Layout 6
1
ANNALS OF GEOPHYSICS, 62, 2, VO216, 2019; doi: 10.4401/ag-7859
“ADVANCES IN THE RHEOLOGY OF NATURAL MULTIPHASE SILICATE MELTS: IMPORTANCE FOR MAGMA TRANSPORT AND LAVA FLOW
EMPLACEMENT„
Daniele Giordano*,1,2,3
(1) Università degli Studi di Torino, Dipartimento di Scienze della Terra, Torino, Italy
(2) Istituto Nazionale di Geofisica e Vulcanologia−Sezione di Pisa, Pisa, Italy
(3) Institute of Geoscience and Earth Resources (IGG−CNR), Italian National Research Council (CNR), Pisa, Italy
1. INTRODUCTION
The transport of magmas and volcanic materials is
characterized by very dynamic, interdependent and com−
plex, physical and chemical processes that all are affected
by and affect the materials physical properties. Under−
standing the dynamic processes operating during magma
ascent and eruption and the timescales and mechanisms
of emplacement, welding and remobilization of frag−
mental or massive volcanic deposits, constitutes one of
the main challenges in the Earth sciences [Dingwell,
1996; Papale, 1999; Sparks, 2004; Russell and Quane,
2005; Giordano et al., 2005]. Accurate description of
these processes requires the characterization of a wide
range of transport and thermodynamic properties for the
melt or magma (e.g. viscosity, density, enthalpy, entropy,
heat capacity, thermal conductivity, solubility of volatile
phases). These properties play crucial roles at micro− to
macroscopic scale and many are correlated, in a non−lin−
ear manner [e.g. Richet et al., 1984; Giordano et al.,
2008a; Russell and Giordano, 2017].
Lava flow dynamics are strongly governed by sub−
surface buoyancy forces, resulting from the density con−
trast with the host rock, which push the magma toward
the surface [e.g. Wilson and Head, 2016a; Wieczorek et al.,
2001] and by the evolving internal and external frictional
forces (e.g. with dyke, conduit wall and topography) that
oppose to the movement of magmas and lavas [e.g.
Nemeth, 2010; Cañón−Tapia, 2016, Dragoni, 1993; Drag−
oni et al., 2005; Giordano et al., 2007; Cashman et al.,
2013; Kolzenburg et al., 2016a,b; 2018a,b; Hulme, 1974;
Hiesinger et al., 2007; Chevrel et al., 2013, 2015; Cas−
truccio et al., 2014].
The rheological properties of magmas undergo
tremendous changes from transport in the subsurface to
eruption or emplacement at the surface and to final de−
Article history
Receveid July 17, 2018; accepted March 18, 2019.
Subject classification:
Multicomponent and Multiphase silicate melts; Rheology.
ABSTRACT
A review of recent advances in the field of rheology of multicomponent silicate melts and multiphase silicate melt and multiphase silicate
melt and analogue material suspensions is presented. is presented here. The advances include the development of new experimental de−
vices and field and remote sensing methods for measuring the rheological properties of natural melts and magmas as well as new mod−
elling strategies. These promising approaches combine laboratory experiments, theoretical models, numerical simulations and remote sens−
ing data derived from ground, airborne and satellite−based tools. Each of these sub−disciplines has evolved rapidly in recent years and
the growing range of complementary data appears now to provide an opportunity for the development of multi−disciplinary research. Ul−
timately, these multidisciplinary initiatives seek to provide near−real−time forecasting of hazardous volcanic processes such as lava flow
field evolution. The results and approaches described here focus on multiphase (i.e. melts, bubbles, crystals) rheology of natural systems
and are pertinent to the effusive emplacement of lavas, dykes and sills, as well as, to the eruption dynamics attending explosive eruptions.
position and cooling. These changes are caused domi−
nantly by the evolving of thermo−chemical and defor−
mational conditions, imposing phase transitions and
therewith heterogeneous textural and morphological
variations of the magmatic and volcanic suspensions
which evolve in space and time. The complex rheologi−
cal evolution of lava flows can tentatively be constrained
by carrying out laboratory measurements under con−
trolled conditions, simulating natural systems, and by
monitoring flow emplacement at the field−scale and via
satellite−based platforms. In parallel with this, the so−
phistication of physical models of lava flows and domes
have improved significantly and are capable of provid−
ing fast simulations [see, amongst the others, Costa and
Macedonio, 2003, 2005; Del Negro et al., 2008, 2013,
2016; Melnik and Sparks, 1999, 2005; Melnik et al.,
2009; Kilburn 2015 for reviews on this topic]. These
models are increasingly informed by, or validated by,
satellite−derived parameters such as lava flow discharge
rate or periodic updates on flow advance/geometry. To−
gether these capabilities represent an emergent strategy
that may provide timely reliable projections of lava flow
field evolution and derive information for hazard assess−
ment and mitigation measures. Yet, to date they do not
always provide coherent results reproduced in nature.
This highlights the necessity to estimate the rheolog−
ical properties of magmas and volcanic materials at con−
ditions pertinent to nature and to investigate the effect of
each variable over the range of relevant environmental
conditions (e.g. pressure, temperature, volatile contents)
during varying thermodynamic (equilibrium and non−
equilibrium) conditions, and deformation regimes.
Our understanding of the single− and multi−phase
(liquid+crystals+bubbles) rheology of magmas and vol−
canic products has greatly improved in the last two
decades. This can largely be attributed to the growing
availability of empirical data from the following sources
(each of which will be reviewed in detail below):
1) laboratory experimentation on natural and simpli−
fied silicate melts. These data support the creation
of robust models for predicting the Newtonian vis−
cosity of pure liquid natural melts as a function of
temperature (T), pressure (P) composition (X),
volatile content (Xv) and structural features (see
Chapter 2).
2) the rheological experimentation and modelling of
non−reactive multiphase suspensions (liquid+bub−
bles; liquid+crystal and liquids+bubbles+crystals)
constituted by analogue materials or simplified or
natural silicate melts mixtures (Chapter 4);
3) dynamic cooling rheological measurements on nat−
ural multiphase suspensions at non−isothermal and
non−equilibrium conditions to explore the interde−
pendent effects of composition, cooling−rate, shear−
rate and oxygen fugacity acting during magma
and lava transport in nature (Chapter 5);
4) rheological measurements of actively flowing lava.
These represent snapshots of actual lava flow rheol−
ogy at specific conditions and provide data that helps
to constrain the conditions required to be reproduced
in systematic laboratory studies (Chapter 6).
5) studies on the 3D and 4D evolution of lava flows at
increasing spatial and temporal resolution and con−
temporary estimates of effusion rate and flow de−
velopment from satellite data. These provide data
for cross correlation and benchmarking of labora−
tory measurements (Appendix A1) and to re−visit
long standing methods for deriving rheological pa−
rameters from morphologic data (Chapter 6).
These studies document that the effective viscosity of
natural silicate melts and magmas can span more than 15
orders of magnitude (10 1 – 1014 Pa s), primarily in re−
sponse to variations in melt composition (X), dissolved
volatile content (Xv), temperature (T), pressure (P), as well
as the proportions, size, and shape distributions of sus−
pended solid and/or exsolved fluid phases (i.e. crystals and
bubbles). The deformation rate, which in nature would
depend on the discharge rate will determine whether
flow behavior will be Newtonian (i.e. one for which there
is a linear relationship between stress and strain rate; or
spatial variation of velocity) or non−Newtonian [e.g.
Caricchi et al., 2007, 2008; Costa et al., 2007a, 2009; Vona
et al., 2011; Hess et al., 2009]. Deformation rate also ex−
erts an influence on the crystallization kinetics [Vona et
al., 2013; Kouchi, 1986; Kolzenburg, 2018]. It may fur−
ther determine whether the melt will deform viscously or
elastically and, therewith, whether or not it will eventu−
ally fracture giving origin to effusive rather than explo−
sive eruptive styles [Dingwell, 1996]. Combined the above
experimental data and computational models form a ba−
sis from which to understand the flow behavior of nat−
ural magmatic and volcanic suspensions.
In the following I present a review of the research ad−
vances in the rheological characterization of pure silicate
melts and multiphase silicate mixtures (i.e. lavas and
magmas) achieved in the past decades. I follow the struc−
ture of points 1−5 outlined above to group the individ−
ual fields. In the Appendices (A1−A3) I summarize the
Daniele GIORDANO
2
most commonly employed experimental devices and
technological advances to measure the single and mul−
tiphase silicate melts also reporting the most common
equations used to describe the viscosity variation as a
function of P, T, X (Appendix A1) as well as suspended
solids phase and/or porosity (Appendices A2 and A3). I
conclude with a discussion on how new laboratory de−
velopments together with the growth in complementary
datasets (e.g. remote−sensing; drone technology; high−
speed calculation facility) is providing greater under−
standing of magma and lava transport on Earth.
2. PURE LIQUID MELT NEWTONIAN VISCOSITY
EXPERIMENTS AND MODELS
2.1 T – DEPENDENT MODELS FOR PREDICTING MELT
VISCOSITY
The first step toward characterizing multiphase rhe−
ology of natural silicate melts mixture is the knowledge
of multicomponent viscosity of pure liquids as a function
of their composition (including dissolved volatile species
such as H2O, C and S –species, F, Cl) temperature (T) and
pressure (P). Early models for predicting the viscosity of
silicate melts were developed using data that spanned rel−
atively small ranges of temperature (T) and viscosity (η).
These experimental data, restricted to superliquidus tem−
peratures and a narrow compositional range, showed a
nearly linear trend of viscosity in reciprocal temperature
space. Thus, early models adopted an Arrhenian formu−
lation of the temperature−viscosity relationship [Shaw,
1972; Bottinga and Weill, 1972]. Expansion of the melt
viscometry database over a wider range of compositions
and temperatures exposed the limitations of Arrhenian
models. With the emergence of viscometry data closer to
the glass transition temperature (Tg) (i.e. the temperature
of transition between a liquid−like and a solid−like be−
havior) [e.g. Angell, 1991, Giordano et al., 2005], the Ar−
rhenian models proved unsuitable to describe the tem−
perature dependence of silicate melt viscosity. These
measurements were enabled by experimental devices that
allow very small displacements to be monitored (e.g.
Linear Voltage Displacement Transducers) and, the pro−
duction of quenched glasses, freezing in the crystal free
melt structure. In these experiments, supercooled glasses
are reheated above Tg, where the “relaxed melt” viscos−
ity [e.g. Angell, 1991; Scherer, 1984] could then be mea−
sured. These experiments are performed at timescales
shorter than phase transitions timescale, therewith al−
lowing anhydrous and hydrous pure liquid viscosity
measurements [Angell, 1991; Scherer, 1984; Giordano et
al., 2008b].
Based on the large number of experimental studies
[e.g. Richet et al., 1995, 1996; Hess and Dingwell, 1996;
Whittington et al., 2000, 2001; Giordano et al., 2009
amongst the others], models of melt viscosity were de−
veloped [e.g. Avramov, 1998; Angell, 1991; Russell et al.,
2003; Giordano and Dingwell, 2003a, b; Russell and
Giordano, 2005; Giordano and Russell, 2007; Hui and
Zhang, 2007; Giordano et al., 2006, 2008a,b; Ardia et al.,
2008; Mauro et al., 2009], also accounting for the non−
Arrhenian viscosity behaviour [e.g. Vogel, 1921, Fulcher,
3
ADVANCES IN RHEOLOGY: APPLICATION TO LAVA FLOWS EMPLACEMENT
FIGURE 1. The figure shows the variation of viscosity as a function of the reverse of temperature for the anhydrous melts (a) and,
per comparison, the anhydrous and hydrous melts (b) as reported by Giordano et al. (2008). The curves in a) represent
the most Arrhenian (continuous line in a))(strong) and the least Arrhenian (dashed curve in a)) (fragile) melts amongst
those reported in panel of Figure 1a. The effect of water is that of significantly reducing viscosity and the fragility (de−
viation from Arrhenian behavior) of the melts [details in Giordano et al., 2008].
Daniele GIORDANO
4
1925; Tammann and Hess, 1926; Adam and Gibbs, 1965].
These models describe the P−T−X dependence of the
viscosity of silicate melts. Some of the most relevant em−
pirical and theoretical formulations describing the T−
dependence of silicate melts and the relationships between
constitutive parameters are reported in Appendix A2.
The growing database and the new models show that
silicate melts display various degrees of non−Arrhenian
behavior, from strong to fragile [Angell, 1991; Russell et
al., 2002, 2003], which depend on composition and dis−
solved volatile content (Figure 1).
All these models provide viscosity predictions based on
composition commonly expressed in terms of oxide
abundances or combination of oxides and a range of ad−
justable parameters. Of the various models only the HZ
model [Hui and Zhang, 2007] and the GRD model [Gior−
dano et al., 2008a] accounts for the effects of dissolved
volatile species (H2O, F). The GRD model is based on the
well−known VFT (Vogel−Fulcher−Tammann) equation,
such that:
log [η (Pa s)] = AVFT+BVFT/(T−CVFT) (1)
where AVFT is the pre−exponential factor, BVFT is the pseu−
do−activation energy and CVFT is the VFT−temperature.
In contrast the HZ model uses a purely empirical T−de−
pendent viscosity formulation of non straightforward cor−
relation with thermo−physical amounts. The GRD mod−
el has gained support due to its simplicity and direct cor−
relation of constitutive parameters (i.e. Appendix A2) to
others important physical and structural properties such
as the glass transition (Tg), the fragility (m) (i.e. the rate
at which viscosity varies with temperature, that is an in−
dication of melts capacity to store energy), the calorimetric
properties (configurational entropy, Sconf and the config−
urational heat capacity Cp
conf; see Equation A2.4) [e.g. Gior−
dano and Dingwell, 2003a; Giordano et al., 2008b;
Chevrel et al., 2013; Giordano and Russell, 2017; Russell
and Giordano, 2017] and the structural properties (e.g. Qn−
species and Raman Ratio) [i.e. Le Losq and Neuville, 2017;
Giordano and Russell, 2018; Giordano et al., 2019]. These
models show that, to a first approximation, the viscosi−
ty of silicate melts and the descriptive parameters of Equa−
tion 1) can be correlated at constant temperature to em−
pirical, composition−based pseudo−structural parameter
(i.e. the SM − structural modifiers − and the NBO/T − i.e.
the Non Bridging Oxygen over Tetrahedra − parameters).
The NBO/T and SM parameters are commonly assumed as
proxies for the degree of polymerization of silicate melts
and glasses [e.g Giordano and Dingwell, 2003a, b; Gior−
dano and Russell, 2018; Giordano et al., 2019] (Figures 2,3).
Compositions with low values of the SM−parameter (or
low NBO/T values) are associated to strong (Arrhenian−
like) rheological behavior, i.e. a linear behavior in the logη−
1/T space, and more polymerized melts. On the other hand
high values of SM (or high NBO/Ts) are related to more
depolymerized melts which show fragile rheological be−
havior (i.e. the logη vs 1/T paths are significantly non−
linear) [e.g. Angell, 1991; Giordano and Dingwell, 2003]
(Figures 1,2). Russell et al. [2003], in agreement with ear−
ly theoretical studies [e.g. Angell, 1991 amongst others],
showed that the pre−exponential factor of the VFT and
AG formulations, i.e. the viscosity at infinite temperature
(Appendix A2), is a constant independent of compositions
[Russell et al., 2003; Giordano et al., 2008a]. In addition,
approximately 1 logunit distinguishes the AVFT and the
AAG values. The current models are applicable within the
compositional space that they are based upon, but some
compositional regions (e.g. peralkaline compositions)
still remain unmapped and the models struggle to repro−
duce measured viscosity values [Giordano et al., 2006,
2008a, Di Genova et al., 2017]. Those formulations also
put in evidence that the role of water (H2O) dissolved in
the melt is counterintuitive being opposite to that of net−
work modifier cations. In fact, although dissolved H2O
strongly decreases the viscosity of silicate melts (Figure
1b), the parameters describing the T−dependence of vis−
cosity (e.g. BVFT and CVFT in Equation 1) are differently af−
fected by H2O and by the most common structure mod−
ifiers (Figure 2).
