14	of	of	ADP
cana-5235	300	15	a	a	DET
cana-5235	300	16	shear	shear	NOUN
cana-5235	300	17	-	-	PUNCT
cana-5235	300	18	imposed	impose	VERB
cana-5235	300	19	fluid	fluid	NOUN
cana-5235	300	20	flowing	flow	VERB
cana-5235	300	21	down	down	ADP
cana-5235	300	22	a	a	DET
cana-5235	300	23	compliant	compliant	ADJ
cana-5235	300	24	substrate	substrate	NOUN
cana-5235	300	25	,	,	PUNCT
cana-5235	300	26	j.	j.	PROPN
cana-5235	300	27	fluid	fluid	PROPN
cana-5235	300	28	.	.	PUNCT
cana-5235	300	29	mech	mech	PROPN
cana-5235	300	30	.	.	PUNCT
cana-5235	300	31	,	,	PUNCT
cana-5235	300	32	920(2021	920(2021	NOUN
cana-5235	300	33	)	)	PUNCT
cana-5235	300	34	,	,	PUNCT
cana-5235	300	35	a23	a23	PROPN
cana-5235	300	36	.	.	PUNCT
cana-5235	301	1	[	[	X
cana-5235	301	2	23	23	NUM
cana-5235	301	3	]	]	X
cana-5235	301	4	s.	s.	PROPN
cana-5235	301	5	pal	pal	PROPN
cana-5235	301	6	,	,	PUNCT
cana-5235	301	7	a.	a.	PROPN
cana-5235	301	8	samanta	samanta	PROPN
cana-5235	301	9	,	,	PUNCT
cana-5235	301	10	linear	linear	VERB
cana-5235	301	11	stability	stability	NOUN
cana-5235	301	12	analysis	analysis	NOUN
cana-5235	301	13	of	of	ADP
cana-5235	301	14	a	a	DET
cana-5235	301	15	shear	shear	NOUN
cana-5235	301	16	-	-	PUNCT
cana-5235	301	17	imposed	impose	VERB
cana-5235	301	18	oldroyd	oldroyd	NOUN
cana-5235	301	19	-	-	PUNCT
cana-5235	301	20	b	b	NOUN
cana-5235	301	21	liquid	liquid	NOUN
cana-5235	301	22	flowing	flow	VERB
cana-5235	301	23	down	down	ADP
cana-5235	301	24	a	a	DET
cana-5235	301	25	slippery	slippery	ADJ
cana-5235	301	26	inclined	inclined	ADJ
cana-5235	301	27	plane	plane	NOUN
cana-5235	301	28	,	,	PUNCT
cana-5235	301	29	bulletin	bulletin	NOUN
cana-5235	301	30	of	of	ADP
cana-5235	301	31	the	the	DET
cana-5235	301	32	american	american	ADJ
cana-5235	301	33	phys	phys	PROPN
cana-5235	301	34	.	.	PUNCT
cana-5235	302	1	soc	soc	PROPN
cana-5235	302	2	.	.	PUNCT
cana-5235	302	3	,	,	PUNCT
cana-5235	302	4	67(2022	67(2022	NOUN
cana-5235	302	5	)	)	PUNCT
cana-5235	302	6	.	.	PUNCT
cana-5235	303	1	[	[	X
cana-5235	303	2	24	24	NUM
cana-5235	303	3	]	]	PUNCT
cana-5235	303	4	m.	m.	NOUN
cana-5235	303	5	sani	sani	PROPN
cana-5235	303	6	,	,	PUNCT
cana-5235	303	7	h.	h.	PROPN
cana-5235	303	8	behera	behera	PROPN
cana-5235	303	9	,	,	PUNCT
cana-5235	303	10	s.	s.	PROPN
cana-5235	303	11	ghosh	ghosh	PROPN
cana-5235	303	12	,	,	PUNCT
cana-5235	303	13	stability	stability	NOUN
cana-5235	303	14	analysis	analysis	NOUN
