Rheological properties of basaltic lavas at sub-liquidus temperatures: laboratory and field measurements on lavas from Mount Etna

Journalof vokanologv and geothermal research

ELSEVIER Journal of Volcanology and Geothermal Research 68 ( 199.5) 307-323

Rheological properties of basaltic lavas at sub-liquidus temperatures: laboratory and field measurements on lavas from

Mount Etna

Harry Pinkerton a**, Gill Norton b ‘I Environmental Science Division, Luncaster University, Lancaster LA1 4YQ, UK

’ British Geological Survey, Kingsley Dunham Centre, Keyworth, Nottingham NG12 SGG, UK

Received I1 July 1994; accepted 25 January 1995

Abstract

Models of many magmatic processes require accurate data on the rheological properties of lava at sub - liquidus temperatures. Laboratory measurements of the rheological properties of basalts erupted on Mount Etna in 1983 were made at various crystal concentrations in a specially designed furnace using a Haake Rotovisco viscometer attached to a spindle designed to eliminate slippage at the melt-spindle interface. Measurements were made at strain rates between 0.3 and 5 s- ’ over the range of eruption

temperatures on Mount Etna ( 1084-I 125’C). At temperatures above 1120°C the 1983 lava behaves as a Newtonian fluid. At lower temperatures, the lava is a thixotropic, pseudoplastic fluid with a maximum yield strength of 78 Pa at a temperature of

1087°C. In view of its low yield strength over this temperature range, the rheological behaviour of the lava approximates to that

of a power law fluid. Apparent viscosities at unit shear strain rates increase from 150 Pa s at 1125°C to 3000 Pa s at 1084°C. Unit strain rate apparent viscosities measured in the field using a rotating vane viscometer range from 1385 Pa s to 1630 Pa s.

These values are in close agreement with those measured at the same temperature in the laboratory and with those calculated theoretically from the physico-chemical properties of the lava.

1. Introduction

Models of most volcanic processes require accurate data on the physico-chemical properties of lava. Since

the viscosity of lava changes by several orders of mag-

nitude during crystallisation, the rates of volcanic proc-

esses are more strongly influenced by the rheological properties of lava than by any other physico-chemical property. Rheological properties are a function of the

chemistry, temperature, crystallinity and vesicularity of lava and they are related in a complex way to the degassing and thermal history of a flow (Sparks and

* Corresponding author.

Pinkerton, 1978; Marsh, 1981, 1987; Lipman et al.,

1985). At temperatures above the liquidus, the viscos-

ity of lava at any given temperature is readily estimated

from its chemical composition (e.g., Shaw, 1972). At

lower temperatures, shear stress-shear strain rate rela-

tionships can be calculated from crystal sizes, shapes

and size distributions using methods developed by Pin-

kerton and Stevenson (1992). However, the accurate

rheological data required by predictive lava flow mod-

els cannot be calculated using crystal size and shape

data from quenched samples; they should be calculated

from the crystallisation and degassing history of lava

from the modelled flow. While this is known for a few

lava flows (Cashman, 1988; Cashman and Marsh,

0377.0273/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDlO377-0273(9S)OOOl8-6

308 H. Pinkerton. G. Norton /Journal of Volcanology and Geothermal Research 68 (1995) 307-323

1988; Rowland and Walker, 1988; Walker, 1989; Man-

gan, 1990; Mangan et al., 1993; Armienti et al., 1994;

Cashman et al., 1994; Crisp et al., 1994) there is, as yet, no simple method of calculating these parameters

for any lava flow. Consequently, reliable estimates of

rheological properties of lava can best be obtained

either using appropriate rheological equipment in the

field or from laboratory measurements on quenched

samples from active lava flows.