2.2 P – DEPENDENT MODELS FOR PREDICTING MELT
VISCOSITY
Measuring the effect of pressure (P) on the viscosity
of melts is a complex experimental task and, as a result,
has not been investigated extensively. A short summa−
ry of applied techniques and technological advances is
reported in Appendix A1, together with some of the main
results. Largely, and oppositely to silica−rich melts, the
viscosity of silica−poor melts increases as pressure in−
creases [Liebske et al., 2005; Ardia et al., 2008 and ref−
erences therein]. However, the available data suggest that
the effect of P is negligible at near surface conditions per−
tinent to explosive and effusive volcanism. As a con−
sequence this effect will not be discussed any further in
this contribution. Figure A2.1 shows for the Ab−Di sys−
tem what is the effect of P which changing composition
in the binary system, by using fitting procedure as adopt−
5
ADVANCES IN RHEOLOGY: APPLICATION TO LAVA FLOWS EMPLACEMENT
ed by Ardia et al. [2008]. This system is considered to
show what is the effect of P on polymerized (Ab) to de−
polymerized (Di) synthetic compositions from low to high
P. Similar behaviours is expected for natural composi−
tions, but, as shown by previous authors [e.g. Giordano
et al., 2008b; Chevrel et al., 2013; Whittington et al.,
2009], simplified systems (e.g. An, Di, Ab) should not be
considered as proxies for natural compositions.
2.3 TOWARD A STRUCTURAL MODEL FOR GEOLOGICAL
MELTS
More recently, Le Losq and Neuville [2017], Giordano
and Russell [2018] and Giordano et al. [2019], following
different approaches, showed that the viscosity of sim−
ple and multicomponent anhydrous silicate melts over a
temperature interval of ~ 700 to 1600°C, can be predicted
from the Raman spectra obtained from the correspond−
ing glasses (i.e. fast quenched melts). These methods
prove to be very promising methods for in situ rheolog−
ical investigations and may have great importance for
planetary sciences studies [Angel et al., 2012; Giordano
and Russell, 2018]. Le Losq and Neuville [2017] developed
a 13 − parameters model for melt viscosity in the simple
system SiO2−Na2O−K2O which connects the transport
and thermodynamic properties of these simple melts ex−
plicitly to the structural state of the melt expressed via the
FIGURE 2. Relationships between constitutive parameters of the GRD model (Giordano et al., 2008), based on the VFT formulation
(Equation 1), as a function of the modified SM (Structure Modifiers) parameter (Giordano and Dingwell, 2003). The role
of increasing SM on the constitutive parameters of anhydrous melts (black symbols) is that of decreasing BVFT and in−
creasing CVFT (Figure 2a, b) while increasing the fragility (m) (Figure 2e). On the other hand adding H2O to the melt struc−
ture (gray symbols) results in decreasing BVFT while decreasing CVFT , the glass transition temperature Tg (as taken at a
viscosity of 1012 Pas) (Figure 2d) and the fragility (m). This observation put in evidence that the structural role of H2O
is different from that of those cations which simply modify silicate melts structure (Giordano et al., 2008, 2009).
abundances of Qn −species recovered from Raman spec−
tral analysis of the glasses. Giordano and Russell [2018]
first and Giordano et al. [2019], later, the presented a first
order model predicting the viscosity of multicomponent
natural melts by the employment of the so−called Raman
ratio (R) [Giordano and Russell, 2018] and normalized Ra−
man ratio (Rn) [Giordano et al., 2019] derived by Raman
spectra measured on the corresponding glasses as defined
by Mercier et al. [2009, 2010]. As shown in Figure 3 a
strong relationship exists between BVFT and CVFT param−
eters and R which allows the viscosity of anhydrous
multicomponent natural melts to be predicted with a
great accuracy. Although, the model requires expansion
to use of the structural information of volatile−bearing
melts, it allows accurate description of the viscosity of
anhydrous melts by the employment of a simple equa−
tion with 6 adjustable parameters and the measured R.
Also the SM and NBO/T parameters, calculated from
compositions, are shown to be strongly correlated with R.
3. FROM PURE LIQUIDS TO MULTIPHASE ANA-
LOGUES AND MAGMAS: ADVANTAGES AND
DISADVANTAGES OF THE DIFFERENT EXPER-
IMENTAL APPROACHES
Being magmas and volcanic materials complex,
texturally evolving (reactive) mixtures of crystals and
vesicles suspended in a silicate melt phase which
evolve as a function of the evolving P, T and compo−
sitional variations and dynamic regimes, the descrip−
tion of effect of suspended phases on the viscosity of
these natural suspensions has followed different ap−
proaches. The early models devoted to describe the
multiphase rheology were historically based on the in−
vestigation of analogue materials [e.g. Einstein, 1906;
Einstein and Roscoe, 1952]. More recently, the basis for
the description of natural multiphase suspensions has
been largely developed using natural and simplified
silicate melts mixtures at experimental conditions at
around thermodynamic equilibrium [e.g. Campagnola
et al., 2016; Chevrel et al., 2015; Robert et al., 2014;
Sehlke et al., 2014; Soldati et al., 2016; Vona and Ro−
mano, 2013; Vona et al., 2011, 2013]. As such, their ap−
plication to natural environments requires extrapola−
tion into the thermal and deformational disequilibrium
state at which magmatic and volcanic processes com−
monly operate. This is only possible to a limited ex−
tent, as natural magmatic and volcanic processes of−
ten operate quite far from equilibrium. Recent studies
on the disequilibrium rheology of crystallizing natu−
ral silicate melts have documented that deformation−
rate and cooling−rate may significantly affect the
phase transitions of magmatic mixtures so to forcing
the material toward a thermal and mechanical dise−
Daniele GIORDANO
6
FIGURE3. Model VFT parameters BVFT (R)(A) and CVFT (R)(B) as
defined by Giordano and Russell (2018) (panels A, B)
and relationships between pseudo−structural parame−
ters (SM, NBO/T)(C), as a function of the Raman ratio
(R). According to the above mentioned authors:
BVFT (R) = b1R
b2 and CVFT (R)=c1R
c2+c3 where b1, b2,
c1, c2, c3 are adjustable parameters.
quilibrium state [e.g. Giordano et al., 2007; Kolzenburg
et al., 2016, 2017a, b; 2018a,b; Arzilli and Carroll,
2013].
Following, the experimental efforts aimed at re−
trieving information of the multiphase rheology of
natural silicate mixtures have been broadly summa−
rized by subdividing it into, experiments on non reac−
tive materials (Chapter 4) or reactive silicate melts
mixtures undergoing variable thermal or deforma−
tional variation (Chapter 5). These kinds of experiments
can be further subdivided into three main categories:
a) experimentation on analogue materials; b) experi−
ments on simplified silicate mixtures and c) experi−
ments on natural volcanic products. Each of these ex−
perimental approaches has different
advantages/disadvantages which are listed below.
3.1 ANALOGUE MATERIALS
Multiphase analogue materials are commonly con−
stituted by non−reactive mixtures of mono− or poly−
disperse particles and/or bubbles, with varying content
and shape and size distributions, immersed in some
Newtonian synthetic fluid (e.g. silicon oil, syrup, liq−
uid paraffin), which can be investigated at room tem−
perature. These multiphase mixtures can normally be
investigated at room temperature conditions and
therefore their rheological characterization is simpli−
fied as it does not involve the need for high tempera−
ture or pressure equipment and the sample texture
can readily be controlled (e.g. the solid/bubble pro−
portion or variation). These kinds of experiments are
commonly performed on transparent multiphase mix−
tures and therefore allow observing and characteriz−
ing strain partitioning processes occurring amongst the
phases during the deformation. The main disadvantage
of this kind of experimentation is that it cannot re−
produce neither the transient disequilibrium processes
occurring in natural mixtures (e.g. crystallization or
degassing stages) nor the natural dynamic physical
properties of silicate melts (e.g. viscous and cohesive
forces between the natural residual melt and sus−
pended particles and bubbles). The largest part of these
studies investigate two phase suspensions of either
liquid and solid particles (simulating crystal bearing
magma) or liquid and bubbles or vesicles (simulating
the exsolution of volatile gases).
3.2 MULTIPHASE SILICATE MELT SUSPENSIONS
The experiments of categories b) and c), above men−
tioned, require significantly more complex experimental
infrastructure and are substantially more complex to be
characterized in terms of textural parameters (crystal and
bubble content; crystals and bubbles size and shape dis−
tributions) but they offer the opportunity to perform
measurements on materials with direct application to
the Earth Sciences. The inherent inhomogeneity of geo−
materials and the large variations of the size– and
shape−distributions found in natural products can, to
date, not be captured in a satisfactory manner by the
available theoretical or empirical models. Experiments
on natural materials at controlled conditions have the
advantage of being representative of natural scenar−
ios and, in most cases, they allow retrieving, at least,
the final stage of textural evolution as a function of the
imposed environmental conditions (i.e. isothermal;
non−isothermal; isobaric; non−isobaric) as well as
varying deformation regimes (i.e. constant or varying
stress and/or strain rate). This allows the reconstruc−
tion of the rheological parameters in a tightly con−
strained parameter space, however it requires unique
experimental characterization for each studied sce−
nario. When volatile free samples are investigated,
this kind of experiments can be performed, using a va−
riety of experimental techniques (e.g. rotational con−
centric cylinder/Patterson deformation rig and uniax−
ial compression and/or micropenetration and parallel
plates techniques; see Appendix A1 for details), over
the entire temperature−viscosity interval from super−
to sub−liquidus conditions that are characteristic of
natural environments. For volatile−bearing natural
melts and suspensions, this becomes more complex as
limited experimental infrastructures exist to date to
measure at the elevated pressures required to maintain
volatiles in solution. There have been some recent ad−
vances which take advantage of the metastable liquid
state close to Tg or by using devices which allow the
sample to be pressurized [Paterson, 1978; Paterson
and Olgaard, 2000; Caricchi et al., 2007; 2008; Ardia
et al., 2008; Robert et al., 2008a, b; Piermarini et al.,
1978]. A further advancement is the 4D characteriza−
tion of the sub liquidus evolution of natural melts is
represented by experiments within synchrotron facil−
ities which allow real time monitoring of the textural
evolution of samples of volcanological interest during
crystallization and/or degassing [e.g. Ohtani et al.,
2005; Pistone et al., 2015; Pleše et al., 2018; Polacci et
al., 2018; Polacci et al., 2010; Song et al., 2001]. These
techniques are starting to be coupled with devices for
7
ADVANCES IN RHEOLOGY: APPLICATION TO LAVA FLOWS EMPLACEMENT
rheometry, which may in the future allow for in situ es−
timates of both the crystallization kinetics and the rhe−
ological response of evolving natural systems [Coats
et al., 2017; Dobson et al., 2015; Dobson et al., 2016;
Raterron and Merkel, 2009]. The results of experi−
mental campaigns and modelling of the multiphase
rheology of natural magmatic suspensions performed
on natural or analogue silicate melts at high temper−
atures will be presented in Section 4.2.
4. EXPERIMENTS AND MODELS OF NON-RE-
ACTIVE MULTIPHASE MIXTURES
Following the results obtained on isothermal bub−
ble−bearing or particle−bearing suspensions rheology
of analogue materials, simplified silicate melt mixtures
and natural melts and magmas are here first intro−
duced. Finally I summarize what is known on the ef−
fect of the presence of bubbles+crystals on suspension
rheology measurements performed at constant tem−
perature.
4.1 MODELS OF BUBBLE SUSPENSION RHE-
OLOGY
Early studies estimating the effect of void spaces
within natural and simplified silicate melts [e.g. Bag−
dassarov and Dingwell, 1992, 1993; Lejeunne et al.,
1999; Vona et al., 2016; Ryan et al., 2019] or synthetic
analogues [e.g. Manga et al., 1998; Llewellin et al.,
2002a, b; Llewellin and Manga, 2005] has been car−
ried out by several authors. Those investigations
showed, largely, that, two end member cases can be
considered: 1) bubbles behave as rigid objects (capil−
lary number Ca<1); 2) bubble are deformed (Ca>1)
[Llewellin et al., 2002a,b]. For the different regimes
various empirical equations were proposed [Bagdas−
sarov and Dingwell, 1992; Lejeunne et al., 1999;
Llewellin et al., 2002; Llewellin and Manga, 2005]
(details in Appendix A3) which suggested that, dur−
ing steady flow: a) an increase in relative viscosity
in the case of the first end−member (Ca<1) and b) a
decrease of the relative viscosity in the case of sec−
ond end member condition (Ca>1) can be observed.
Additional complexities are introduced, as discussed
in Appendix A3, for non−steady flow for which the
definition of a dynamic capillary number (Cd) is re−
quired. The same authors [e.g. Lejeune and Richet,
1996; Bagdassarov and Pinkerton, 2004, Llewellin et
al., 2002, Llewellin and Manga, 2005] also provided
important attainments concerning the understanding
of the effect of closed and opened voids on liquid
viscosity [e.g. Lejeune et al., 1999; Bagdassarov and
Dingwell, 1992; Quane and Russell, 2004; Llewellin
et al., 2002a, b; Llewellin and Manga, 2005; Mader
et al., 2013; Vona et al., 2016; Ryan et al., 2019]. A
summary of recent formulations and works related to
both crystal bearing and bubble bearing rheological
studies is reported in Appendix A3.
4.2 FROM SHEAR-RATE INDEPENDENT TO SHEAR-
RATE DEPENDENT PARTICLE SUSPENSION RHE-
OLOGY MODELS OF ANALOGUE MATERIALS
Early studies on the rheological behavior of mul−
tiphase suspensions [e.g. Einstein, 1906; Roscoe,
1952; Krieger and Dougherty, 1959; Gay et al., 1969;
Pinkerton and Stevenson, 1992] suggested a thresh−
old in solid fraction, the so−called crystal maximum
packing fraction (φc), that separates a liquid domi−
nated rheology from a solid−dominated rheology.
For dilute suspensions of solid mono−disperse spher−
ical particles (φ < 3 vol%) Einstein [1906] proposed that
the relative viscosity ηr (i.e. the ratio between the vis−
cosity of the particle−bearing suspension and that of
the particule−free melts) could be calculated as: ηr =
(1+ Bφ), where B is a constant depending on object ge−
ometrical features (B=2.5 for spheres). Roscoe [1952]
extended Einstein’s expression to higher concentration
of spheres, by first defining the maximum crystal
packing fraction (φm) and providing for the relative
viscosity the following expression: ηr = (1 + φ/φm)
−2.5.
Different φm values were proposed by different authors
depending on crystal geometry (see appendix A3 for
more details). Later, Krieger and Daugherty [1959]
generalized the previous expressions as it follows: ηr
= (1 + φ/φm)
−Beφm where Be is a constant called the
Einstein coefficient (KD model). Others similar ex−
pressions were formulated for which different value of
the Be coefficients were determined (see appendix A3).