cana-5235	303	15	of	of	ADP
cana-5235	303	16	a	a	DET
cana-5235	303	17	film	film	NOUN
cana-5235	303	18	flow	flow	NOUN
cana-5235	303	19	down	down	ADP
cana-5235	303	20	an	an	DET
cana-5235	303	21	incline	incline	NOUN
cana-5235	303	22	in	in	ADP
cana-5235	303	23	the	the	DET
cana-5235	303	24	presence	presence	NOUN
cana-5235	303	25	of	of	ADP
cana-5235	303	26	a	a	DET
cana-5235	303	27	floating	float	VERB
cana-5235	303	28	flexible	flexible	ADJ
cana-5235	303	29	membrane	membrane	NOUN
cana-5235	303	30	,	,	PUNCT
cana-5235	303	31	math	math	NOUN
cana-5235	303	32	.	.	PUNCT
cana-5235	304	1	model	model	PROPN
cana-5235	304	2	.	.	PUNCT
cana-5235	305	1	sci	sci	PROPN
cana-5235	305	2	.	.	PUNCT
cana-5235	305	3	comput	comput	PROPN
cana-5235	305	4	.	.	PUNCT
cana-5235	306	1	appl	appl	PROPN
cana-5235	306	2	.	.	PROPN
cana-5235	306	3	,	,	PUNCT
cana-5235	306	4	19	19	NUM
cana-5235	306	5	(	(	PUNCT
cana-5235	306	6	2020	2020	NUM
cana-5235	306	7	)	)	PUNCT
cana-5235	306	8	,	,	PUNCT
cana-5235	306	9	253	253	NUM
cana-5235	306	10	-	-	SYM
cana-5235	306	11	263	263	NUM
cana-5235	306	12	.	.	PUNCT
cana-5235	307	1	[	[	X
cana-5235	307	2	25	25	NUM
cana-5235	307	3	]	]	PUNCT
cana-5235	307	4	m.	m.	PROPN
cana-5235	307	5	sani	sani	PROPN
cana-5235	307	6	,	,	PUNCT
cana-5235	307	7	s.	s.	PROPN
cana-5235	307	8	ghosh	ghosh	PROPN
cana-5235	307	9	,	,	PUNCT
cana-5235	307	10	h.	h.	PROPN
cana-5235	307	11	behera	behera	PROPN
cana-5235	307	12	,	,	PUNCT
cana-5235	307	13	effect	effect	NOUN
cana-5235	307	14	of	of	ADP
cana-5235	307	15	a	a	DET
cana-5235	307	16	floating	float	VERB
cana-5235	307	17	elastic	elastic	ADJ
cana-5235	307	18	membrane	membrane	NOUN
cana-5235	307	19	for	for	ADP
cana-5235	307	20	stabilizing	stabilize	VERB
cana-5235	307	21	the	the	DET
cana-5235	307	22	film	film	NOUN
cana-5235	307	23	flow	flow	VERB
cana-5235	307	24	down	down	ADP
cana-5235	307	25	a	a	DET
cana-5235	307	26	porous	porous	ADJ
cana-5235	307	27	inclined	inclined	ADJ
cana-5235	307	28	plane	plane	NOUN
cana-5235	307	29	,	,	PUNCT
cana-5235	307	30	j.	j.	PROPN
cana-5235	307	31	appl	appl	PROPN
cana-5235	307	32	.	.	PROPN
cana-5235	307	33	math	math	PROPN
cana-5235	307	34	.	.	PUNCT
cana-5235	308	1	mach	mach	PROPN
cana-5235	308	2	.	.	PUNCT
cana-5235	308	3	,	,	PUNCT
cana-5235	308	4	101.2	101.2	NUM
cana-5235	308	5	,	,	PUNCT
cana-5235	308	6	(	(	PUNCT
cana-5235	308	7	2021	2021	NUM
cana-5235	308	8	)	)	PUNCT
