HUNGARIAN JOURNAL 
OF INDUSTRIAL CHEMISTRY 

VESZPREM 
Vol. 29. pp. 149- 154 (2001) 

RHEOLOGY OF ALUMINA SLIPS 

A. P APO * and L. PlANt* 

(Dipartimento di Scienze e Tecnologie Chimiche, Universita degli Studi di Udine, 
Via Cotonificio,108, 33100 Udine, ITALY) 

Received: October 31, 2001 

The aim of the present work is to study the rheological behaviour of concentrated aqueous alumina suspensions. Aqueous 
alumina suspensions were prepared at various solid contents (65 to 77.5 wt% ). Rheological tests were carried out at 
25±0.1°C by using the rate controlled coaxial cylinder viscometer Rotovisko-Haake 20, system M5-osc., measuring 
device SV2P with serrated surfaces. The tests were performed under both continuous and oscillatory flow conditions. All 
the suspensions studied show a rheological behaviour of the shear-thinning type; in addition. the presence of a yield stress 
is noticed. Some rheological equations of both 't=f( y ) and 11rf(<P, y ) type have been taken into consideration for 
describing the flow behaviour of the alumina slips investigated. A master-curve procedure was applied in order to give a 
compact representation of the flow curves drawn for the alumina suspensions examined. Finally, the effect of the addition 
of a dispersing agent (sodium polyphosphate) on the rheology of alumina slips was investigated and its optimum dosage 
was determined as well. 

Introduction 

For the preparation of ceramic suspensions by means of 
techniques such as slip casting and tape casting, 
submicron sized ceramic powders are needed. However, 
since very fine ceramic particles spontaneously 
agglomerate owing to attractive van der Waals forces, 
they must be dispersed in liquid phase using suitable 
dispersing agents. Moreover, different polymeric 
binders as well as processing aids are u~ually added to 
the suspension in order to obtain final products with the 
optimum properties. The mixing of dispersants, binders 
and processing aids greatly complicates the rheology of 
the system. 

Alumina is a material widely used in a lot of 
industrial applications which presuppose the presence of 
concentrated suspensions. In the light of what said 
above, the knowledge and control of the rheological 
properties of alumina suspensions is of paramount 
importance for improving both the production processes 
and the quality of final products. However, the rheology 
of concentrated alumina suspensions is very complex, it 
being dependent on several factors, which include solid 
content as well as particle morphology, size and size 
distribution, surface charge, presence of impurities, 
aggregation conditions; these latter are strongly 
influenced by the addition of dispersing agents and/or 
pii. Hence, concentrated alumina suspensions clearly 

show non-Newtonian flow characteristics as well as 
viscoelastic properties. 

This article is part of a research program which has 
been undertaken in order to thorougly characterise the 
rheological behaviour of alumina suspensions under 
both continuous and oscillatory flow conditions. 
Particular attention will be focused on the employment 
of deflocculants of different chemical nature and 
concentration. Here, the aim is to contribute deeper 
understanding of the applicability in continuous flow 
conditions of some rheological equations to alumina 
suspensions prepared at different solid content as well 
as to investigate their oscillawry shear behaviour and 
the effect of addition of a commercial dispersing agent 
on the flow characteristics of these materials. 

In the last years, several papers regarding the 
rheology of alumina suspensions have been published; 
here, mention is made of most papers [ 1-7]. 