Although widely applied, a limitation of those empir−
ical or semi−empirical laws is that they do not account
for neither the strain−rate dependence nor the exis−
tence of, although still debated, yield strength [Moitra
and Gonnermann, 2015] of multiphase mixtures typ−
ical of non−Newtonian fluid (see appendix A3 for
more details). For a review on the two phase rheology
of particle bearing analogue suspensions the reader can
refer to Mader et al. [2013], who presented a compre−
hensive review on this topic
Daniele GIORDANO
8
4.3 NON-NEWTONIAN MODELS FOR PARTICLE SUS-
PENSION RHEOLOGY OF SIMPLIFIED SILICATE MIX-
TURES
Concerning magma−equivalent suspensions, more
recently, Caricchi et al. [2007], Costa et al. [2007a, 2009],
based on the available experimental data obtained at
constant temperature, presented models describing the
non−Newtonian strain−rate−dependent rheological ef−
fects of crystals in the range of solid fractions from 0 to
0.8 and over. These models cover the transition from the
regime where the deformation behavior is controlled by
melt viscosity up to the beginning of the regime where
the deformation behavior is controlled by a solid frame−
work of interlocking particles. The most detailed and
comprehensive model to date proposed by Costa et al.
[2009] model (CM) (Eqs. A3.3−A3.4.), describes the rel−
ative viscosity ηr (i.e. the viscosity of a crystal melt mix−
ture (ηmix) divided by the viscosity of the melt phase
(ηr)). The CM model is the result of the combined math−
ematical and experimental efforts condensed in the
works of Costa [2005], Costa et al. [2007a] that was used
by Caricchi et al. [2007] to describe their experimental
data. Compared to previous models [e.g., Einstein−
Roscoe, 1952; Costa, 2005; Caricchi et al., 2007], the CM
model accounts for the strain−rate dependent changes
in the rheology of liquid+crystal mixtures. The model in
particular shows that the strain rate dependence of the
relative viscosity at varying crystal volume fractions
follows a sigmoid curve with exponential increase above
a critical solid fraction (φc ~ 0.3−0.4) which is also a
function of strain rate and crystal shape. This model is
consistent with the early Einstein−Roscoe equation [Ein−
stein, 1906; Roscoe, 1952] for crystal fractions in the
range of 0 to 0.1−0.3 depending on crystal shape and
size [e.g. Cimarelli et al., 2011]. A summary of the main
results obtained by the employment of the CM and a
summary of its original formulation are reported in
Appendix A3. Extension of CM devoted to characterize
the effect of crystal size and shape distribution and sus−
pended particle ratio and particle roughness are dis−
cussed in Appendix A3.
4.4 NON-NEWTONIAN STRAIN-RATE DEPENDENT MOD-
ELS FOR PARTICLE SUSPENSION RHEOLOGY OF
NATURAL MIXTURES
The fermenting production of studies [Shaw et al.,
1968; Lejeune and Richet, 1995; Giordano et al., 2007;
Caricchi et al., 2007, 2008; Ishibashi, 2009; Vetere et al.,
2010, 2017; Vona et al., 2011; Pistone et al., 2012, 2016;
Chevrel et al., 2015, 2017; Campagnola et al., 2016] de−
voted to the characterization of the isothermal viscos−
ity evolution of silicate melts at subliquidus tempera−
ture as a function of presence and size and shape
distributions of crystals and bubbles and deformation
regimes of the last twenty years has permitted extraor−
dinary advances that are condensed in empirical and
theoretical models of suspension rheology [Saar et al.,
2001; Caricchi et al., 2007; Costa et al., 2009; Mueller et
al., 2011; Vona et al., 2011; Moitra and Gonnermann,
2015]. According to the comprehensive model of Costa
et al. [2009] (CM) (see Section 3.1), inspired by the pre−
vious work of Costa [2005], Costa et al. [2007a] and Car−
icchi et al. [2007], the relative viscosity of two−phase
mixture increases following a sigmoid curve with ex−
ponential increase above a critical solid fraction (φc)
corresponding to the first (phi~0.3−0.4) inflection point.
A second inflection point (φm) at phi ~0.6−0.7 is deter−
mined by the beginning of crystal dominated rheology
(Figure A3.3).
Since the seminal contributions of Caricchi et al.
[2007] and Costa et al. [2009], numerous scientists pro−
vided new and more complete formulation of the crit−
ical crystal fraction (φc) for the natural variability in of
crystal size and shape distribution which would also ac−
count for new variables (e.g. crystal surface roughness)
[e.g. Mueller et al., 2011; Klein et al., 2018]. The em−
ployment of these critical contributions have allowed
interpreting, based on model calculations, the effect of
rheological constraints on eruptive behavior.
4.5 MODELS FOR PARTICLES AND BUBBLES SUSPEN-
SION RHEOLOGY
Complex three−phase suspensions (i.e. liquid+bub−
bles+crystals) have been investigated in only a few
studies [Cordonnier et al., 2009; Robert et al., 2008a, b;
Lavalleé et al., 2007, 2008; Vona et al., 2013, 2017;
Campagnola et al., 2016; Pistone et al., 2012, 2015,
2016]. Given their complexity only a fewer studies have
provided preliminary models describing the complex
rheology of three−phase mixtures [Pistone et al., 2012,
2013, 2015, 2016]. The viscosity data presented in those
studies are the same as those presented in Pistone et al
[2012], but the authors apply their results to different
geological context by showing that size− and shape−
distributions of crystals and bubbles may significantly
vary while undergoing certain stress−strain regimes.
The experiments by Pistone et al. [2012] were per−
formed at pressurized and isothermal temperature con−
9
ADVANCES IN RHEOLOGY: APPLICATION TO LAVA FLOWS EMPLACEMENT
ditions in a Paterson device (Appendix A1) on samples
for which the liquid+crystal rheology was characterized
by Caricchi et al. [2007]. They show that bubbles
strongly affect the rheological properties of crystal−
rich mushes. By presenting a comprehensive review of
existing literature and performing new measurements,
they estimated that a decrease of up to 4 orders of
magnitude is observed by the addition of only 9 vol%
of bubbles to a liquid+crystals suspension containing 70
vol% of crystals. They also established that two non−
Newtonian deformation regimes originate as a conse−
quence of the bubble and crystal interaction: i) a shear
thinning behavior result of the crystal size reduction and
shear banding due to strain localization [also observed
by Caricchi et al., 2008] which is typical of magmas
which are transported and emplaced in Earth’s crust and
may feed eruptions; ii) a shear thickening behavior
which is the consequence of crystal interlock and flow
blockage which they argue locks plutonic rocks in the
lower and upper crust, inhibiting eruptions. More details
of the results obtained by the works of Pistone and
coauthors are provided in Appendix A3.3.
5. NON-ISOTHERMAL COOLING-RATE AND
STRAIN-RATE DEPENDENT RHEOLOGY OF
VOLCANIC MATERIALS
Efforts to systematically describe and predict magma
migration and lava flow behavior rely heavily on these
experimental measurements to derive empirical models.
However, during migration and transport of silicate melts
in the Earth’s crust and at its surface magma/lava can ex−
perience varying cooling and deformation conditions
which may drastically influence its thermorheological
evolution; see for example Rhéty et al. [2017] and Robert
et al. [2014]. As a consequence, data intended for appli−
cation to the natural environment will have to account for
the disequilibrium behavior of natural magmatic sus−
pensions. Cooling rates of basaltic lavas, measured at the
surface and within active lava channels during emplace−
ment range from ~0.01 to 15 C/min [Cashman et al., 1999;
Flynn and Mouginis−Mark, 1992; Hon et al., 1994; Wit−
ter and Harris, 2007; Kolzenburg et al., 2017]. These val−
ues are largely representative for the exterior part of
lava flows or for the initial cooling of newly emplaced
dikes. They can, therefore, be taken as maximum cool−
ing rates that are expected to be lower in the interior of
the lava flow or a cooling dike. The importance of vary−
ing thermal conditions on the crystallization kinetics and
textural development of silicate melts has been recognized
for decades and inspired disequilibrium experimentation
in petrology and volcanology [e.g. Walker et al., 1976;
Arzilli and Carroll, 2013; Coish and Taylor, 1979; Gam−
ble and Taylor, 1980; Hammer, 2006; Lofgren, 1980;
Long and Wood, 1986; Pinkerton and Sparks, 1978;
Giordano et al., 2007; Vetere et al., 2013]. These studies
highlight that significant differences in textures and par−
agenesis emerge when moving from equilibrium to dis−
equilibrium conditions that can, in turn, affect the flow
behavior. Albeit a growing experimental disequilibrium
database is becoming available no models for the dise−
quilibrium phase dynamics of natural silicate melts have
been developed to date.
Understanding the rheological evolution of crystalliz−
ing melts, magmas and volcanic products requires direct
measurement of the flow properties of investigated ma−
terials at such disequilibrium conditions in the field or in
the laboratory. In such environments, the studied mate−
rials are degassed and undergoes transient increases in
viscosity as it is increasingly undercooling until a “rhe−
ological cut−off temperature” [Giordano et al., 2007;
Kolzenburg et al., 2016, 2017, 2018a, b, c; 2019] is reached
and the lava rheologically solidifies. This transient rhe−
ological gradient, which occurs in all natural, non−
isothermal environments, governs the lavas emplacement
style. In recent years, the first sets of measurements were
presented that constrain the rheological evolution of
natural silicate melts under temperature− and deforma−
tion−conditions pertinent to the transport of silicate melts
on the earth’s surface and in shallow magma plumbing
systems. The recovered data show a strong dependence of
composition [Kolzenburg et al., 2017, 2018a], cooling−rate
[Giordano et al., 2007; Kolzenburg et al., 2016, 2017],
oxygen fugacity [Kolzenburg et al., 2018a] and shear−rate
[Kolzenburg et al., 2018] on the thermorheological evo−
lution of natural silicate melts. They represent the first
contributions to a growing database of lava rheology un−
der natural conditions. However, significant experimen−
tal effort in this field is required to expand the range of
available data to cover the most relevant compositions
and to experimentally map the range of parameters per−
tinent to flow of natural silicate melts under disequilib−
rium. Such a database would then allow deducing the un−
derlying processess and expanding these into a theoretical
description of the flow behavior of magma and lava. So
far, the main limitation of this kind of studies is the dif−
ficulty to monitor, and therefore extend, the results to
Daniele GIORDANO
10
non−degassed materials and therefore the application to
intra−crustal magmatic or explosive volcanic processes.
According to previous authors [e.g. Melnik and Sparks,
1999, 2005; Costa and Macedonio, 2003, 2005; Costa et
al., 2007b; Hess et al., 2008; Cordonnier et al., 2012] an
additional complexity could be due to the effects of non−
linear thermal effects, potentially generated by viscous
dissipation and loss by conduction at the contact between
the molten material and the hosting rock, in conduits, and
channels or tunnels after eruption to the surface. The
nonlinear behaviour of thermal effect are mainly gov−
erned by specific non−dimensional numbers (Graetz;
Nahme; Prandtl; Reynolds regimes), which according to
Costa et al. [2007b], amongst the others above mentioned,
may determine the necessity to distinguish between three
main regimes − a conductive−heat−loss−dominated
regime, an intermediate regime and a viscous−heating−
dominated − may have significant effects for the defini−
tion of the rheological behaviour and emplacement dy−
namics of lava flows and lava domes.
Figure 4 shows a summary of rheological data recov−
ered using a variety of experimental methods on Etna
melts. The melt compositions, albeit stemming from dif−
ferent eruptions, are similar for most major oxides with
the exception of the sample from Vona et al. [2017], that
is more rich in silica and poor in iron and, as a result,
more viscous than the samples in Vona et al. [2011] and
Kolzenburg [2018].
For the investigated degassed materials these data
summary highlights a number of effects acting during the
transport of magma and lava at sub liquidus conditions.
Comparison of the pure liquid viscosity of the remelted
bulk rock and the separated groundmass [Vona et al.,
2017]; triangles documents that, for basaltic melts, crys−
tallization induced changes in melt composition result in
relatively small changes in the viscosity of the liquid
phase of the evolving suspension.
Therefore, the variations of the flow behavior of crys−
tallizing basalts are controlled by variations in the vol−
umetric fractions of crystals and bubbles. These data also
reflect the measurement limits of the respective methods
that are described in more detail in Kolzenburg et al.
[2016a]. Concentric cylinder suspension viscometry for
these Etnean lavas is confined to <104 Pa s and shows that
the measured viscosities at constant temperature (i.e. at
or near thermodynamic and textural equilibrium) are
commonly higher than non−isothermal measurements
at the same temperature. This is due to the fact that un−
der dynamic thermal conditions, the crystal nucleation
and growth kinetics lag behind the equilibrium state and
commonly produce lower crystal contents. The non−
isothermal viscosity data from Kolzenburg et al. [2018c]
document that both cooling−rate (blue circles vs. red
squares) and shear rate (open vs. filled symbols) exert a
modulating effect on the disequilibrium rheology of the
Etna melt. Measurements beyond the mechanical limit of
concentric cylinder (CC) viscometry were presented in
Vona et al. [2017] who employed parallel plate (PP) vis−
cometry via unconfined uniaxial deformation (open black
stars) to measure the viscosity of three phase magmatic
suspensions. The data form an apparent continuing trend
with respect to the concentric cylinder viscometry mea−
surements but document lower lava viscosities than ex−
trapolation from the two phase measurements would
suggest. This is likely a result of the differences in sam−
ple texture, where all CC data are restricted to bubble free
two phase suspensions of crystals and melt, whereas the
PP data are measured on three phase (i.e. crystal and bub−
ble bearing) suspensions.
In summary, the rheological evolution of lava at sub−
liquidus conditions can be reconstructed neatly by com−
bination of datasets from differing sources. This is also
11
ADVANCES IN RHEOLOGY: APPLICATION TO LAVA FLOWS EMPLACEMENT
FIGURE 4. Summary of available melt and crystal−suspension vis−
cosity data on remelted Etnean lava as a function of
temperature. Melt viscosity measurements (open black
diamonds, black circles and black triangles) were per−
formed via concentric cylinder viscometry, micro
penetration and differential scanning calorimetry;
Sub liquidus viscosity measurements were preformed
using 1) concentric cylinder viscometry at constant tem−
perature (black circles), 2) concentric cylinder viscometry
at varying cooling− and shear−rates (open and filled
red squared and blue diamonds) and 3) parallel plate
viscometry via unconfined uniaxial deformation (open
black stars). K&' 18; V& '11 and V& '17 refer to work
published by Kolzenburg et al (2018), Vona et al. (2011)
and Vona et al (2017).
shown in Figure 3 in Kolzenburg et al., [2019, this issue],
where laboratory and field estimates of lava rheology at
emplacement conditions are compared and the respective
data fall within a range of similar values. This highlights
the potential of cross correlation of data from different
experimental and field sources and the need to expand the
available experimental database in order to generate a
holistic view of the dynamics of magma and lava trans−
port.