cana-5235	308	9	,	,	PUNCT
cana-5235	308	10	e201900246	e201900246	NOUN
cana-5235	308	11	.	.	PUNCT
cana-5235	309	1	[	[	X
cana-5235	309	2	26	26	NUM
cana-5235	309	3	]	]	X
cana-5235	309	4	i.r	i.r	PROPN
cana-5235	309	5	.	.	PROPN
cana-5235	309	6	siqueira	siqueira	PROPN
cana-5235	309	7	,	,	PUNCT
cana-5235	309	8	r.l	r.l	PROPN
cana-5235	309	9	.	.	PROPN
cana-5235	309	10	thompson	thompson	PROPN
cana-5235	309	11	,	,	PUNCT
cana-5235	309	12	m.s	m.s	PROPN
cana-5235	309	13	.	.	PROPN
cana-5235	309	14	carvalho	carvalho	PROPN
cana-5235	309	15	,	,	PUNCT
cana-5235	309	16	p.r	p.r	PROPN
cana-5235	309	17	.	.	PROPN
cana-5235	309	18	de	de	PROPN
cana-5235	309	19	souza	souza	PROPN
cana-5235	309	20	mendes	mende	NOUN
cana-5235	309	21	,	,	PUNCT
cana-5235	309	22	slot	slot	NOUN
cana-5235	309	23	coating	coating	NOUN
cana-5235	309	24	of	of	ADP
cana-5235	309	25	viscoplastic	viscoplastic	ADJ
cana-5235	309	26	materials	material	NOUN
cana-5235	309	27	:	:	PUNCT
cana-5235	309	28	a	a	DET
cana-5235	309	29	computational	computational	ADJ
cana-5235	309	30	study	study	NOUN
cana-5235	309	31	of	of	ADP
cana-5235	309	32	the	the	DET
cana-5235	309	33	effects	effect	NOUN
cana-5235	309	34	of	of	ADP
cana-5235	309	35	viscoplasticity	viscoplasticity	NOUN
cana-5235	309	36	on	on	ADP
cana-5235	309	37	the	the	DET
cana-5235	309	38	flow	flow	NOUN
cana-5235	309	39	dynamics	dynamic	NOUN
cana-5235	309	40	and	and	CCONJ
cana-5235	309	41	low	low	ADJ
cana-5235	309	42	flow	flow	NOUN
cana-5235	309	43	limit	limit	NOUN
cana-5235	309	44	,	,	PUNCT
cana-5235	309	45	j.	j.	PROPN
cana-5235	309	46	non	non	ADJ
cana-5235	309	47	-	-	ADJ
cana-5235	309	48	newtonian	newtonian	ADJ
cana-5235	309	49	fluid	fluid	ADJ
cana-5235	309	50	mech	mech	NOUN
cana-5235	309	51	.	.	PUNCT
cana-5235	309	52	,	,	PUNCT
cana-5235	309	53	327	327	NUM
cana-5235	309	54	(	(	PUNCT
cana-5235	309	55	2024	2024	NUM
cana-5235	309	56	)	)	PUNCT
cana-5235	309	57	,	,	PUNCT
cana-5235	309	58	105222	105222	NUM
cana-5235	309	59	.	.	PUNCT
cana-5235	310	1	[	[	X
cana-5235	310	2	27	27	NUM
cana-5235	310	3	]	]	PUNCT
cana-5235	310	4	m.	m.	NOUN
cana-5235	310	5	sivapuratharasu	sivapuratharasu	PROPN
cana-5235	310	6	,	,	PUNCT
cana-5235	310	7	s.	s.	PROPN
cana-5235	310	8	hibberd	hibberd	PROPN
cana-5235	310	9	,	,	PUNCT
cana-5235	310	10	m.e	m.e	PROPN
cana-5235	310	11	.	.	PROPN
cana-5235	310	12	hubbard	hubbard	PROPN
cana-5235	310	13	,	,	PUNCT
cana-5235	310	14	h.	h.	PROPN