Experimental Settion 

Materials employed 

Suspensions were prepared with a vane stirrer (Ultra~ 
Turrax TSO. Janke & Kunkel, IKA~Labortechnik) from 
deionized water and an alumina powder. whose 

Contact information: E-mail: *Adriano.Papo@dstc.uniud.it; **Luciano.Piani @dstc.uniud.it 



150 

Table 1 Description of the alumina powder employed 

Trade name: 

Purity: 
dso 
Particle size distribution: 
Density: 
Specific surface: 
Chemical composition: 

H.P. Alumina AKP-15, Sumitomo 
Chemical Co. Ltd. (Japan) 
99.99% 
0.68 ~m 
83 %< 1 ~m 
3.97 g/cm3 

3.8 m2/g 
Si=22 ppm; Na=5 ppm; Mg= 6 
ppm; Cu< 1 ppm; Fe= 19 ppm 

characteristics are reported in Table 1. Solid volume 
fractions varied in the range 0.319 to 0.464 (65 wt% to 
77.5 wt% of solid content). Solid contents higher than 
77.5 wt% were not taken into consideration owing to the 
very high viscosity of samples. A sodium polyphosphate 
(molecular weight=1733.39) by Aldrich-Sigma was 
selected as dispersing agent; different dispersant 
concentrations were considered, ranging from 0.01 to 
1.0 wt% as calculated on the alumina powder, solid dry 
weight basis. 

Apparatus and experimental procedure 

Rheological measurements were carried out using the 
rate controlled coaxial cylinder viscometer Rotovisko-
Haake 20. system M5-0sc., measuring device SV2P 
with serrated surfaces. Temperature was kept strictly 
constant at 25 ±0.1 °C. The tests were accomplished 
under both continuous and oscillatory flow conditions. 
Flow curves were achieved under continuous flow 
conditions by ascending shear rates ramps from 0 to 389 
s-1 at the constant shear ~cceleration of 6.49 s-2, after 
preshearing at a high constant shear rate carried out in 
order to suppress the previous rheological history of the 
sample tested; down curves from 389 to 0 s-1 at the 

constant deceleration of 6.49 s-2 were also determined. 
A 0.1 to 1 Hz frequency sweep with a 0.7 rad of 
constant strain was applied as oscillatory testing 
procedure, in the region of linear viscoelasticy, which 
was previously determined by applying a 0.2 to 1.3 rad 
strain sweep with a 0.1 Hz constant frequency. 

Results, Data Reduction and Discussion 

Cmztinuous flow tests 

Time~dependent effects under continuous shearing 
conditions were negligible with aU the alumina 
suspensions examined. A rather good superposition of 
up and down curves is obsen·ed in the whole range of 
particle concentration. Hence. in the present work 
attention has been essentially focused on the shear-
dependent behaviour of alumina suspensions. 

The shear stress vs. shear rate flow curves obtained 
for the alumina slips investigated are drawn in Fig./: it 
can be seen that all the alumina suspensions studied 

~00~======~------------------------~ 

't 

[Pa] 

2000 

1000 

"' 77.5wt% 
v 75wt% 
• 72.5wt% 
t>. 70wt% 
• 65wt% 

o+---~---.--~~--.---~---.--~--~ 0 100 200 300 y [s-1 ] 400 

Fig. I Shear stress ('t) vs. shear rate ( y ) flow curves for the 
alumina suspensions studied. 

show a rheological behaviour of the shear-thinning type; 
in addition, the presence of a yield stress is made 
evident. A great increase in viscosity is noticed by 
passing from 75 to 77.5 wt%. In order to obtain the 
most suitable equation for describing as well as 
predicting the rheological behaviour of alumina aqueous 
suspensions some models of the literature of both 
't=f( r ) and rtr=f( <I>' r ) type were taken into 
consideration. 

Models of the 'i=f( y) type 

Among the rheological models which correlate shear 
stress with shear rate, only the following literature 
equations which take into consideration the presence of 
yield stress were tested: 

The Bingham model 

(1) 

The Casson model 

't=='to+TJoo Y +2['t'o11oo]112y 112 (2) 
The generalized Casson model 

'tn='t'o n+[TJoo Y Jll (3) 
The Herschel-Bulkley model 

't='to+Ky n 

The Sisko modified model 

't='t'o+lloo Y +K Y n 

(4) 

(5) 

From a deep examination of Figs.2-5 the following 
general considerations can be put on: 