6. ALTERNATIVE WAYS OF RETRIEVING RHEO-
LOGICAL INFORMATION FROM REMOTE
SENSING GROUND- OR SATELLITE-BASED
TECHNIQUES
Besides laboratory viscometry (i.e. the direct mea−
surement of melt / suspension viscosity under controlled
conditions) there are several other sources of rheological
information that are useful to place the laboratory mea−
surements in context of the natural environment. This
kind of information is important as it allows accounting
for the multiphase nature of lava bodies and can serve to
place the laboratory measurements within the framework
of conditions relevant in natural scenarios. However, to
date such data only represents a very limited source of in−
formation of the rheological evolution of lava flows, in
space and time. This is largely due to large logistical and
financial efforts required for some of these measurements
and to the uncertainties associated. Broadly these ap−
proaches can be separated into:
1. Direct measurement of viscosity on active lava flows
via penetration− or rotational−viscometry [Einars−
son, 1949; Gauthier, 1973; Panov et al., 1988; Pinker−
ton and Sparks, 1978; Belousov et al., 2015; Belousov
and Belousova, 2018; Shaw et al., 1968; Pinkerton
and Norton, 1995; Pinkerton and Wilson, 1994;
Chevrel et al., 2018]. These represent snapshots of
actual lava flow rheology at specific conditions and
provide data that help to constrain the conditions re−
quired to be reproduced in systematic laboratory
studies. However, such measurements are quite dif−
ficult and require significant logistical effort and
manpower. Further, the available devices [e.g. Be−
lousov and Belousova, 2018; Chevrel et al., 2018] for
such measurements are only slowly advancing to be
able to measure all relevant parameters sufficient−
ly well to recover high quality viscosity data (Ap−
pendix, A1.5).
2. Calculation of the apparent viscosity based on Jef−
freys’ equations [e.g. Jeffrey, 1925; Hulme, 1974] (Ap−
pendix 4, SMO) using flow rate measurements of ac−
tive lavas in channelized flows [Naboko, 1938;
Nichols, 1939; Minakami, 1951; Einarsson, 1966;
Walker, 1967; Gautier, 1973; Moore, 1978; Andreev,
1978; Fink and Zimbelman, 1986; Vande−Kirkov,
1987; Panov, 1988; Soldati, 2016; Belusov and Be−
lousova, 2018]. Such data are still few due to the dif−
ficulty of accessing active lava flows. However, the
development of affordable unmanned aerial vehi−
cles (UAV’s) in recent years appears to be promis−
ing making this method widely applicable with the
opportune considerations. In fact, the above men−
tioned approach has strong limitations as it is based
on the assumption of parabolic velocity profile that
is not generally valid because of thermal effects [e.g.
Costa and Macedonio, 2003, 2005; Costa et al., 2007b;
Filippucci et al., 2013 and Filippucci et al., 2019, this
issue] (details at Section 3.1.2). Such aspect is still
never considered to describe the nonlinear dynam−
ic of lava flows and lava domes rheology [Melnik
and Sparks, 1999, 2005; Melnik et al., 2009]. To an
adequate analysis of this contribution for specific cas−
es, it is recommended to refer, for instance, to the
above mentioned works and e.g. Filippucci et al.
[2019, this issue].
3. Ties between lava flow geometry and viscosity. Mor−
phological−derived rheological parameters (i.e. vis−
cosity and yield strength) are commonly obtained
in planetary sciences [Heisinger et al., 2007; Cas−
truccio et al., 2010 and Chevrel et al., 2015] provide
excellent reviews of the employed equations and re−
sults). Rheological information is obtained by re−
trieving, in the field or remotely also from satellites,
length, width, thickness and slope of emplacement
of lava flows. This methodology has also been ap−
plied based remote sensing data collected during ac−
tive flow emplacement [James et al., 2015; Farquarson
et al., 2015; Kolzenburg et al., 2018a]. Also in this
case, the emplacement of lava flows is commonly
modelled using a single rheological parameter (ap−
parent viscosity or apparent yield strength) calcu−
lated from morphological dimensions using Jeffreys’
and Hulme’s [Jeffrey and Acrivos, 1976; Hulme, 1974]
equations. The rheological parameters are then
typically further interpreted in terms of the nature
and chemical composition of the lava (e.g., mafic or
felsic). Chevrel et al. [2013, 2015] employing this
Daniele GIORDANO
12
methodology has shown that providing an unique
factor to describe rheology of lava flows is definitely
far from being representative of the real emplace−
ment dynamics of lava flows. As above mentioned
(Point 2), given the nonlinear dynamics of lava flows
and domes, which may determine significant ther−
mal effects, significant limitations may be observed
and should be carefully considered before applying
to any natural context [e.g. Costa and Macedonio,
2003, 2005; Costa et al., 2007b; Filippucci et al., 2013
and Filippucci et al., 2019, this issue].
4. Ties between the intensity of thermal anomalies
generated by actively flowing lava and its silica
content and therewith discharge rate of lavas [e.g.
Coppola et al., 2013, 2017]. This approach takes ad−
vantage of the fact that low viscosity lavas are
readily able to spread into thin sheets during flow,
whereas high viscosity lavas usually retain low−
er aspect ratios. Since the heat loss of a lava is
largely governed by its surface to volume ratio, its
spreading ability (i.e. viscosity) can, empirically,
be correlated to the measured heat loss. Over the
last decades such satellite−based remote sensing
and data processing techniques have proved well
suited to complement field observations and to al−
low timely eruption detection, as well as for flow
tracking.
7. CONCLUDING REMARKS AND OUTLOOK
The present review shows the extraordinary improved
knowledge of rheological properties of multicomponent
and multiphase silicate melts occurring in the last twenty
years. Such knowledge advancement has been due to the
necessity of constraining natural processes and parallel
the development of new technological advances, fre−
quently obtained to face specific problems. It has been
observed that the continuously evolving rheology of
magmas and eruptive products during their ascent, erup−
tion and emplacement can be described with increasing
accuracy and specifically applied to geological issues
with improved confidence. The observed transition be−
tween Newtonian to strongly non−Newtonian rheologi−
cal behaviour is typical of both simple liquids and/or
multiphase natural mixtures. These transitions govern the
observed eruption dynamics and the eruption dynamic
transitions, potentially determining also whether an erup−
tion will be effusive or explosive.
The employment of the rheological flow laws for mul−
ticomponent and multiphase silicate melts find a very
promising application to constraining the advancement
and halting of lava flows. For these superficial phenom−
ena, the opportunity of monitoring important variables
such as the discharge rate and the topography of em−
placement provide fundamental advantage for the em−
ployment of numerical simulations tools. These have al−
lowed showing that more accurate estimates of the effects
of crystals and bubbles during lava flow emplacement can
be obtained only by real−time monitoring of lava flows
through field and remote sensing methods paralleled by
a proper experimental campaign, which in particular
would account and would be related to the non−equilib−
rium, non−isothermal rheology of multiphase mixtures.
This progress in understanding the mechanisms of ad−
vancement and emplacement of lava flows and domes has
also been made possible recently thanks to the recent em−
placement of large long−lasting silicic to basaltic effusive
eruptions. Prior to 2008, for instance, no rhyolite lava
flow−forming eruptive event was observed or docu−
mented. Hence, the real−time observations of active rhy−
olitic flow and dome emplacement at the Chilean volca−
noes of Chaitén [Carn et al., 2009; Lara 2009; Bernstein
et al., 2013; Pallister et al., 2013] and Puyehue−Cordón
Caulle significantly developed our knowledge of rhyolitic
lava emplacement [Castro et al., 2013; Schipper et al.,
2013; Tuffen et al., 2013; Bertin et al., 2015; Farquhar−
son et al., 2015; Magnall et al., 2017]. Analogously the
long lasting 2014−2015 basaltic eruption at Holuhraun,
Bardarbunga system, Iceland [e.g. Pedersen et al., 2017],
offered the opportunity to establish/calibrate, through the
contemporaneous employment of field work, remote
sensing techniques [Kolzenburg et al., 2018a] and labo−
ratory experimentation [Kolzenburg et al., 2017], which
allow retrieving thermal properties, estimates of effusion
rate [Coppola et al., 2013, 2017] and evaluate the effect
of bubbles by comparison with experimental campaign on
liquid+ crystals material as collected during eruption
[Kolzenburg et al., 2017, 2018 a,b]. Worth mentioning is
also the integrated field, remote sensing, physical prop−
erties and physical modelling and numerical simulations
studies performed in the recent years for intermediate
compositions producing effusive activities [Chevrel et
al., 2013 a,b; 2015]. For andesitic domes huge progresses
in understanding the non−linear thermal effects which
determine non−linear eruption dynamics has been made
by previous authors [e.g. Costa et al., 2007b; Melnik and
Sparks, 1999, 2005; Melnik et al., 2009]. Although the
13
ADVANCES IN RHEOLOGY: APPLICATION TO LAVA FLOWS EMPLACEMENT
purposes of this paper is to mostly describe the develop−
ment of rheological properties in relationship to the em−
placement of lavas, most of the general results obtained
here, and in particular those related to the effect of crys−
tals and vesicle on multiphase rheology, can be extended
to eruption dynamics of explosive phases.
Some of the main results deduced by application of
the existing rheological models and experimental stud−
ies, supported by petrological analysis and field work, al−
lowed to unequivocally show that lava flow emplace−
ment may be a long lasting process also for silicic
magmas and that flow may continued also unrooted
from the vent for long times [e.g. Farquarson et al.,
2015] and that extremely voluminous silicic lava flows
may be emplaced in relatively short time without giv−
ing origin to significant explosive stages [Tuffen et al.,
2013; Farquarson et al., 2015; Giordano et al., 2017; Polo
et al., 2018a, b]. In addition, Kolzenburg et al [2016, 2017,
2018] showed that disequilibrium, cooling− and shear−
rate controlled rheological properties may have funda−
mental influence in determining the effective length of
basaltic lava flows.
Although the results evidenced by performing non−
equilibrium, non−isothermal, transient rheology of
basaltic lava flows, are promising and provided a first
understanding of lava flow rheology under natural con−
ditions, it is possible to anticipate that future studies will
require performing this kind of experiments also to a
wider range of effusive products.
I would like to thank Stephan Kolzen-
burg and Kelly Russell for sharing ideas and help in the reor-
ganization of the manuscript. Fabio Arzilli and an anonymous
reviewer are also acknowledged for the careful revision of the
manuscript. Daniele Giordano acknowledges the University of
Turin for support provided by the local research funds
(2017/2020).
REFERENCES
Adam G., Gibbs J.H. (1965). On temperature dependence
of cooperative relaxation properties in glass−form−
ing liquids. J. Chem. Phys. 43, 139–146.
Andreev, V.I., Gusev, N.A., Kovalev, G.N., Slezin, Y.B.
(1978). Dynamics of lava flows of southern break−
through of great Tolbachik fissure eruption, 1975–
76. Bull Volcanol Stations 55:18–26 (in Russian).
Angel, S.M., Gomer, N.R., Sharma, S.K. & McKay, C.
(2012). Remote Raman Spectroscopy for Planetary
Exploration: A Review. Applied Spectroscopy 66.
Angell, C.A., Relaxations in Complex Systems, (1995).
U.S. Department of Commerce National Technical
Information Service, ed. K. L. Ngai and G. B.
Wright, 1985. pp. 3–11.
Angell, C.A. (1991). Relaxation in liquids, polymers and
plastic crystals – strong fragile patterns and prob−
lems. J. Non−Cryst. Solids 131, 13–31.
Ardia, P., Giordano, D., Schmidt, M.W. (2008). A model
for the viscosity of rhyolite as a function of H2O−
content and pressure: a calibration based on cen−
trifuge piston cylinder experiments. Geochim. Cos−
mochim. Acta 72, 6103–6123.
Arzilli, F., Carroll, M.R. (2013). Crystallization kinetics of
alkali feldspars in cooling and decompression−
induced crystallization experiments in trachytic
melt. Contrib. Miner. Petrol. 166, 1011−1027.
Audetat, A., Keppler, H. (2004). Viscosity of Fluids in
Subduction Zones. Science 303, 513 – 516.
Avard, G., and Whittington, A. G. (2011). Rheology of arc
dacite lavas: experimental determination at low
strain rates. Bull. Volcanol. 74, 1039–1056.
Avramov I. (1998). Viscosity of glassforming melts. J.
Non−Cryst. Solids 238, 6−10.
Bachmann, O. and Bergantz, G. (2006) Gas percolation
in upper−crustal silicic crystaal crystal mushes as
a mechanism for upward heat advection and re−
juvination of near−solidus magma bodies. J. Vol−
canol. Geoth. Res. 149, 85 – 102.
Bagdassarov, N.S., Dingwell, D.B. (1992). A rheological
investigation of vesicular rhyolite. J. Volcanol.
Geoth. Res. 50, 307−322.
Bagdassarov, N.S., Dingwell, D.B. (1993). Deformation of
foamed rhyolites under internal and external
stresses: an experimental investigation. Bull. Vol−
canol. 55, 147−154.
Bagdassarov, N., and H. Pinkerton (2004). Transient
phenomena in vesicular lava flows based on lab−
oratory experiments with analogue materials. J.
Volcanol. Geoth. Res. 132, 115 – 136.
Bagdassarov, N. and Dorfman, A. (1998). Granite rhe−
ology: magma flow and melt migration. J. Geol.
Soc. 155, 863−872.
Baker, D.R., Vaillancourt, J. (1995). The Low Viscosities
of F+ H2O−Bearing Granitic Melts and Implications
for Melt Extraction and Transport. Earth Planet.
Sci. Lett. 132, 199−211.
Daniele GIORDANO
14
Behrens, H. and Schulze, F. (2003). Pressure depen−
dance of melt viscosity in the system NaAlSi3O8−
CaMgSi2O6. Am. Min. 88, 1351−1363.
Belousov, A., and M. Belousova. (2018). Dynamics and
Viscosity of ’A ’ā and Pāhoehoe Lava Flows of the
2012−2013 Eruption of Tolbachik Volcano, Kam−
chatka (Russia). Bull. Volcanol. 80.
Belousov A, Belousova M, Edwards B, Volynets A, Mel−
nikov D (2015). Overview of the precursors and
dynamics of the 2012–13 basaltic fissure eruption
of Tolbachik Volcano, Kamchatka, Russia. J. Vol−
canol. Geotherm. Res. 307, 22–37.
Bernstein, M., Pavez, A., Varley, N,, Whelley, P., Calder, E.
(2013). Rhyolite lava dome growth styles at Chaitén
volcano, Chile (2008−2009): interpretation of ther−
mal imagery. Andean Geol 40, 295–309.
Bertin, D., Lara, L.E, Basualto, D., Amigo, Á., Cardona, C.,
Franco, L., Gil, F., Lazo, J. (2015) High effusion rates
of the Cordón Caulle 2011–2012 eruption (southern
Andes) and their relation with the quasi−harmon−
ic tremor. Geophys. Res. Lett. 42, 7054–7063.
Bottinga, Y., Weill, D. (1972). The viscosity of magmatic
silicate liquids: a model for calculation. Am. J. Sci.
272, 438–475.
Brearley, M., Dickinson, J. E., Scarfe, C. M. (1986). Pres−
sure−Dependence of Melt Viscosities on the Join
Diopside−Albite. Geochim. Cosmochim. Acta 50,
2563−2570.
Brearley, M. and Montana, A. (1989). The Effect of Co2
on the Viscosity of Silicate Liquids at High−Pres−
sure. Geochim. Cosmochim. Acta 53, 2609−2616.
Burnham, C.W. (1963). Viscosity of a water rich peg−
matite. Spec. Pap. Geol. Soc. Am. 76, 26.
Campagnola, S., Vona, A., Romano, C., Giordano, G.