cana-5235	310	15	power	power	PROPN
cana-5235	310	16	,	,	PUNCT
cana-5235	310	17	inertial	inertial	ADJ
cana-5235	310	18	effects	effect	NOUN
cana-5235	310	19	on	on	ADP
cana-5235	310	20	thin	thin	ADJ
cana-5235	310	21	-	-	PUNCT
cana-5235	310	22	film	film	NOUN
cana-5235	310	23	wave	wave	NOUN
cana-5235	310	24	structures	structure	NOUN
cana-5235	310	25	with	with	ADP
cana-5235	310	26	imposed	impose	VERB
cana-5235	310	27	surface	surface	NOUN
cana-5235	310	28	shear	shear	NOUN
cana-5235	310	29	on	on	ADP
cana-5235	310	30	an	an	DET
cana-5235	310	31	inclined	inclined	ADJ
cana-5235	310	32	plane	plane	NOUN
cana-5235	310	33	,	,	PUNCT
cana-5235	310	34	phys	phy	NOUN
cana-5235	310	35	.	.	PUNCT
cana-5235	311	1	d	d	X
cana-5235	311	2	:	:	PUNCT
cana-5235	311	3	nonlinear	nonlinear	ADJ
cana-5235	311	4	phenom	phenom	NOUN
cana-5235	311	5	.	.	PUNCT
cana-5235	312	1	,325	,325	PUNCT
cana-5235	312	2	(	(	PUNCT
cana-5235	312	3	2016	2016	NUM
cana-5235	312	4	)	)	PUNCT
cana-5235	312	5	,	,	PUNCT
cana-5235	312	6	86	86	NUM
cana-5235	312	7	-	-	SYM
cana-5235	312	8	97	97	NUM
cana-5235	312	9	.	.	PUNCT
cana-5235	313	1	[	[	X
cana-5235	313	2	28	28	NUM
cana-5235	313	3	]	]	X
cana-5235	313	4	s.a	s.a	PROPN
cana-5235	313	5	.	.	PROPN
cana-5235	313	6	selvan	selvan	PROPN
cana-5235	313	7	,	,	PUNCT
cana-5235	313	8	s.	s.	PROPN
cana-5235	313	9	ghosh	ghosh	PROPN
cana-5235	313	10	,	,	PUNCT
cana-5235	313	11	h.	h.	PROPN
cana-5235	313	12	behera	behera	PROPN
cana-5235	313	13	,	,	PUNCT
cana-5235	313	14	m.h	m.h	PROPN
cana-5235	313	15	.	.	PROPN
cana-5235	313	16	meylan	meylan	PROPN
cana-5235	313	17	,	,	PUNCT
cana-5235	313	18	hydroelastic	hydroelastic	ADJ
cana-5235	313	19	response	response	NOUN
cana-5235	313	20	of	of	ADP
cana-5235	313	21	a	a	DET
cana-5235	313	22	floating	float	VERB
cana-5235	313	23	plate	plate	NOUN
cana-5235	313	24	on	on	ADP
cana-5235	313	25	the	the	DET
cana-5235	313	26	falling	fall	VERB
cana-5235	313	27	film	film	NOUN
cana-5235	313	28	:	:	PUNCT
cana-5235	313	29	a	a	DET
cana-5235	313	30	stability	stability	NOUN
cana-5235	313	31	analysis	analysis	NOUN
cana-5235	313	32	,	,	PUNCT
cana-5235	313	33	wave	wave	NOUN
cana-5235	313	34	motion	motion	NOUN
cana-5235	313	35	,	,	PUNCT
cana-5235	313	36	104	104	NUM
cana-5235	313	37	(	(	PUNCT
cana-5235	313	38	2021	2021	NUM
cana-5235	313	39	)	)	PUNCT
cana-5235	313	40	,	,	PUNCT
cana-5235	313	41	102749	102749	NUM