1) No satisfactory correlation with solid volume 
fraction can be noticed for the generalized Casson 
infinite viscosity; on the other hand, a distinct fitting 
was obtained by correlating with <P the lloo values 
determined with Eqn. {5) and using the sigmoidal 
Boltzman equation : 



Table 2 Standard deviations (STD) and coefficient of 
determination values.(COD) for the alumina suspensions 

studied 

Eqn.(l) 

Eqn.(2) 

Eqn.(3) 

Eqn.(4) 

Eqn.(5) 

SID 
COD. 
STD 

. COD 
STD 
COD 
STD 
COD 
STD 
COD 

Alumina concentration (wt%) 
65.0 70.0 72.5 75.0 77.5 
5.78 14.9 17.8 31.1 131 
0.982 0.955 0.965 0.976 0.807 
8.26 8.07 21.5 20.7 98.4 

0.963 0.987 0.950 0.989 0.892 
5.90 8.15 18.0 20.2 85.4 

0.982 0.987 0.966 0.990 0.922 
5.91 8.04 18.0 20.0 84.3 

0.982 0.988 0.966 0.991 0.924 
5.81 7.99 18.3 19.9 85.0 

0.983 0.988 0.966 0.991 0.924 

0.319 0.370 0.399 
<P 

0.430 0.464 

Fig.2 Yield stress (,;0 ) variation with solid volume fraction 

(<I>) for the alumina suspensions studied. 

~~ ~ Eqn.2 
[mPa.s] - Eqn. 3 

- Eqn.S 

0.319 0.370 0.399 
<P 

0.430 

Fig.3 Infinite viscosity (floc) variation with solid volume 

fraction (<I>) for the alumina suspensions studied. 

floo=A+(B-A)/(l+expi (<1>-<P')/d<P t) (6) 
The following values for the Boltzman parameters 
were determined: A::0.809; B=0.336; <P~=0.399; 
dt.P=3.05·104 ; STD=0.0768; COD:::::0.991. 

2) An irregular variation of the Herschel-Bulkley 
consistency with <P can be observed. 

3) An irregular variation with 4> can also be noticed for 
the n parameter of Eqn. (5). 

4) Very close 't
0 

values were obtained with Eqns. { 14). 

0.370 0.399 
cP 

0.430 

151 

0.464 

Fig.4 Consistency values (K) variation with soiid volume 
fraction (<1>) for the alumina suspensions studied. 

n 

0.1 

0.01 
0.319 0.370 0.399 

<P 

0 Eqn.3 
-Eqn.4 

- Eqn.5 

0.430 0.464 

Fig.S n parameter values variation with solid volume fraction 
(<P) for the alumina suspensions studied. 

5) Higher values of the Casson generalized '1 parameter 
were obtained with respect to those determined by 
Zupancic et al. in (2). 

As can be seen from an examination of both 
standard deviations estimates (STD) and determination 
coefficient values (COD), which are reported in Tabh 2. 
all the models considered gave a distinct fitting for all 
the slips investigated except for the most concentrated 
suspension. Obviously, a slightly superior fitting was 
achieved by applying Eqn. (5). it being a model with 
four adjustable parameters. In addition. as regards the 
choice of the most suitable model for application to 
alumina suspensions, no indication can be obtained by 
comparing experimental and calculated shear stress 
data. Hence, a final contribution to screening among the 
models proposed may be gained by considering another 
criterion of choice, i.e. that consisting of checking 
whether the parameters of the selected models can be 
assigned a physical meaning. Accordingly. the physical 
consistency of the yield value~ determined by fitting 
was checked by using the following equation; 

1:o=K'[{4Mf>o)/(4>m·«~>Hm {7) 

where ¢
0 

(percolation threshold) is the n1lume fraction 

corresponding to transition from the Newtonian or 
shear-thinning behaviour to the plastic one. i.e. the 



152 

Table 3 Parameters ofEqn. (7) 