(2016). Crystallization kinetics and rheology of
leucite−bearing tephriphonolite magmas from the
Colli Albani volcano (Italy). Chem. Geol. 424, 12−
29.
Cañón−Tapia, E., Walker G. (2004). Global aspects of
volcanism: the perspectives of ‘‘plate tectonics’’
and ‘‘volcanic systems’’. Earth Sci. Rev. 66, 163–
182.
Cañón−Tapia, E. (2016). Reappraisal of the significance
of volcanic fields. J. Volcanol. Geotherm. Res. 310,
26−38.
Caricchi, L., Burlini, L., Ulmer, P., Gerya, T., Vassalli, M.,
Papale, P. (2007). Non−Newtonian rheology of
crystal−bearing magmas and implications for
magma ascent dynamics. Earth Planet. Sci. Lett.
264, 402–419.
Caricchi, L., Giordano, D., Burlini, L., Ulmer, P., Romano,
C. (2008). Rheological properties of magma from
the 1538 eruption of Monte Nuovo (Phlegrean
Fields, Italy): an experimental study. Chem. Geol.
256, 158–171.
Carn SA, Pallister JS, Lara L, Ewert JW, Watt S, Prata AJ,
Thomas RJ, Villarosa G (2009). The unexpected
awakening of Chaitén volcano, Chile. EOS Trans
Am Geophys Union 90, 205–206.
Cashman, K.V., Thornber, C., Kauahikaua, J.P. (1999).
Cooling and crystallization of lava in open chan−
nels, and the transition of P¯ahoehoe Lava to’A’¯a.
Bull. Volcanol. 61, 306–323.
Cashman KV, Soule S, Mackey B, Deligne N, Deardorff
N, Dietterich H (2013). How lava flows: New in−
sights from applications of lidar technologies to
lava flow studies. Geosphere 9, 1664−1680.
Castro, J. Schipper, C.I. Mueller, S.P. Militzer, A.S.,
Amigo, A. et al. (2013). Storage and eruption of
near−liquidus rhyolite magma at Cordón Caulle,
Chile. Bull. Volcanol. 75, 1−17.
Castruccio, A., Rust, A.C., Sparks R.S.J. (2010). Rheol−
ogy and flow of crystal−bearing lavas: Insights
from analogue gravity currents. Earth Planet. Sci.
Lett. 297, 471–480.
Castruccio, A, Rust, AC Sparks, RSJ (2014). Assessing
lava flow evolution from post−eruption field data
using Herschel−Bulkley rheology. J. Volcanol.
Geoth. Res. 275, 71−84.
Champallier, R., Bystricky, M., Arbaret, L. (2008). Ex−
perimental investigation of magma rheology at
300 MPa: From pure hydrous melt to 75 vol. % of
crystals, Earth Planet. Sci. Lett. 267, 571–583.
Chang, C., Powell, R.L. (1994). Effect of particle size dis−
tributions on the rheology of concentrated bi−
modal suspensions. J. Rheol. 38, 85–98.
Chevrel, M.O., Platz, T., Hauber, E., Baratoux, D., Laval−
lée, Y., Dingwell, D.B. (2013a). Lava flow rheology:
a comparison of morphological and petrological
methods. Earth Planet. Sci. Lett. 384, 109–120.
Chevrel, M.O., Giordano, D., Potuzak, M., Courtial, P.,
Dingwell, D.B. (2013b). Physical properties of
CaAl2Si2O8–CaMgSi2O6–FeO–Fe2O3melts: ana−
logues for extra−terrestrial basalt. Chem. Geol.346,
93–105.
Chevrel, M.O., Cimarelli, C., deBiasi, L., Hanson, J.B.,
Lavallée, Y., Arzilli, F., Dingwell, D.B., (2015). Vis−
cosity measurements of crystallizing andesite from
15
ADVANCES IN RHEOLOGY: APPLICATION TO LAVA FLOWS EMPLACEMENT
Tungurahua volcano (Ecuador). Geochem. Geo−
phys. Geosyst. 16, 870–889.
Chevrel, M.O., Harris, A., James, M., Gurioli, L., Patrick,
M. (2017). Measuring the viscosity of lava using a
field rheometer. MemoVolc Meeting Abstract. 21 –
23 February, 2017, Catania, Italy.
Chevrel, M.O., Harris, A.J.L., James, M.R., Calabrò, L.,
Gurioli, L., Pinkerton, H. (2018). The viscosity of
pāhoehoe lava: In situ syn−eruptive measurements
from Kilauea, Hawaii. Earth and Planetary Science
Letters, 493, 161−171.
Chong, J.S., Christiansen E.B., Baer, A.D. (1971). Rheol−
ogy of concentrated suspensions. J. Appl. Polym.
Sci.15, 2007–2021.
Cimarelli, C., Costa, A., Mueller, S., Mader, H.M. (2011).
Rheology of magmas with bimodal crystal size
and shape distributions: Insights from analog ex−
periments. Geochemistry Geophysics Geosystems
12, 1−14.
Coats, R., Cai, B., Kendrick, J., Wallace, P., Hornby, A.,
Miwa, T., von Aulock, F., Ashworth, J., Godinho,
J., Atwood, R. (2017). Understanding the rheology
of two and three−phase magmas. In: AGU Fall
Meeting Abstracts.
Coish, R., and Taylor, L.A. (1979) The effects of cooling
rate on texture and pyroxene chemistry in DSDP
Leg 34 basalt: a microprobe study. Earth and plan−
etary science letters, 42(3), 389−398.
Coppola, D., Piscopo, M.L.D., Cigolini, C. (2013). Rheo−
logical Control on the Radiant Density of Active
Lava Flows and Domes. 239, 39 – 48.
Coppola, D., Laiolo, M., Franchi, A., Massimetti, F.,
Cigolini, C., Lara, L.E. (2017). Measuring effusion
rates of obsidian lava flows by means of satellite
thermal data. J. Volcanol. Geoth. Res. 347, 82 – 90.
Cordonnier, B., Hess, K.−U., Lavallée, Y., and Dingwell,
D.B. 2009. Rheological properties of dome lavas:
Case study of Unzen volcano. Earth and Planetary
Science Letters 279, 263–272.
Cordonnier, B., Schmalholz, S. M., Hess, K.−U., Dingwell,
D. B. (2012). Viscous heating in silicate melts: An
experimental and numerical comparison. J. Geo−
phys. Res. 117, B02203.
Costa, A., Macedonio, G. (2003). Viscous heating in
fluids with temperature−dependent viscosity: im−
plications for magma flows. Nonlinear Processes in
Geophysics 10, 545−555.
Costa, A. (2005). Viscosity of high crystal content melts:
dependence on solid fraction. Geophysical Re−
search Letters 32, 5.
Costa A., Macedonio G. (2005). Computational model−
ing of lava flows: A review. Geological Society of
America Special Papers 396, 209−218.
Costa, A., Macedonio, G. (2005). Numerical simulation
of lava flows based on depth−averaged equations.
Geophysical Res. Lett. 32, L05304.
Costa, A, Melnik O.,Vedeneeva E. (2007a). Thermal ef−
fects during magma ascent in conduits. J.
Gepophys. Res. 112, B12205.
Costa, A, Melnik O., R.S.J. Sparks (2007b). Controls of con−
duit geometry and wallrock elasticity on lava dome
eruptions. Earth Planet. Sci. Lett 260, 137 – 151.
Costa, A., Caricchi, L., Bagdassarov, N.S., (2009). A
model for the rheology of particle bearing sus−
pensions and partially molten rocks. Geochem.
Geophys. Geosyst. 10, 1–13.
Del Gaudio, P., Behrens, H., Deubener, J. (2007). Vis−
cosity and glass transition temperature of hydrous
float glass. Journal of Non−Crystalline Solids 353,
223−236.
Del Negro, C., Fortuna, L., Herault, A., Vicari, A. (2008).
Simulations of the 2004 lava flow at Etna volcano
by the MAGFLOW Cellular Automata model. Bull
Volc. 70, 805 − 812.
Del Negro, C., Cappello, A., Neri, M., Bilotta, G., Herault,
A., Gnci, G. (2013). Lava flow hazards at Mount
Etna: constraints imposed by eruptive history and
numerical simulations. Sci. Rep. 13, 3493.
Del Negro, C., Cappello, A., Ganci, G. (2016). Quantify−
ing lava flow hazards in response to effusive erup−
tion. GSA Bull. 128, 752−763.
Di Genova, D., Kolzenburg, S., Wiesmaier, S., Dallanave,
E., Neuville, D., Hess, K−U, Dingwell, D.B. (2017).
A chemical tipping point governing mobilization
and eruption style of rhyolitic magma. Nature
552, 235 – 238.
Dingwell DB (1986). Viscosity−temperature relation−
ships in the system Na2Si2O5−Na4Al2O5.
Geochim. Cosmochim. Acta 50,1261−1265.
Dingwell DB (1989). Shear viscosities of ferrosilicate liq−
uids. American Mineralogist (9−10):1038−1044.
Dingwell, D.B., Virgo, D., (1987). The effect of oxidation
state on the viscosity of melts in the system Na2O−
FeO−Fe2O3−SiO2. Geochimica et Cosmochimica
Acta 51, 195−205.
Dingwell, D.B., Virgo, D., (1988). Viscosities of melts in
the Na2O−FeO−Fe2O3−SiO2 system and factors
controlling relative viscosities of fully polymerized
Daniele GIORDANO
16
silicate melts. Geochim. Cosmochim. Acta 52,
395−403.
Dingwell, D.B., Bagdassarov, N.S., Bussod, G.Y, Webb,
S.L. (1993). Magma Rheology. Am. Min. Ass. Can.,
Short Course Handbook 21, 131 – 196.
Dingwell, D.B. (1996). Volcanic dilemma: flow or blow?
Science, 273, 1054−1055.
Dobson K, Pistone M, Fife J, Cordonnier B, Blundy J,
Dingwell D, Lee P (2015). Quantifying dynamic
rheology, phase interactions and strain localisation
in deforming three phase magmas using high−
speed x−ray tomography. In: EGU General As−
sembly Conference Abstracts.
Dobson K, Wadsworth F, Di Genova D, Kolzenburg S,
Vasseur J, Marone F, Dingwell D (2016). Magmas
on the Move: in situ 4D Experimental Investiga−
tion into the Rheology and Mobility of Three−
Phase Magmas Using Ultra Fast X−ray Tomogra−
phy. In: AGU Fall Meeting Abstracts.
Dorfman, A., Hess, K.−U., Dingwell, D. B. (1996). Cen−
trifuge−assisted falling−sphere viscometry. Eur. J.
Mineral. 8, 507−514.
Dorfman, A., Dingwell, D. B., Bagdassarov, N. S. (1997).
A rotating autoclave for centrifuge studies: falling
sphere viscometry. Eur. J. Mineral. 9, 345−350.
Dragoni, M. (1993). Modelling the rheology and cool−
ing of lava flows, in Active Lavas: Monitoring
and Modelling, edited by C. R. J. Kilburn and G.
Luongo, pp. 235– 261, Univ. Coll. of London Press,
London.
Dragoni, M., Borsari, I., Tallarico, A. (2005). A model for
the shape of lava flow fronts. J. Geophys. Res., 110,
B09203, doi:10.1029/2004JB003523.
Einstein, A. (1906). A new determination of molecular
dimensions. Ann. Phys. 19, 289 – 306.
Einarsson T (1966) Studies of temperature, viscosity,
density and some types of materials produced in
the Surtsey eruption. Surtsey Res Progr Rep 1,
163–179.
Farquharson, J., James, M., Tuffen, H. (2015). Examin−
ing rhyolite lava flow dynamics through photo−
based 3D reconstructions of the 2011–2012 lava
flowfield at Cordón−Caulle, Chile. J. Volcanol.
Geotherm. Res. 304, 336–348.
Faxèn, H. (1922). The resistance against the movement
of a rigour sphere in viscous fluids, which is em−
bedded between two parallel layered barriers. An−
nalen Der Physik 68, 89−119.
Filippucci, M., Tallarico, A., Dragoni, M. (2013). Role of
heat advection in a channeled lava flow with
power law, temperature−dependent rheology. J.
Geophys. Res. 118, 2764 – 2776.
Filippucci, M., Tallarico, A., Dragoni, M. (2019). Far−field
boundary conditions in channeled lava flow with
viscous dissipation. An. Geophys. 61, ag−7782,
this issue.
Fink, J. H., J. R. Zimbelman (1986). Rheology of the
1983 Royal Gardens basalt flows, Kilauea vol−
cano, Hawaii. Bulletin of Volcanology 48, 87−96.
Flynn, L.P., and Mouginis−Mark, P.J. (1992). Cooling rate
of an active Hawaiian lava flow from nighttime
spectroradiometer measurements. Geophysical Re−
search Letters, 19(17), 1783−1786.
Frankel, N.A., Acrivos A. (1970). A versatile parallel−
plate viscometr for glass viscosity measurement to
1000°C. J. Fluid Mech. 44, 65 – 78.
Fulcher G.S. (1925). Analysis of recent measurements of
the viscosity of glasses, J. Am. Ceramic Soc. 8(6),
339−355.
Gamble, R.P., and Taylor, L.A. (1980). Crystal/liquid
partitioning in augite: effects of cooling rate. Earth
Planet. Sci. Lett. 47, 21−33.
Gay, E.C., Nelson, P.A., Armstrong, W.P. (1969). Flow
properties of suspensions with high solids con−
centration. Aiche Journal 15, 815−822.
Gauthier, F. 1973. “Field and Laboratory Studies of the
Rheology of Mount Etna Lava. Philosophical
Transactions of the Royal Society of London A:
Mathematical, Physical and Engineering Sciences
274, 83–98.
Gent, A.N. (1960). Theory of parallel plate viscometer.
Brit. J. Appl. Phys. 11, 85 – 88.
Giordano, D. and Dingwell, D. B. (2003a). Non−Arrhe−
nian multicomponent melt viscosity: a model.
Earth Planet. Sci. Lett. 208, 337−349.
Giordano, D., Dingwell, D.B. (2003b). The kinetic
fragility of natural silicate melts. J. Phys.: Condens.
Matter 15, S945–S954.
Giordano, D., Nichols, A.R.L., Dingwell, D.B. (2005)
Glass transition temperatures of natural hydrous
melts: a relationship with shear viscosity and im−
plications for the welding process. J. Volcanol.
Geoth. Res. 142, 105–118.
Giordano, D., Polacci, M., Longo, A., Papale, P., Ding−
well, D., Boschi, E., Kasereka, M. (2007). Thermo−
rheological magma control on the impact of highly
fluid lava flows at Mt. Nyiragongo. Geophys. Res.
Lett. 34. L06301.
17
ADVANCES IN RHEOLOGY: APPLICATION TO LAVA FLOWS EMPLACEMENT
Giordano, D., Mangicapra, A., Potuzak, M., Russell, J.K.,
Romano, C., Dingwell, D.B., Di Muro, A. (2006). An
expanded non−Arrhenian model for silicate melt
viscosity: A treatment for metaluminous, peralu−
minous and peralkaline melts. Chem. Geol. 229,
42–56.
Giordano, D., Russell, J.K., (2007). A rheological model
for glassforming silicate melts in the systems CAS,
MAS, MCAS. J. Phys. Condens. Matter 19, 205148.
Giordano, D., Russell, J.K., Dingwell, D.B. (2008a). Vis−
cosity of magmatic liquids: a model. Earth Planet.
Sci. Lett.271, 123–134.