cana-5235	313	42	.	.	PUNCT
cana-5235	314	1	[	[	X
cana-5235	314	2	29	29	NUM
cana-5235	314	3	]	]	X
cana-5235	314	4	y.y	y.y	PROPN
cana-5235	314	5	.	.	PROPN
cana-5235	314	6	suy	suy	PROPN
cana-5235	314	7	,	,	PUNCT
cana-5235	314	8	the	the	DET
cana-5235	314	9	stability	stability	NOUN
cana-5235	314	10	of	of	ADP
cana-5235	314	11	superposed	superpose	VERB
cana-5235	314	12	polymeric	polymeric	ADJ
cana-5235	314	13	fluids	fluid	NOUN
cana-5235	314	14	flowing	flow	VERB
cana-5235	314	15	down	down	ADP
cana-5235	314	16	an	an	DET
cana-5235	314	17	inclined	inclined	ADJ
cana-5235	314	18	plane	plane	NOUN
cana-5235	314	19	and	and	CCONJ
cana-5235	314	20	its	its	PRON
cana-5235	314	21	application	application	NOUN
cana-5235	314	22	to	to	ADP
cana-5235	314	23	coating	coating	NOUN
cana-5235	314	24	processes	process	NOUN
cana-5235	314	25	,	,	PUNCT
cana-5235	314	26	polymer	polymer	NOUN
cana-5235	314	27	-	-	PUNCT
cana-5235	314	28	plastics	plastic	NOUN
cana-5235	314	29	tech	tech	NOUN
cana-5235	314	30	.	.	PUNCT
cana-5235	315	1	eng	eng	PROPN
cana-5235	315	2	.	.	PROPN
cana-5235	315	3	,	,	PUNCT
cana-5235	315	4	34.2	34.2	NUM
cana-5235	315	5	(	(	PUNCT
cana-5235	315	6	1995	1995	NUM
cana-5235	315	7	)	)	PUNCT
cana-5235	315	8	,	,	PUNCT
cana-5235	315	9	243	243	NUM
cana-5235	315	10	-	-	SYM
cana-5235	315	11	269	269	NUM
cana-5235	315	12	.	.	PUNCT
cana-5235	316	1	[	[	X
cana-5235	316	2	30	30	NUM
cana-5235	316	3	]	]	X
cana-5235	316	4	e.o	e.o	PROPN
cana-5235	316	5	.	.	PROPN
cana-5235	316	6	tuck	tuck	PROPN
cana-5235	316	7	,	,	PUNCT
cana-5235	316	8	continuous	continuous	ADJ
cana-5235	316	9	coating	coating	NOUN
cana-5235	316	10	with	with	ADP
cana-5235	316	11	gravity	gravity	NOUN
cana-5235	316	12	and	and	CCONJ
cana-5235	316	13	jet	jet	NOUN
cana-5235	316	14	stripping	stripping	NOUN
cana-5235	316	15	,	,	PUNCT
cana-5235	316	16	phys	phy	NOUN
cana-5235	316	17	.	.	PUNCT
cana-5235	317	1	fluid	fluid	NOUN
cana-5235	317	2	.	.	PUNCT
cana-5235	317	3	,	,	PUNCT
cana-5235	317	4	26.9	26.9	NUM
cana-5235	317	5	(	(	PUNCT
cana-5235	317	6	1983	1983	NUM
cana-5235	317	7	)	)	PUNCT
cana-5235	317	8	,	,	PUNCT
cana-5235	317	9	2352	2352	NUM
cana-5235	317	10	2358	2358	NUM
cana-5235	317	11	.	.	PUNCT
cana-5235	318	1	[	[	X
cana-5235	318	2	31	31	NUM
cana-5235	318	3	]	]	X
cana-5235	318	4	c.y	c.y	PROPN
cana-5235	318	5	.	.	PROPN
cana-5235	318	6	wang	wang	PROPN
cana-5235	318	7	,	,	PUNCT
cana-5235	318	8	thin	thin	ADJ