Rheological properties of basaltic lava have been measured on Kilauea, Mount Etna and Mauna Loa

(Shaw et al., 1968; Pinkerton and Sparks, 1978; Fink

and Zimbelman, 1986; Moore, 1987; Fink and Zim-

belman, 1990). In view of the problems associated with

field measurements of rheological properties, other

workers have directed their attention to measuring these

properties in the laboratory (e.g., Shaw, 1969; Spera

et al., 1982, 1988; McBirney and Murase, 1984; Ryan

and Blevins, 1987; Ryerson et al., 1988; Webb and

Dingwell, 1990; Stein and Spera, 1992; Dingwell et

al., 1993; Bagdassarov et al., 1994). However, there

have been few rheological measurements at typical eruptive temperatures, and only Shaw’s (1969) meas-

urements can be compared with field measurements on

the same lava at similar temperatures. The present study investigates the rheological prop-

erties of lavas from Mount Etna at typical eruption temperatures ( 1084-l 125°C). We begin by reviewing

the factors which influence the rheological properties

of lavas and then discuss the equipment we have

designed to obtain rheological data in the laboratory.

In the second half of the paper we present our laboratory

and field measurements of the rheological properties of lavas erupted on Mount Etna in 1983 and we compare the measured values with those calculated from their

physico-chemical properties. Lavas used in this study are chemically and mineralogically very similar to many historic Etna lavas, including those erupted dur-

ing the 1991-93 eruption of Etna, the largest historic eruption of the volcano during the past 3 centuries (Armienti et al., 1994).

2. Factors controlling the rheological properties of natural melts

The rheological properties of a magma are a function of its chemical composition, temperature and pressure,

thermal history, and crystal, bubble and volatile con-

tents (Holloway, 1973; Hess, 1980). Other properties,

e.g., shearing-induced crystallisation, bubble deformation during shearing and crystal migration from

regions of high to low shearing stress, can also affect

the measurements. The importance of each of these will

be assessed in the following section.

2.1. Effects of melt chemistry and volatile content

The viscosities of silicate magmas vary by several

orders of magnitude at a given temperature. For exam-

ple, at 1300°C a basaltic melt may have a viscosity of

10 Pa s compared with 10’ Pa s for a rhyolitic magma (Murase and McBirney, 1973).

Several workers (Bottinga and Weill, 1972; Shaw,

1972; Urbain et al., 1982) have developed methods for

calculating the viscosities of natural rock melts from

their chemical composition. While there is reasonable

agreement between calculated and measured viscosi-

ties, there are several limitations of these empirical

methods. Firstly, the calculated viscosities have been compared only with the measured values for superli-

quidus melts. Brandeis and Jaupart ( 1986) note that,

below the liquidus, the activation energy of flow for a supercooled rhyolitic melt increases by up to three

times that at superliquidus temperatures. Hence empirical methods must be used with caution when calculat-

ing the viscosity of a supercooled melt. Secondly, at

subliquidus temperatures the composition of the resid-

ual melt will change during crystallisation and therefore

the composition of the melt must be determined and

the viscosity recalculated during crystallisation. Thirdly, the above models assume that magmas are

Newtonian if there are no bubbles or crystals present.

However, Spera et al. ( 1988) measured the rheology of rhyolitic lavas over a range of temperatures and shear strain rates and concluded that bubble- and crystal-free high-silica melts may show power law behaviour.

When a volatile species is dissolved in a melt, its effect on the melt structure depends on its chemical behaviour. Shaw (1963) measured the effect of up to 10 wt.% H,O on the viscosity of obsidian at 1 and 2 kbar, and concluded that water significantly reduces melt viscosity at constant temperature and pressure. Studies on the speciation of water in silicate melts (e.g., Stolper, 1982) indicate that at low total water content water is present mostly as OH-. The role of OH- in

H. Pinkerton, G. Norton /Journal of Volcanology and Geothermal Research 68 (1995) 307-323 309

the structure of silicate melts is similar to that of a

network modifier. It will break the strong Si-0-Si bonds, and produce Si-OH bonds (Dingwell et al., 1985); thus, the melt is depolymerised and its viscosity

decreases. However, the proportion of molecular water

increases at higher water contents. The effect of molec-

ular water on the viscosity of silicate melts is less than

that of OH- as water molecules are less polarised. While fluorine and, to a lesser extent, dissolved carbon

dioxide significantly reduce the viscosity of high-silica melts, their influence on the rheological properties of

basaltic melts can be ignored (Dingwell and Mysen,

1985; Dingwell, 1989; Brearley and Montana, 1989).