Model K' q,Q <Pm m STD COD 
Eqn.(l) 284 0.170 0.496 0.769 32.1 0.999 
Eqn.(2) 256 0.183 0.487 0.648 37.7 0.998 
Eqn.(3) 291 0.116 0.563 1.01 82.2 0.980 
Eqn.(4) 330 0.144 0.565 1.03 82.3 0.984 
Eqn.(5) 10.4 0.264 0.602 4.73 4.16 0.989 

lower limit of the solid volume fraction at which the 
disperse phase behaves as a three-dimensional network 
structure~ and <Pm is the maximum volume fraction, i.e. 

that corresponding to the maximum particle packing in 
quiet conditions. Eqn. (7) has been already applied to 
alumina slips by Kristoffersson et al. in [1] and by 
Zupancic et al. in (2]. As can be seen in Table 3, data 
regression according Eqn. (7) gave the best fitting by 
using the 1:0 values given by Eqns. (1) and (2); 

moreover, both the Bingham and the Casson 1:0 
parameters can be assigned a physical meaning, in that a 
good agreement has been evaluated between the <Pm 

values calculated by means of Eqn. (7) and that 
experimentally determined by centrifugation 
(<Pm,exp=0.51). 

Very low values of <P0 with respect to the volume 

fraction of random particle packing <Prp, calculated 

equal to 0.64 in (8] for suspensions of monomodal non-
interactive hard spheres, denote the presence of strong 
attractive forces among particles, i.e. the formation of 
floes and/or clusters. The size distribution of the 
alumina particles used being hot monomodal, the <Prp 

should be slightly higher than 0.64. For the alumina 
suspensions investigated pecolation limit values lower 
than those found by Zupancic et al. in [2] were 
determined; this means that the formation of a three-
dimensional network can be expected at solid volume 
fractions considerably lower than <Prp=0.64. 

Models of the 1Jr =f(t1>, Y) t}'pe 

As far as the tlr =f(<P~ i ) rheological models are 
concerned only the Quemada equation [9-l I J in its first 
formulation was considered. This model, which is based 
on the dissipation energy by viscous friction, can be 
written as follows: 

.k=[ko +k00( y I y c}P}/{ l +( y I y c)P] (9} 
where k is an intrinsic viscosity with the limiting values 
Ito and too for very low and very high shear rates. 
respectively. y c is a critical shear rate, beyond which 
the disaggregation process of the disperse phase prevails 
over the aggregation one. and p is an empirical 
exponent .. lying in the range 0 to 1. The p quantity was 
tentath·ely associated by Quemada with particle shape 

Table 4 Variation of Quemada intrinsic viscosities ko and k.x. 
and critical shear rate y c with solid volume fraction 

q, ko koo r c (s-1) 
0.319 6.27 5.76 1790 
0.370 5.41 5.03 1220 
0.399 5.01 4.20 14700 
0.430 4.65 4.41 1710 
0.464 4.31 3.74 36400 

(p=O.S: asymmetric particles; p=l: symmetric particles); 
better, the p parameter should be connected to the shape 
of the minimum-dimension aggregates, present even at 
very high shear rates. By a previous linear regression on 
the four Quemada parameters, p values slightly superior 
to 0.5 were found, in accordance to the asymmetric 
shape of alumina particles. Accordingly, a new fitting 
was performed keeping p equal to 0.5. The application 
of the Quemada equation with three adjustable 
parameters provided very satisfactory results. As for the 
ko-«P dependence, the hyperbolic law k0 =2/<P was 

found; as for the koo-<P dependence, a satisfactory 

correlation was also found by using the law of 
hyperbolic type: k00=1.8/ci>. Accordingly, the Quemada 

equation becomes a model with only one adjustable 
parameters ( r c), which can be rewritten in this very 
simple form: 

fri: =10·(1+1/ .JY:) (10) 
where: 

(11) 

Accordingly, the Quemada model leads to the 
Casson one. The Quemada k

0
, koo and y c values are 

listed in Table 4: no regular variation of y c with <P has 
been noticed, even if their evident increase. with solid 
volume fraction is in fully agreement with its physical 
meaning. 