cana-5235	318	9	film	film	NOUN
cana-5235	318	10	flowing	flow	VERB
cana-5235	318	11	down	down	ADP
cana-5235	318	12	a	a	DET
cana-5235	318	13	curved	curved	ADJ
cana-5235	318	14	surface	surface	NOUN
cana-5235	318	15	,	,	PUNCT
cana-5235	318	16	j.	j.	PROPN
cana-5235	318	17	appl	appl	PROPN
cana-5235	318	18	.	.	PROPN
cana-5235	318	19	math	math	PROPN
cana-5235	318	20	.	.	PUNCT
cana-5235	319	1	phys	phy	NOUN
cana-5235	319	2	.	.	PUNCT
cana-5235	319	3	,	,	PUNCT
cana-5235	319	4	35	35	NUM
cana-5235	319	5	(	(	PUNCT
cana-5235	319	6	1984	1984	NUM
cana-5235	319	7	)	)	PUNCT
cana-5235	319	8	,	,	PUNCT
cana-5235	319	9	532	532	NUM
cana-5235	319	10	-	-	SYM
cana-5235	319	11	544	544	NUM
cana-5235	319	12	.	.	PUNCT
cana-5235	320	1	communications	communication	NOUN
cana-5235	320	2	on	on	ADP
cana-5235	320	3	applied	apply	VERB
cana-5235	320	4	nonlinear	nonlinear	ADJ
cana-5235	320	5	analysis	analysis	NOUN
cana-5235	320	6	issn	issn	NOUN
cana-5235	320	7	:	:	PUNCT
cana-5235	320	8	1074	1074	NUM
cana-5235	320	9	-	-	PUNCT
cana-5235	320	10	133x	133x	NUM
cana-5235	320	11	vol	vol	VERB
cana-5235	320	12	32	32	NUM
cana-5235	320	13	no	no	NOUN
cana-5235	320	14	.	.	PUNCT
cana-5235	321	1	10s	10	NOUN
cana-5235	321	2	(	(	PUNCT
cana-5235	321	3	2025	2025	NUM
cana-5235	321	4	)	)	PUNCT
cana-5235	321	5	1337	1337	NUM
cana-5235	321	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5235	322	1	[	[	X
cana-5235	322	2	32	32	NUM
cana-5235	322	3	]	]	X
cana-5235	322	4	c.s	c.s	PROPN
cana-5235	322	5	.	.	PROPN
cana-5235	322	6	yih	yih	PROPN
cana-5235	322	7	,	,	PUNCT
cana-5235	322	8	stability	stability	NOUN
cana-5235	322	9	of	of	ADP
cana-5235	322	10	liquid	liquid	ADJ
cana-5235	322	11	flow	flow	NOUN
cana-5235	322	12	down	down	ADP
cana-5235	322	13	an	an	DET
cana-5235	322	14	inclined	inclined	ADJ
cana-5235	322	15	plane	plane	NOUN
cana-5235	322	16	,	,	PUNCT
cana-5235	322	17	world	world	NOUN
cana-5235	322	18	scientific	scientific	NOUN
cana-5235	322	19	,	,	PUNCT
cana-5235	322	20	(	(	PUNCT
cana-5235	322	21	1991	1991	NUM
cana-5235	322	22	)	)	PUNCT
cana-5235	322	23	,	,	PUNCT
cana-5235	322	24	357	357	NUM
cana-5235	322	25	-	-	SYM
cana-5235	322	26	370	370	NUM
cana-5235	322	27	.	.	PUNCT
cana-5235	323	1	[	[	X
cana-5235	323	2	33	33	NUM
cana-5235	323	3	]	]	PUNCT
cana-5235	323	4	c.	c.	PROPN
cana-5235	323	5	canuto	canuto	PROPN
cana-5235	323	6	,	,	PUNCT
cana-5235	323	7	m.	m.	PROPN
cana-5235	323	8	y.	y.	PROPN