Giordano, Potuzak M, Romano C, Dingwell DB, Nowak
M (2008b). Viscosity and glass transition temper−
ature of hydrous melts in the system CaAl2Si2O28–
CaMgSi2O6. Chemical Geology 256, 203−215.
Giordano, D., Ardia, P., Romano, C., Dingwell, D.B., Di
Muro, A., Schmidt, M.W., Mangiacapra, A., Hess K−
U. (2009). The rheological evolution of alkaline
Vesuvius magmas and comparison with alkaline se−
ries from the Phlegrean Fields, Etna, Stromboli and
Teide. Geochim. Cosmochim. Acta 73, 6613– 6630.
Giordano D., La Felice S., Arzilli F., De Cristofaro S.P.,
Masotta M., Polo L. (2017). Il vulcanismo effusivo
acido del Monte Amiata: stima delle condizioni
pre−eruttive ed implicazioni vulcanologiche. Ef−
fusive acidic volcanism of Monte Amiata: esti−
mates of pre− and syn−eruptive conditions and
volcanological implications. Capitolo monografia
Amiata. ISBN 978−88−99742−32−4.
Giordano, D., Russell, J.K. (2018). Toward a Structural
Model for the Viscosity of Geological Melts. Earth
Planet. Sci. Lett. 501, 202−212.
Giordano, D., González−García, D., Russell, J.K, Raneri,
S., Bersani, D., Fornasini, L., Di Genova, D., Fer−
rando, S., Kaliwoda, M, Lottici, P.P., Smit .,
and Dingwell, D.B. (2019). A calibrated database of
Raman spectra for natural silicate glasses:
implications for modelling melt physical
properties. J Raman Spectrosc. 2019;1–17.
https://doi.org/10.1002/jrs.5675
Glasstone, S., Laidler, K.J., Eyring, H. (1941). The The−
ory of Rate Processes. McGraw−Hill, New−York.
Hammer, J.E. (2006). Influence of fO2 and cooling rate
on the kinetics and energetics of Fe−rich basalt
crystallization. Earth and Planetary Science Letters,
248(3), 618−637.
Harris, A.J., Allen, J.S. III (2008). One−, two− and three−
phase viscosity treatments for basaltic lava flows.
J Geophys Res. 1;113. B09212.
Herschel, W.H., Bulkle, R. (1926). Konsistenzmessungen
von Gummi−Benzollösungen. Kolloid Z. 39:291–
300.
Hess, K.−U., and Dingwell, D.B. (1996). Viscosities of hy−
drous leucogranitic melts: A non−Arrhenian
model. Am. Min. 81, 1297−1300.
Hess, K.−U., Cordonnier, B., Lavallée, Y., and Dingwell,
D.B. (2008) Viscous heating in rhyolite: An in situ
experimental determination. Earth Planet. Sci. Lett.
275, 121−126.
Hiesinger, H., Head III, J.W., Neukum, G. (2007). Young
lava flows on the eastern flank of Ascreus Mons:
Rheological properties derived from High Resolu−
tion Stereo Capera (HRSC) images and Mars Orbiter
Laser Altimeter (MOLA) data. J. Geophy. Res. 112,
E05011, doi:10.1029/2006JE002717.
Hinch, E. J. & Acrivos, A. 1980 Long slender drops in a
simple shear flow. J. Fluid Mech. 98, 305.
Hon, K, J Kauahikaua, R Denlinger, and K Mackay.
1994. “Emplacement and Inflation of Pahoehoe
Sheet Flows: Observations and Measurements of
Active Lava Flows on Kilauea Volcano, Hawaii.”
Geol. Soc. Am. Bull. 106: 351–70.
Hui, H.J., Zhang, Y. (2007). Toward a general viscosity
equation for natural anhydrous and hydrous sili−
cate melts. Geochim. Cosmochim. Acta 71, 403−416.
Hui, H., Zhang, Y., Xu, Z., Del Gaudio, P., Behrens, H.
(2009). Pressure dependence of viscosity of rhy−
olitic melts. Geochim. Cosmochim. Acta 73, 3680
– 3693.
Hulme, G. (1974). The interpretation of lava flow mor−
phology, Geophys. J. R. Astron. Soc., 39, 361– 383.
Hsueh. C.H., Becher, P.F. (2005). Effective Viscosity of
Suspensions of Spheres. J. Am. Ceram. Soc. 88,
1046 – 1049.
Ishibashi, H. and Sato, H. (2007). Viscosity measure−
ments of subliquidus magmas: Alkali olivine basalt
from the Higashi−Matsuura district, Southwest
Japan. J. Volcanol. Geoth. Res. 160, 223 – 238
Ishibashi, H. (2009). “Non−Newtonian Behavior of Pla−
gioclase− Bearing Basaltic Magma: Subliquidus Vis−
cosity Measurement of the 1707 Basalt of Fuji Vol−
cano, Japan.” J. Volcanol. Geoth. Res. 181: 78–88.
James, M. R., Pinkerton, H., Robson., R. (2007). Image−
Based Measurement of Flux Variation
in Distal Regions of Active Lava Flows.” Geo−
chemistry, Geophysics, Geosystems 8 (3).
doi:10.1029/2006GC001448.
Daniele GIORDANO
18
Jeffrey, H. (1925). The flow of water in an inclined
channel of rectangular section. Philos. Mag. J.
Sci. 49, 793 – 807.
Jeffrey, D.J., Acrivos, A. (1976). The rheological prop−
erties of suspensions of rigid particles. − AIChE
Journal, 1976 − Wiley Online Library
Kanzaki, M., Kurita, K., Fujii, T., Kato, T., Shimomura, O.,
Akimoto, S. (1987). A new technique to measure
the viscosity and density of silicate melts at high
pressure. In: Manghnani, M. H. a. S., S. (Ed.),
High−Pressure research in Mineral Physics, Wash−
ington.
Kahle, A., Winkler, B., Hennion, B. (2003). Is Faxe´n’s cor−
rection function applicable to viscosity measurements
of silicate melts with the falling sphere method?. J.
Non−Newtonian Fluid Mech. 112 203–215.
Kilburn, C.R.J. (2015). Chapter 55 − Lava Flow Hazards
and Modeling A2 − Sigurdsson, Haraldur. In: The
Encyclopedia of Volcanoes (Second Edition). Aca−
demic Press, Amsterdam, pp 957−969.
Klein, J., Mueller, S.P., Castro, J.M. (2017). The influence
of crystal size distribution on the rheology of
magmas: new insights from analogues experi−
ments. Geochem. Geophys. Geosyst, 18.
Klein, J., Mueller, S.P., Helo, C., Schweitzer, S., Gurioli,
L., Castro, J.M. (2018). An expanded model and
application of the combined effect of crystal−size
distribution and crystal shape on the relative vis−
cosity of magmas. J. Volcanol. Geoth. Res. 357,
127 – 133.
Kohlstedt, D.L., & Zimmerman, M. E. (1996). Rheology
of partially molten mantle rocks. Annual Review
of Earth and Planetary Sciences, 24, 41−62.
Kolzenburg, S., Favalli, M., Fornaciai, A., Isola, I., Har−
ris, A.J.L., Nannipieri, L., Giordano, D. (2016a).
Rapid Updating and Improvement of Airborne LI−
DAR DEMs Through Ground−Based SfM 3−D
Modeling of Volcanic Features. IEEE Transactions
on Geoscience and Remote Sensing 99, 1−13.
Kolzenburg, S., Giordano, D., Cimarelli, C., Dingwell, D.B.
(2016b) In Situ thermal characterization of cool−
ing/crystallizing lavas during rheology measure−
ments and implications for lava flow emplacement.
Geochim. Cosmochim. Acta 195, 244−258.
Kolzenburg, S., Giordano, D., Thordarson, T., Höskulds−
son, A., Dingwell, D.B. (2017). The rheological
evolution of the 2014/2015 eruption at Holuhraun,
central Iceland. Bull. Volcanol. 79, 45.
Kolzenburg, S., Jaenicke, J., Münzer, U., Dingwell, D.B.
(2018a). The effect of inflation on the morphology−
derived rheological parameters of lava flows and its
implications for interpreting remote sensing data −
A case study on the 2014/2015 eruption at Holuhraun,
Iceland. J. Volc. Geoth. Res. 357, 200−212.
Kolzenburg S., Di Genova D., Giordano D., Hess K.U.,
Dingwell D.B. (2018b). The effect of oxygen fu−
gacity on the rheological evolution of crystalliz−
ing basaltic melts. Earth Planet. Sci. Lett. 487, 21
– 32.
Kolzenburg, S.; Giordano, D., Di Muro, A., Dingwell, D.B.
(2019). Equilibrium Viscosity and Disequilibrium
Rheology of a high Magnesium Basalt from the
2007 eruption of Piton De La Fournaise volcano,
La Reunion, Indian Ocean, France. AG, this issue.
Kolzenburg, S.; Giordano, D., Hess, K.U., Dingwell, D.B.
(2018d). Shear Rate−Dependent Disequilibrium
Rheology and Dynamics of Basalt Solidification.
10.1029/2018GL077799
Kouchi, A., Tsuchiyama, A., Sunagawa, I. (1986). Effect
of stirring on crystalization kinetics of basalt:
Texture and element partitioning. Contrib. Mineral.
Petrol. 93, 429 – 438.
Krieger, I. and Dougherty, T. (1959). A mechanism for
non−Newtonian flow in suspension of rigid sphere.
Trans. Soc. Rheol., 3, 137 – 152.
Kushiro, I. (1976). Changes in Viscosity and Structure of
Melt of NaAlSi2O8 Composition at High Pres−
sures. Journal of Geophysical Research 81, 6347−
6350.
Kushiro, I., Yoder, J., H.S., Mysen, B. O. (1976). Viscosi−
ties of Basalt and Andesite Melts at High Pressures.
Journal of Geophysical Research 81, 6351−6356.
Kushiro, I. (1977). Phase Transformation in silicate melts
under upper−mantle conditions. In: Akimoto, M.
H. M. a. S. (Ed.), High Pressure Research Applica−
tions in Geophysics.
Kushiro, I. (1978). Viscosity and structural changes af Al−
bite (NaAlSi3O8) melt at high pressures. Earth Plan−
et. Sci. Lett. 41, 87−90.
Lara L.E. (2009). The 2008 eruption of the Chaitén vol−
cano, Chile—a preliminary report. Andean Geol., 36,
125–129.
La Spina, G., Burton, M., Vitturi, M.D.M. (2015). Tem−
perature evolution during magma ascent in
basaltic effusive eruptions: a numerical applica−
tion to Stromboli volcano. Earth Planet. Sci.
Lett.426, 89–100.
La Spina, G., Burton, M., Vitturi, M.D.M., Arzilli, F. (2016).
19
ADVANCES IN RHEOLOGY: APPLICATION TO LAVA FLOWS EMPLACEMENT
Role of syn−eruptive plagioclase disequilibrium
crystallization in basaltic magma ascent dynam−
ics. Nature Communications 7, 13402.
Lavallée, Y., Hess, K.−U., Cordonnier, B., Dingwell, D.B.
(2007). Non−Newtonian rheological law for high−
ly crystalline dome lavas. Geology 35, 843.
Lavalleé, Y., Meredith, P.G., Dingwell, D.B., Hess, K. U.,
Wassermann, J., Cordonnier, B., Gerik, A. and Kruhl,
J.H. (2008). Seismogenic lavas and explosive
eruption forecasting. Nature 453, 507–510.
Lejeune, A.M., and P. Richet (1995). Rheology of crys−
tal−bearing silicate melts: An experimental study
at high viscosities, J. Geophys. Res., 100, 4215–4229.
Lejeune, A.M., Bottinga, Y., Trull, T.W., Richet, P. (1999).
Rheology of bubble−bearing magmas, Earth
Planet. Sci. Lett. 166, 71–84.
LeLosq, C., Neuville, D. (2017). Molecular structure,
configurational entropy and viscosity of silicate
melts: Link through the Adam and Gibbs theory of
viscous flow. J. Non−Cryst. Solids 463, 175−188.
Liebske, C., Behrens, H., Holtz, F. Lange, R. (2003). The
influence of pressure and composition on the vis−
cosity of andesitic melts. Geochim. Cosmochim.
Acta 67, 473 – 485.
Liebske, C, Schmickler, B., Terasaki, H., Poe, B., Suzuki,
A., Funakoshi, K.I, Ando, R., Rubie, D.C. (2005).
Viscosity of peridotite liquid up to 13 GPa: Impli−
cations for magma ocean viscosities. Earth Planet.
Sci. Lett. 240, 589 – 604.
Llewellin, E.W., Mader, H.M., Wilson, S.D.R., (2002a). The
rheology of a bubbly liquid. Proc. R. Soc. London,
Ser. A 458, 987–1016.
Llewellin, E.W., Mader, H.M., Wilson, S.D.R. (2002b). The
constitutive equation and flow dynamics of bub−
bly magmas. Geophys. Res. Lett. 29:23.1–23.4,
(doi:10.1029/2002GL015697).
Llewellin, E.W., Manga, M., 2005. Bubble suspension
rheology and implications for conduit flow. J.
Volcanol. Geotherm. Res. 143, 205–217.
Lofgren, G. (1980.) Experimental studies on the dynamic
crystallization of silicate melts. Physics of mag−
matic processes, 487.
Long, P.E., and Wood, B.J. (1986). Structures, textures,
and cooling histories of Columbia River basalt
flows. Geological Society of America Bulletin, 97,
1144−1155.
Mader, H.M., Llewellin, E.W., Mueller, S.P. (2013). The
rheology of two−phase magmas: A review and
analysis. J. Volcanol. Geoth. Res. 257, 135−15
Manga, M., J. Castro, K. Cashman, and M. Loewenberg
(1998). Rheology of bubble−bearing magmas, J.
Volcanol. Geoth. Res., 87, 15–28.
Magnall N, James MR, Tuffen H, Vye−Brown C (2016)
Similarities in basalt and rhyolite lava flow em−
placement processes. Geophys Res Abstr 18:9199
Magnall N, James MR, Tuffen H, Vye−Brown C (2017)
Emplacing a cooling limited rhyolite flow. Volcanic
and Magmatic Studies Group Annual Meeting,
Liverpool, Abstr, p 141.
Maron, S.H. and Pierce, P.E. (1956). Application of ree−
eyring generalized flow theory to suspensions of
spherical particles. J. Colloid Sci. 11, 80–95.
Marsh B.D. (1981). On the crystallinity, probability of
occurrence, and rheology of lava and magma.
Contrib. Mineral. Petrol. 78, 85–98.
Mauro, J.C. , Yue, Y. , Ellison,, A.J. , Gupta P.K. , Allan
D.C. (2009). Proc. Natl. Acad. Sci. USA., 106, 19780
McBirney, A.R., Murase, T. (1984). Rheological proper−
ties of magmas. Ann. Rev. Sci. 12, 337 – 357.;
Melnik, O., and Sparks, R.S.J. (1999). Nonlinear dynamics
of lava dome extrusion. Nature 402, 37 – 41.
Melnik, O. and Sparks, R.S.J. (2005). Controls of conduit
magma flow dynamics during lava dome building
eruptions. J. Geophys. Res. 110, B02209.
Melnik, O., Sparks, R.S.J., Costa, A., Barmin, A.A. (2009).
Volcanic Eruptions: Cyclicity during Lava Dome
Growth. Encyclopedia of Complexity and Systems
Science 9763 −9784.