In the light of the above reported considerations, the 
Casson equation seems to be the most suitable model 
for correlating shear stress and shear rate data for the 
alumina slips investigated. 

Finally, in order to give a compact representation of 
the flow behaviour of the individual members for the 
alumina suspensions family a master-curve was traced. 
The master-curve of reduced viscosity, 11R• vs. reduced 
shear stress, 'tR, is shown in Fig.6. For the alumina 
suspensions family considered the flow curve at «P 
=0.319 was assumed as reference curve; reduced 
variables are defined as fol1ows: 

11R=anrt tR=ar't (12) 

Shift factors a11 and a. were evaluated starting from the 
'to and T}~e values determined by fitting the experimental 
data with the Casson equation. So, they are defined as: 

(13) 

Where: 



65.0 
1.00 
1.00 

Table 5 Shift factors 

Alumina concentration (wt%) 
70.0 72.5 75.0 77.5 

0.712 0.473 0.350 0.176 
0.549 0.471 0.150 0.136 

100.,..---------------------. 

llR 
[Pa-s] 

10 

"Y 77.5 wt"/o 
v 75 wt% 
• 72.5wt% 
A 70wt% 
• 65wt% 

0,1 +------.-----.----...---.--.--.,..-...,-......--j 
100 'tR [Pa} 1000 

Fig.6 Reduced viscosity (YJR) vs. reduced shear stress master-

curve for the alumina slips investigated. 

1~0~--------------------~ 

G',G" 
[Pa] 

1000 

• 
0 ,. •••••••••••••••••• 

ooooooooo 
• oooooo 00 o 0 

¢··················· ¢ ¢ ¢ 0 0 
00 ¢ 0 oooo 

0 77.5wt% 
o 72.5wt% 
0 65wt% 

ro [s·1J 

¢<> 0 o¢o 

10 

Fig.7 Storage (G') and loss (G") moduli variation with angular 
velocity (m) for some of the alumina suspensions studied.(0.7 

rad of constant strain). 

1l"",ref and 'to,ref are the Casson parameters of the 
reference curve ( ci> =0.319), whereas r}oo,<P and 
't"o,cll are the corresponding parameters of the 
suspension at ci> solid volume fraction. 

Shift factors al} and ar are reported in Table 5. 

Oscillatory tests 

It can be observed that dynamic viscosity always 
decreases monotonically with frequency for all the 
alumina slips investigated. An inspection of the 
mechanical spectra determined for the alumina slips 
formulated without deflocculant, i.e. the plots of storage 
(G') and loss (G") moduli vs. angular velocity, shows 
that G" is always greater than G'; hence, one can state 

153 

"" <> 0.03wt% 

A 
A 

"" A 0.05wl"k 
""" • 0.10wt"k 

10000 At:. 
"" ....... , ., ... 1.00 wt% 

., ".,"., "".,.., ".,.., 
AAI:.A 

A I:.AA A A 1:. A A A A A A A 6 A A A 

10 +o---.----1~00--~--200r--.,..---3~00~-Y-. ~[-s·-1)~400 

Fig.8 Apparent viscosity (YJ) vs. shear rate ( y ) tlow curves 
for the 77.5 wt% alumina+ sodium polyphosphate 

suspensions studied. 

100 

lJ,'l]' 
[Pa·s} rt' n 

--•- -o--
10 

1 

0.1 

0.01 
0.005 0.01 

Fig.9 Apparent (YJ) and dynamic (T} ') viscosit;. -. ~ 

deflocculant concentration ( y =200s- 1 ;m =2s · 1 ). 

that no gel-like to sol-like transition occurred over the 
all frequency sweep explored. In addition, it results that 
both G' and G" are nearly independent of ro within the 
whole frequency range investigated. An example of 
both G' and G" variation with angular velocity i ~ 
reported in Fig. 7. 