cana-5235	323	9	hussaini	hussaini	PROPN
cana-5235	323	10	,	,	PUNCT
cana-5235	323	11	a.	a.	NOUN
cana-5235	323	12	quarteroni	quarteroni	NOUN
cana-5235	323	13	,	,	PUNCT
cana-5235	323	14	and	and	CCONJ
cana-5235	323	15	t.a	t.a	PROPN
cana-5235	323	16	.	.	PROPN
cana-5235	323	17	zang	zang	PROPN
cana-5235	323	18	,	,	PUNCT
cana-5235	323	19	spectral	spectral	ADJ
cana-5235	323	20	methods	method	NOUN
cana-5235	323	21	:	:	PUNCT
cana-5235	323	22	evolution	evolution	NOUN
cana-5235	323	23	to	to	ADP
cana-5235	323	24	complex	complex	ADJ
cana-5235	323	25	geometries	geometry	NOUN
cana-5235	323	26	and	and	CCONJ
cana-5235	323	27	applications	application	NOUN
cana-5235	323	28	to	to	ADP
cana-5235	323	29	fluid	fluid	ADJ
cana-5235	323	30	dynamics	dynamic	NOUN
cana-5235	323	31	.	.	PUNCT
cana-5235	324	1	springer	springer	NOUN
cana-5235	324	2	science	science	PROPN
cana-5235	324	3	and	and	CCONJ
cana-5235	324	4	business	business	NOUN
cana-5235	324	5	media	medium	NOUN
cana-5235	324	6	,	,	PUNCT
cana-5235	324	7	2007	2007	NUM
cana-5235	324	8	.	.	PUNCT
cana-5235	325	1	[	[	X
cana-5235	325	2	34	34	NUM
cana-5235	325	3	]	]	X
cana-5235	325	4	r.w	r.w	PROPN
cana-5235	325	5	.	.	PROPN
cana-5235	325	6	chin	chin	PROPN
cana-5235	325	7	,	,	PUNCT
cana-5235	325	8	f.h	f.h	PROPN
cana-5235	325	9	.	.	PROPN
cana-5235	325	10	abernath	abernath	PROPN
cana-5235	325	11	,	,	PUNCT
cana-5235	325	12	and	and	CCONJ
cana-5235	325	13	j.r	j.r	PROPN
cana-5235	325	14	.	.	PROPN
cana-5235	325	15	bertschy	bertschy	PROPN
cana-5235	325	16	,	,	PUNCT
cana-5235	325	17	gravity	gravity	NOUN
cana-5235	325	18	and	and	CCONJ
cana-5235	325	19	shear	shear	NOUN
cana-5235	325	20	wave	wave	NOUN
cana-5235	325	21	stability	stability	NOUN
cana-5235	325	22	of	of	ADP
cana-5235	325	23	free	free	ADJ
cana-5235	325	24	surface	surface	NOUN
cana-5235	325	25	flows	flow	NOUN
cana-5235	325	26	.	.	PUNCT
cana-5235	326	1	part	part	NOUN
cana-5235	326	2	1	1	NUM
cana-5235	326	3	.	.	PUNCT
cana-5235	326	4	numerical	numerical	PROPN
cana-5235	326	5	calculations	calculation	NOUN
cana-5235	326	6	.	.	PUNCT
cana-5235	327	1	j.	j.	PROPN
cana-5235	327	2	fluid	fluid	PROPN
cana-5235	327	3	mech	mech	NOUN
cana-5235	327	4	.	.	PUNCT
cana-5235	328	1	168	168	NUM
cana-5235	328	2	(	(	PUNCT
cana-5235	328	3	1986	1986	NUM
cana-5235	328	4	)	)	PUNCT
cana-5235	328	5	,	,	PUNCT
cana-5235	328	6	501–513	501–513	NUM
cana-5235	328	7	.	.	PUNCT