Minakami, T., Ishikawa, T., Yagi, K. (1951). The 1944
eruption of Volcano Usu in Hokkaido, Japan. Bull.
Volcanol. 11, 45 – 157.
Moitra, P. and Gonnermann, H.M. (2015). Effects of crys−
tal shape− and size−modality on magma rheolo−
gy. Geochemistry, Geophysics, Geosystems, 16, 1−
26.
Moore, H., Arthur, D., Schaber, G. (1978). Yield Strengths
of Flows on the Earth, Mars, and Moon, Lunar and
Planetary Science Conference Proceedings. pp.
3351–3378.
Morgavi, D., Petrelli, M., Vetere, F., González−García, D.,
Perugini, D. (2015). High−temperature apparatus
for chaotic mixing of natural silicate melts. Review
of Scientific Instruments 86(10):105108.
Mueller, S., Llewellin, E.W., Mader, H.M. (2011). The
rheology of suspensions of solid particles. Proc. R.
Soc. London, Ser. A 466, 1201–1228.
Naboko, S.I. (1947). Bilyukai Eruption in 1938. Tr Lab
Vulkanol 5:122– 134.
Daniele GIORDANO
20
Németh, K. (2010). Monogenetic volcanic fields: origin,
sedimentary record, and relationship with polyge−
netic volcanism. Geological Society of America
Special Papers, 470, 43−66.
Nicolas, A. and Ildefonse, B. (1996). Flow mechanism
and viscosity in basaltic magma chambers. Geo−
phys. Res. Lett. 23, 2013−2016.
Nichols, R L. (1939). Viscosity of Lava. The Journal of
Geology 47, 290–302.
Ohtani, E., Suzuki, A., Ando, R., Urakawa, S., Funakoshi,
K., Katayama, Y. (2005). Viscosity and density
measurements of melts and glasses at high pres−
sure and temperature by using the multi−anvil
apparatus and synchrotron X−ray radiation. In:
Advances in High−Pressure Technology for Geo−
physical Applications. Elsevier, pp 195−209.
Pal, R. (2003). Rheological behavior of bubble−bearing
magmas. Earth Planet. Sci. Lett. 207, 165−179.
doi: 10.1016/S0012−821X(02)01104−4.
Pallister, J.S., Diefenbach, A.K., Burton, W.C., Muñoz, J.,
Griswold, J.P., Lara, L.E., Lowenstern, J.B., Valen−
zuela, C.E. (2013). The Chaitén rhyolite lava dome:
eruption sequence, lava dome volumes, rapid ef−
fusion rates and source of the rhyolite magma.
Andean Geol 40(2):277–294.
Panov VK, Slezin YB, Storcheus AV (1988) Mechanical
properties of lava extruded in the 1983 Pred−
skazanny eruption (Klyuchevskoi volcano). J Vol−
canol Seismol 7:25–37.
Papale, P., (1999). Strain−induced magma fragmentation
in explosive eruptions. Nature (London) 397, 425–428.
Paterson, M.S., (1970). Experimental Rock Deforma−
tion—The Brittle Field, 13. Springer−Verlag, Berlin–
Heidelberg–New York.
Paterson, M.S. (1978). Experimental Rock Deforma−
tion—The Brittle Field, 13. Springer−Verlag, Berlin–
Heidelberg–New York.
Paterson, M.S., Olgaard, D.L. (2000). Rock deformation
tests to large shear strains in torsion. Journal of
Structural Geology 22, 1341–1358.
Pedersen, G.B.M., et al. (2017). Lava field evolution and
emplacement dynamics of the 2014–2015 basaltic
fissure eruption at Holuhraun, Iceland. J. Vol−
canol. Geotherm. Res 340, 155–169.
Persikov, E.S., Zharikov, V.A., Bukhitiyarov, P.G., Pol−
skoy, S.F. (1990). The effect of volatiles on the
properties of mgmatic melts. Eur. J. Mineral. 2, 621
– 642.
Petford, N. (2009) Which effective viscosity? Mineral.
Magazine 73, 167 – 171
Phan−Thien, N., and Pham, D.C. (19979. Differential
multiphase models for polydispersed suspensions
and particulate solids. Journal of Non−Newtonian
Fluid Mechanics, 72, 305–318.
Piermarini GJ, Forman RA, Block S. (1978). Viscosity
measurements in the diamond anvil pressure cell.
Rev. Sci. Instrum. 49, 1061
Pinkerton, H, and R S J Sparks. (1978). “Field Measure−
ments of the Rheology of Lava.” Nature 276: 383–
85.
Pinkerton, H, and R J Stevenson. (1992). “Methods of
Determining the Rheological Properties of Magmas
at Sub−Liquidus Temperatures.” Journal of Vol−
canology and Geothermal Research 53: 47–66.
Pinkerton, H, Wilson, L. (1994). Factors controlling the
lengths of channel−fed lava flows. Bull.Volcanol.
56, 108 – 120.
Pinkerton, H, Norton, GE (1995). 'Rheological properties
of basaltic lavas at sub−liquidus temperatures:
laboratory and field−measurements on lavas from
Mount Etna. J. Volcanol. Geoth. Res. 68, 307−323
Pistone, M., Caricchi, L., Ulmer, P., Burlini, L., Ardia, P.,
Reusser, E., Marone, F., Arbaret, L. (2012). Defor−
mation experiments of bubble− and crystal−bear−
ing magmas: rheological and microstructural anal−
ysis. J. Geophys. Res. 117. http://dx.doi.org/10.
1029/2011JB008986.
Pistone, M., Caricchi, L., Ulmer, P., Burlini, L., Reusser,
E., and Ardia, P. (2013). Rheology of volatile−
bearing crystal mushes: mobilization vs. viscous
death. Chem. Geol., 345, 16–39.
Pistone M, Arzilli F, Dobson KJ, Cordonnier B, Reusser
E, Ulmer P, Marone F, Whittington AG, Mancini L,
Fife JL (2015). Gas−driven filter pressing in mag−
mas: Insights into in−situ melt segregation from
crystal mushes. Geology 43(8):699−702.
Pistone, M., Cordonnier, B., Ulmer, P., Caricchi, L. (2016).
Rheological flow laws for multiphase magmas: an
empirical approach. J. Volcanol. Geotherm. Res.
321, 158–170.
Pleše P, Higgins M, Mancini L, Lanzafame G, Brun F, Fife
J, Casselman J, Baker D (2018). Dynamic observa−
tions of vesiculation reveal the role of silicate
crystals in bubble nucleation and growth in an−
desitic magmas. Lithos 296:532−546.
Pocklington, H.C. (1940). Rough measurement of high
viscosities. Proceedings of the Cambridge Philo−
sophical Society 36, 507−508.
21
ADVANCES IN RHEOLOGY: APPLICATION TO LAVA FLOWS EMPLACEMENT
Polacci M., Papale P., Del Seppia D., Giordano D. and
Romano C. (2004) Dynamics of magma ascent and
fragmentation in trachytic versus rhyolitic erup−
tions. J. Volcanol. Geoth. Res. 131, 93–108.
Polacci, M, Arzilli, F, La Spina, G, Le Gall, N, Caiet, B,
Hartley, M.E., Di Genova, D., Vo, N.T., Nonni, S.,
Atwood, R.C., Llewellin, E.W., Lee, P.D. and Bur−
ton, M.R. (2018). Crystallisation in basaltic mag−
mas revealed via in situ 4D synchrotron X−ray
microtomography. Nature.
Polacci M, Mancini L, Baker DR (2010). The contribution
of synchrotron X−ray computed microtomography
to understanding volcanic processes. Journal of
synchrotron radiation 17, 215−221.
Polo L.A., Giordano D., Janasi V., Freitas−Guiaraes L.
(2018). Effusive silicic volcanism in in the Paraná
Magmatic Province, South Brazil: Physico−chem−
ical conditions of storage and eruption and con−
siderations on the rheological behaviour during em−
placement. J. Volcanol. Geoth. Res. 355, 115 − 135.
Polo L.A., Janasi V., Giordano D., E. Canon Tapia, E.
Lima, M. Roverato. (2018). Effusive silicic vol−
canism in the Paraná Magmatic Province, South
Brazil: evidence for local fed lava flows and domes
from detailed field work. J. Volcanol. Geoth. Res.
355, 204 – 218.
Quane SL, Russell JK (2005) Welding: insights from
high−temperature analogue experiments. J Vol−
canol Geotherm Res 142, 67–87.
Ratteron P, Merkel S (2009). In situ rheological mea−
surements at extreme pressure and temperature
using synchrotron X−ray diffraction and radiog−
raphy. Journal of synchrotron radiation 16, 748−
756.
Rhéty M, Harris A, Villeneuve N, Gurioli L, Médard E,
Chevrel O, Bachélery P (2017). A comparison of
cooling and volume limited flow systems: Exam−
ples from channels in the Piton de la Fournaise
April 2007 lava flow field. Geochemistry, Geo−
physics, Geosystems
Richet, P. (1984). Viscosity and configurational entropy
of silicate melts. Geochim. Cosmochim. Acta 48,
471–483.
Richet, P., Bottinga, Y. (1995). In Structure, Dynamics
and Properties of Silicate Melts, eds. J.F. Stebbins,
P.F. McMillan and Dingwell DB, Rev. Mineral. 32,
67−94.
Richet, P., Lejeune, A.−M., Holtz, F., Roux, J. (1996). Wa−
ter and the viscosity of andesite melts. Chem. Geol.
128, 185−197.
Robert; G., Russell, J.K., Giordano, D. (2008a). Rheology
of porous volcanic materials: High−temperature
experimentation under controlled water pressure.
Chem. Geol., 256, 215−229.
Robert; G., Russell, J.K., Giordano, D., Romano, C.
(2008b). High−T deformation of volcanic materi−
als in the presence of water. American Mineralo−
gist 93, 74−80.
Robert B, Harris A, Gurioli L, Médard E, Sehlke A, Whit−
tington A (2014) .Textural and rheological evolu−
tion of basalt flowing down a lava channel. Bul−
letin of Volcanology 76, 1−21.
Roscoe, R. (1952). The viscosity of suspensions of rigid
spheres. British Journal of Applied Physics 3, 306.
Russell, J.K., Giordano, D., Dingwell, D.B., Hess, K.U.,
2002. Modelling the non−Arrhenian rheology of
silicate melts: Numerical considerations. Eur. J.
Mineral. 14, 417–427.
Russell, J. K., Giordano, D., Dingwell, D. B. (2003).
High−temperature limits on viscosity of non−Ar−
rhenian silicate melts. Am. Min. 88, 1390−1394.
Russell, J.K., Giordano, D. (2005). A model for silicate
melt viscosity in the System CaMgSi2O6–
CaAl2Si2O8–NaAlSi3O8. Geochim. Cosmochim.
Acta 69, 5333–5349.
Russell J.K. and Quane S.L. (2005). Rheology of weld−
ing: inversion of field constraints. J. Volcanol.
Geoth. Res. 142,173 – 191.
Russell, J.K., Giordano, D. (2017). Modelling configura−
tional entropy of silicate melts. Chemical Geology
461, 140−151.
Ryan M.P. and James. Y. Blevins, (1987). The viscosity
of synthetic and natural silicate melts and glasses
at high temperatures and 1 bar (105 pascals) pres−
sure and at higher pressures, Bulletin 1764, doi:
https://doi.org/10.3133/b1764.
Ryerson, F.J., Weed, H.C., Piwinskii, A.J. (1988). Rheol−
ogy of subliquidus magmas: 1. Picritic composi−
tions. J. Geophys. Res.: Solid Earth, 93 (B4), 3421−
3436.
Ryan, A., Kolzenburg, S., Vona, A., Heap, M., Russell,
JJ.K. (2019). A proxy for magmatic foams: FOAM−
GLAS®, a closed−cell glass insulation. J. non−
Cryst. Solids: X, 1.
Rust, A.C., Manga, M. (2002). Bubble Shapes and Ori−
entations in Low Re Simple Shear Flow. J. Coll. In−
ter. Sci. 249, 476 – 480.
Saar, M. O., M. Manga, K. V. Cashman, and S. Fremouw
Daniele GIORDANO
22
(2001). Numerical models of the onset of yield
strength in crystal−melt suspensions, Earth Planet.
Sci. Lett., 187, 367–379.
Sato, H. (2005), Viscosity measurement of subliquidus
magmas: 1707 basalt of Fuji Volcano, J. Mineral.
Petrol. Sci., 100, 133–142.
Scarfe, C.M., Mysen, B.O., Virgo, D. (1987). Pressure de−
pendence of the viscosity of silicate melts. In:
Magmatic processes: Physicochemical Principles.
Geochem. Soc. Spec. Pub. 1, 59 −67.
Scherer, G.W. (1984). Use of the Adam−Gibbs equation
in the analysis of structural relaxation, J. Am.
Ceram. Soc. 67, 504 − 511.
Schipper CI, Castro JM, Tuffen H, James MR, How P
(2013) Shallow vent architecture during hybrid
explosive–effusive activity at Cordón Caulle (Chile,
2011–12): evidence from direct observations and
pyroclast textures. J Volcanol Geotherm Res
262:25–37.
Schmidt M. W., Connolly J. A. D., Gu¨nther D. and Bo−
gaerts M. (2006) Element partitioning: the role of
melt structure and composition. Science 312,
1646–1650.
Sehlke A, Whittington A, Robert B, Harris A, Gurioli L,
Médard E (2014) Pahoehoe to `a`a transition of
Hawaiian lavas: an experimental study. Bull. Vol−
canol., 76(11):1−20.
Shaw, H R, T L Wright, D L Peck, and R Okamura. 1968.
“The Viscosity of Basaltic Magma: An Analysis of
Field Measurements in Makaopuhi Lava Lake,
Hawaii.” American Journal of Science 266: 225–64.
Shaw, H R. (1969). Rheology of Basalt in the Melting
Range. J. Petrol. 10, 510–535.
Shaw H. R. (1972) Viscosities of magmatic silicate liq−
uids: An empirical model of prediction. Am. J. Sci.
272, 438–475.
Soldati A, Sehlke A, Chigna G, Whittington A (2016).
Field and experimental constraints on the rheol−
ogy of arc basaltic lavas: the January 2014 Erup−
tion of Pacaya (Guatemala). Bulletin of Volcanol−
ogy 78(6):1−19
Soldati, A., Beem J., Gomez F., Huntley J.W., Robertson
T., Whittington A. (2017). Emplacement dynamics
and timescale of a Holocene flow from the Cima
Volcanic Field (CA): Insights from rheology and
morphology. J. Volc. Geoth. Res. 347, 91 −111.
Song S−R, Jones KW, Lindquist BW, Dowd BA, Sahagian
DL (2001). Synchrotron X−ray computed microto−
mography: studies on vesiculated basaltic rocks.
Bulletin of Volcanology 63(4):252−263.
Sparks, R.S.J. (2004). Dynamics of magma degassing.
Volcanic degassing. Geol. Soc. Lond.Spec. Pub.
213, 5–22.
Stein, D.J., Spera, F.J (2002). Shear viscosity of rhyolite−
vapor emulsions at magmatic temperatures by
concentric cylinder rheometry J. Volcanol. Geoth.
Res. 113, 243 – 258.
Suzuki A., Ohtani E., Terasaki H. and Funakoshi K.
(2005). Viscosity of silicate melts in CaMgSi2O6–
NaAlSi2O6 system at high pressure. Phys. Chem.
Minerals 32, 140–145.