Effect of deflocculant addition 

Figure 8 reports the apparent viscosity vs. ~hear. rate 
flow curves obtained for the 77.5 wt% alumma shp to 
which a sodium polyphosphate was added as dispersing 
agent. From an examination of Fig.B a shear"thinning 
behaviour is registered within an the defloccu~ant 
concentration range examined: hence. sod1um 
polyphosphate behaves in a different manner than in 
kaolin suspensions~ where its presence mv,Jives a 
dilatant behaviour beyond a critical concentrat1''" t 121. 
In addition. a viscosity collapse is made ev1dcnt by 
adding a 0.01 wt% of deflocculant and pa~~u1~ from 
0.01 to 0.03 wt% as welt Final!;. by exam~nmg t~e 
results shown in Figs. 9 and 10 th~ optimum d<)sage_ :~;r 
sodium polyphosphate was determmed for cd:::::0.05 \\:t •c · 



154 

1000~------------------------------~ 
G',G• 

[Pa} 

100 

10 

0.1 -l-.....------.-................. .......---r--..--..-r-T'.........,r---..-~"T"""5 
o.oos om 0.1 cd [wt%J 

Fig./0 Storage (G•) and loss (G'') moduli vs. deflocculant 
concentration (<O =2s'1). 

Conclusions 

As far as the rheological models of the -t=f( i ) type are 
concerned, the Casson model proved to be the most 
suitable to describe the flow behaviour of alumina 
concentrated suspensions in the shear rate range 
explored and for any alumina concentration examined 
as well. As for the rheological models of the 11r=f( c!>, i ) 
type~ the Quemada model gave satisfactory results, it 
reducing to the Casson equation for the alumina slips 
investigated; in addition. the Quemada p parameter can 
be associated tb the asymmetric shape of aggregates. 
The application of oscillatory techniques did not prove 
the existence of a gel-like to sol-like transition. Finally, 
the optimum dosage for a sodium polyphosphate 
employed as dispersing agent was determined by means 
of rheological techniques. 

SYMBOLS 

a11, ar Shift factors 
A, B, dcp Parameters ofEqn. (6) 

Deflocculant concentration, wt% 

G' 
a·~ 

Determination coefficient values 
Storage modulus. Pa 
Loss modulus, Pa 

k 
ko 

Parameter of the Quemada equation 
Quemada intrinsic viscosity for a very low 
shear rate 

. 
koo Quemada intrinsic viscosity for a very high 

shear rate 
K Consistency in Eqns. ( 4*5) 
K' Constant in Eqn. (7) 
m Exponent in Eqn. (7) 
n Exponent in Eqns. (3~5) 
p Exponent in the Quemada equation 
STD Standard deviations estimates 

Greek letters 

y Shear rate, s - 1 
y c Critical shear rate in the Quemada equation." s-1 
Y r Reduced shear rate in Eqn. (11) 

q, Solid (nominal) volume fraction 
cj>' Parameter ofEqn. (6) 
n. Effective volume fraction 'l'eff 
ci> 

0 
Percolation threshold [see Eqn. (7)] 

Maximum solid volume fraction 

Volume fraction of random particle packing 

Apparent viscosity, mPa·s 
Dynamic viscosity, Pa·s 

Plastic viscosity [see Eqn. (1)], Pa·s 
Relative viscosity 

Reduced viscosity , Pa s 

Viscosity at infinite shear rate, mPa·s 

Shear stress, Pa 
Yield value, Pa 

Reduced shear stress, Pa 

Angular velocity, s-1 

REFERENCES 

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8. PUGH R. J. and BERGSTROM L. (eds.): "Rheology of 
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9. QUEMADA D.: Rheol. Acta, 1977, 16, 82-94 
10. QUEMADA D.: Rheol. Acta, 1978., 17,632-642 
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