Tammann, G. and Hesse, W. (1926). Die Abhängigkeit
der Viskosität von der Temperatur bei unterkühlten
Flüssigkeiten. Zeitschrift für anorganische und
allgemeine Chemie 156, 245−257.
Taniguchi H. (1995). Universal viscosity−equation for
silicate melts over wide temperature and pressure
ranges. J. Vol. Geoth. Res. 66, 1–8.
Tobolsky, A.V. and Taylor, R.B. (1963). Viscoelastic
properties of a simple organic glass. J. Phys.
Chemistry 67, 2439−2442.
Torquato, S., (2013). Random Heterogeneous Materials:
Microstructure and Macroscopic Properties. Vol.
16. Springer Science & Business Media.
Truby, J.M., Mueller, S.P., Llewellin, E.W., Mader, H.M.
(2015). The rheology of three−phase
suspensions at low bubble capillary number.
Proc. R. Soc. A 471 (2173):20140557.
https://doi.org/10.1098/rspa.2014.0557.
Tuffen H, James M.R., Castro J.M. Schipper C.I. (2013).
Exceptional mobility of an advancing rhyolitic
obsidian flow at Cordo´n Caulle volcano in Chile.
Nature Communication. doi: 10.1038/ncomms3709
Vande−Kirkov YV (1978). Viscosity of the lavas of the
Northern Breakthrough (Tolbachik), 1975. Bull
Volcanol Stations 55, 13–17.
Vetere F., Behrens H., Holtz F. and Neuville D. R. (2006).
Viscosity of andesitic melts−new experimental
data and a revised calculation model. Chem. Geol.
228, 233–245.
Vetere F., Behrens H., Holtz F., Vilardo G., Ventura G.
(2010). Viscosity of crystal−bearing hydrous an−
desites and its implication for magma ascent.
Journal of Mineralogical and Petrological Sci−
ences 105, 151−163.
Vetere, F., Sato H., Ishibashi H., De Rosa R., Donato P.
(2013). Viscosity Changes during Crystallization of
a Shoshonitic Magma: New Insights on Lava Flow
23
ADVANCES IN RHEOLOGY: APPLICATION TO LAVA FLOWS EMPLACEMENT
Emplacement. J. Mineralogical and Petrological
Sciences 108, 144–160.
Vetere, F., Rossi, S., Namur, O., Morgavi, D., Misiti, V.,
Mancinelli, P., Petrelli, M., Pauselli, C., Perugini, D.
(2017). Experimental constraints on the rheology,
eruption and emplacement dynamics of analog
lavas comparable to Mercury's northern volcanic
plains. Journal of Geophysical Research: Planets.
Vogel, D.H. (1921). Temperaturabhängigkeitsgesetz der
Viskosität von Flüssigkeiten. Physikalische
Zeitschrift 22, 645−646.
Vona, A., Romano, C., Dingwell, D.B., Giordano, D.
(2011). The rheology of crystal−bearing basaltic
magmas from Stromboli and Etna. Geochim. Cos−
mochim. Acta 75, 3214–3236.
Vona, A., Romano, C., Giordano, D., Russell, J.K. (2013a).
The multiphase rheology of magmas from Monte
Nuovo (Campi Flegrei, Italy). Chem. Geol. 346,
213 – 227.
Vona A. and Romano C. (2013). The effects of under−
cooling and deformation rates on the crystalliza−
tion kinetics of Stromboli and Etna basalts. Con−
trib. Mineral. Petrol. 166, 491−509.
Vona, A., Ryan, A., Russell, J.K., Romano, C. (2016). Mod−
els for viscosity and shear localization in bubble−
rich magmas. Earth Planet. Sci. Lett. 449, 26 −38.
Vona, A., Di Piazza, A., Nicotra, E., Romano, C., Viccaro,
M., Giordano G. (2017). The complex rheology of
megacryst−rich magmas: The case of the
mugearitic “cicirara” lavas of Mt. Etna volcano.
Chem. Geol. 458, 48−67.
Wadsworth, F.B., Vasseur, J., Llewellin, E.W., Dingwell,
D.B. (2017). Sintering of polydisperse viscous
droplets. Phys. Rev. E 95, 033114−1, 033114−7.
Walker, D., Kirkpatrick, R., Longhi, J., Hays, J. (1976).
Crystallization history of lunar picritic basalt sam−
ple 12002: phase−equilibria and cooling−rate
studies. Geol. Soc. Am. Bull. 87, 646−656
Wieczorek, M.A., Zuber, M.T, Phillips, R.J. (2001). The
role of magma buoyancy on the eruption of lunar
basalts. Earth Planet. Sci. Lett. 185, 71−83
Whittington, A., Richet, P., Holtz, F. (2000). Water and
the viscosity of depolymerized aluminosilicate
melts. Geochim. Cosmochim. Acta 64, 3725−3736.
Whittington, A., Richet, P., Linard, Y., Holtz, F., (2001)
The viscosity of hydrous phonolites and trachytes.
Chem. Geol. 174, 209−223.
Whittington, A., Bouhifd, M.A., Richet, P. (2009). The
viscosity of hydrous NaAlSi3O8 and granitic melts:
Configurational entropy. Am. Min. 94, 1–16.
Wilson, L., Head J.W (2016). Generation, ascent and
eruption of magma on the Moon: New insights
into source depths, magma supply, intrusions and
effusive/explosive eruptions (Part 1: Theory). Icarus
283, 146−175.
Witter, J.B., Harris A.J. (2007). Field measurements of
heat loss from skylights and lava tube systems. J.
Geophys. Res.: Solid Earth 112, 1978–2012.
*CORRESPONDING AUTHOR: Daniele GIORDANO,
Università degli Studi di Torino, Dipartimento di Scienze della Terra
Torino, Italy
email: daniele.giordano@unito.it
© 2019 the Istituto Nazionale di Geofisica e Vulcanologia.
All rights reserved
Daniele GIORDANO
24
<<
/ASCII85EncodePages false
/AllowTransparency false
/AutoPositionEPSFiles false
/AutoRotatePages /None
/Binding /Left
/CalGrayProfile (Dot Gain 20%)
/CalRGBProfile (sRGB IEC61966-2.1)
/CalCMYKProfile (U.S. Web Coated \050SWOP\051 v2)
/sRGBProfile (sRGB IEC61966-2.1)
/CannotEmbedFontPolicy /Warning
/CompatibilityLevel 1.3
/CompressObjects /Tags
/CompressPages true
/ConvertImagesToIndexed true
/PassThroughJPEGImages true
/CreateJobTicket false
/DefaultRenderingIntent /Default
/DetectBlends true
/DetectCurves 0.1000
/ColorConversionStrategy /LeaveColorUnchanged
/DoThumbnails false
/EmbedAllFonts true
/EmbedOpenType false
/ParseICCProfilesInComments true
/EmbedJobOptions true
/DSCReportingLevel 0
/EmitDSCWarnings false
/EndPage -1
/ImageMemory 1048576
/LockDistillerParams true
/MaxSubsetPct 100
/Optimize false
/OPM 1
/ParseDSCComments true
/ParseDSCCommentsForDocInfo true
/PreserveCopyPage true
/PreserveDICMYKValues true
/PreserveEPSInfo true
/PreserveFlatness true
/PreserveHalftoneInfo false
/PreserveOPIComments false
/PreserveOverprintSettings true
/StartPage 1
/SubsetFonts true
/TransferFunctionInfo /Apply
/UCRandBGInfo /Preserve
/UsePrologue false
/ColorSettingsFile (None)
/AlwaysEmbed [ true
/AndaleMono
/Apple-Chancery
/Arial-Black
/Arial-BoldItalicMT
/Arial-BoldMT
/Arial-ItalicMT
/ArialMT
/CapitalsRegular
/Charcoal
/Chicago
/ComicSansMS
/ComicSansMS-Bold
/Courier
/Courier-Bold
/CourierNewPS-BoldItalicMT
/CourierNewPS-BoldMT
/CourierNewPS-ItalicMT
/CourierNewPSMT
/GadgetRegular
/Geneva
/Georgia
/Georgia-Bold
/Georgia-BoldItalic
/Georgia-Italic
/Helvetica
/Helvetica-Bold
/HelveticaInserat-Roman
/HoeflerText-Black
/HoeflerText-BlackItalic
/HoeflerText-Italic
/HoeflerText-Ornaments
/HoeflerText-Regular
/Impact
/Monaco
/NewYork
/Palatino-Bold
/Palatino-BoldItalic
/Palatino-Italic
/Palatino-Roman
/SandRegular
/Skia-Regular
/Symbol
/TechnoRegular
/TextileRegular
/Times-Bold
/Times-BoldItalic
/Times-Italic
/Times-Roman
/TimesNewRomanPS-BoldItalicMT
/TimesNewRomanPS-BoldMT
/TimesNewRomanPS-ItalicMT
/TimesNewRomanPSMT
/Trebuchet-BoldItalic
/TrebuchetMS
/TrebuchetMS-Bold
/TrebuchetMS-Italic
/Verdana
/Verdana-Bold
/Verdana-BoldItalic
/Verdana-Italic
/Webdings
]
/NeverEmbed [ true
]
/AntiAliasColorImages false
/CropColorImages true
/ColorImageMinResolution 150
/ColorImageMinResolutionPolicy /OK
/DownsampleColorImages true
/ColorImageDownsampleType /Bicubic
/ColorImageResolution 300
/ColorImageDepth -1
/ColorImageMinDownsampleDepth 1
/ColorImageDownsampleThreshold 1.10000
/EncodeColorImages true
/ColorImageFilter /DCTEncode
/AutoFilterColorImages true
/ColorImageAutoFilterStrategy /JPEG
/ColorACSImageDict <<
/QFactor 0.15
/HSamples [1 1 1 1] /VSamples [1 1 1 1]
>>
/ColorImageDict <<
/QFactor 0.15
/HSamples [1 1 1 1] /VSamples [1 1 1 1]
>>
/JPEG2000ColorACSImageDict <<
/TileWidth 256
/TileHeight 256
/Quality 30
>>
/JPEG2000ColorImageDict <<
/TileWidth 256
/TileHeight 256
/Quality 30
>>
/AntiAliasGrayImages false
/CropGrayImages true
/GrayImageMinResolution 150
/GrayImageMinResolutionPolicy /OK
/DownsampleGrayImages true
/GrayImageDownsampleType /Bicubic
/GrayImageResolution 300
/GrayImageDepth -1
/GrayImageMinDownsampleDepth 2
/GrayImageDownsampleThreshold 1.10000
/EncodeGrayImages true
/GrayImageFilter /DCTEncode
/AutoFilterGrayImages true
/GrayImageAutoFilterStrategy /JPEG
/GrayACSImageDict <<
/QFactor 0.15
/HSamples [1 1 1 1] /VSamples [1 1 1 1]
>>
/GrayImageDict <<
/QFactor 0.15
/HSamples [1 1 1 1] /VSamples [1 1 1 1]
>>
/JPEG2000GrayACSImageDict <<
/TileWidth 256
/TileHeight 256
/Quality 30
>>
/JPEG2000GrayImageDict <<
/TileWidth 256
/TileHeight 256
/Quality 30
>>
/AntiAliasMonoImages false
/CropMonoImages true
/MonoImageMinResolution 1200
/MonoImageMinResolutionPolicy /OK
/DownsampleMonoImages true
/MonoImageDownsampleType /Bicubic
/MonoImageResolution 1200
/MonoImageDepth -1
/MonoImageDownsampleThreshold 1.08250
/EncodeMonoImages true
/MonoImageFilter /CCITTFaxEncode
/MonoImageDict <<
/K -1
>>
/AllowPSXObjects false
/CheckCompliance [
/None
]
/PDFX1aCheck false
/PDFX3Check false
/PDFXCompliantPDFOnly false
/PDFXNoTrimBoxError true
/PDFXTrimBoxToMediaBoxOffset [
0.00000
0.00000
0.00000
0.00000
]
/PDFXSetBleedBoxToMediaBox true
/PDFXBleedBoxToTrimBoxOffset [
0.00000
0.00000
0.00000
0.00000
]
/PDFXOutputIntentProfile (None)
/PDFXOutputConditionIdentifier ()
/PDFXOutputCondition ()
/PDFXRegistryName (http://www.color.org)
/PDFXTrapped /Unknown
/CreateJDFFile false
/SyntheticBoldness 1.000000
/Description <<
/ENU (Use these settings to create PDF documents with higher image resolution for high quality pre-press printing. The PDF documents can be opened with Acrobat and Reader 5.0 and later. These settings require font embedding.)
/JPN <FEFF3053306e8a2d5b9a306f30019ad889e350cf5ea6753b50cf3092542b308030d730ea30d730ec30b9537052377528306e00200050004400460020658766f830924f5c62103059308b3068304d306b4f7f75283057307e305930023053306e8a2d5b9a30674f5c62103057305f00200050004400460020658766f8306f0020004100630072006f0062006100740020304a30883073002000520065006100640065007200200035002e003000204ee5964d30678868793a3067304d307e305930023053306e8a2d5b9a306b306f30d530a930f330c8306e57cb30818fbc307f304c5fc59808306730593002>
/FRA <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>
/DEU <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>
/PTB <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>
/DAN <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>
/NLD <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>
/ESP <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>
/SUO <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>
/NOR <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>
/SVE <FEFF0041006e007600e4006e00640020006400650020006800e4007200200069006e0073007400e4006c006c006e0069006e006700610072006e00610020006e00e40072002000640075002000760069006c006c00200073006b0061007000610020005000440046002d0064006f006b0075006d0065006e00740020006d006500640020006800f6006700720065002000620069006c0064007500700070006c00f60073006e0069006e00670020006600f60072002000700072006500700072006500730073007500740073006b0072006900660074006500720020006100760020006800f600670020006b00760061006c0069007400650074002e0020005000440046002d0064006f006b0075006d0065006e00740065006e0020006b0061006e002000f600700070006e006100730020006d006500640020004100630072006f0062006100740020006f00630068002000520065006100640065007200200035002e003000200065006c006c00650072002000730065006e006100720065002e00200044006500730073006100200069006e0073007400e4006c006c006e0069006e0067006100720020006b007200e400760065007200200069006e006b006c00750064006500720069006e00670020006100760020007400650063006b0065006e0073006e006900740074002e>
/KOR <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>
/CHS <FEFF4f7f75288fd94e9b8bbe7f6e521b5efa76840020005000440046002065876863ff0c5c065305542b66f49ad8768456fe50cf52068fa87387ff0c4ee575284e8e9ad88d2891cf76845370524d6253537030028be5002000500044004600206587686353ef4ee54f7f752800200020004100630072006f00620061007400204e0e002000520065006100640065007200200035002e00300020548c66f49ad87248672c62535f0030028fd94e9b8bbe7f6e89816c425d4c51655b574f533002>
/CHT <FEFF4f7f752890194e9b8a2d5b9a5efa7acb76840020005000440046002065874ef65305542b8f039ad876845f7150cf89e367905ea6ff0c9069752865bc9ad854c18cea76845370524d521753703002005000440046002065874ef653ef4ee54f7f75280020004100630072006f0062006100740020548c002000520065006100640065007200200035002e0030002053ca66f465b07248672c4f86958b555f300290194e9b8a2d5b9a89816c425d4c51655b57578b3002>
/ITA <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>
>>
>> setdistillerparams
<<
/HWResolution [2400 2400]
/PageSize [595.000 842.000]
>> setpagedevice