As part of the present investigation, we assess the

effects of degassing of lava by comparing field rheo-

logical measurements close to an eruptive vent on Etna (where the lavas have experienced little post-eruptive

volatile loss) with measurements on degassed samples

at the same temperature in the laboratory. This study

complements the field and laboratory rheological measurements of Shaw and colleagues (Shaw et al., 1968

and Shaw, 1969) on lavas from Makaopuhi lava lake in Hawaii.

2.2. Effects of temperature and pressure

(a) Temperature The viscosity of a silicate melt decreases with

increasing temperature because the higher molecular

kinetic energy at elevated temperatures results in dis-

ruption of Si-0 bonds and hence depolymerisation of the melt structure. The variation of viscosity with tem-

perature is a rate-controlled function, i.e.:

r~ = r], exp( - E,IR*T) (1)

where 77 is the viscosity at temperature T, q,, is the

viscosity at infinite temperature, R’ is the gas constant, and E, is the activation energy for viscous flow. (b) Pressure

Experimental high-pressure work by Kushiro ( 1976,

1978, 1981), Scarfe (1973, 1981) and Scarfe et al. (1987) has shown that the viscosity of a silicate melt

can either increase or decrease as the pressure increases.

For example, the viscosity of a diopside melt will increase, whereas that of an albite melt will decrease over the same pressure interval. This difference is attributed to the degree of polymerisation of the melt.

Brearley et al. ( 1986) suggested that an increase in

pressure will cause an increase in the size of molecular

flow units for a depolymerised melt (e.g., diopside) , leading to an increase in the viscosity. However, the increase in pressure will cause the framework structure

of a polymerised melt (e.g., albite) to collapse, and so

the viscosity will decrease.

2.3. Efsects of crystals

Field measurements of the rheological properties of

lava (Shaw et al., 1968; Gauthier, 1973; Pinkerton and

Sparks, 1978) suggest that crystal-rich magmas are

non-Newtonian with a significant yield strength. Lab-

oratory studies on subliquidus melts (e.g., Shaw, 1969; Ryerson et al., 1988) show that the rheological prop-

erties of a lava depend strongly on its crystal content.

Ryerson et al. ( 1988) measured the rheology of a picri-

tic melt and showed that it was pseudoplastic at subli-

quidus temperatures and that non-Newtonian effects

are more apparent at crystal concentrations greater than

25 vol.%.

Pinkerton and Stevenson (1992) review the factors controlling the development of a non-Newtonian rhe-

ology in crystallising melts, and they argue that many

of the methods used previously to calculate the rheological properties of melts are inappropriate. They

agree with Marsh (1987) that basaltic melts can be

approximated as Newtonian fluids at low crystal concentrations ( < 25 vol.%) and that viscosities increase

with increasing crystal content according to the Ein-

stein-Roscoe equation (with a maximum packing con-

centration of 60%). At concentrations above 25 vol.%,

basalts behave as pseudoplastic materials with a yield

strength, and the rheological effects of crystals can be

calculated using a set of empirical equations based on

experimental data from Gay et al. ( 1969). This method calculates the shear stress-shear strain rate relationship

from measured crystal sizes, shapes and size distributions. The limited data on the rheological properties of lavas at sub-liquidus temperatures are in close agree-

ment with those calculated from the equations in Pin-

kerton and Stevenson ( 1992). However, additional systematic rheological data on lavas at sub-liquidus

temperatures are required to confirm the validity of this approach.

During rheological experiments, viscosity measurements are commonly made at successively higher temperatures on the same sample. As the temperature of a

310 H. Pinkerton, G. Norton /Journal of Volcanology and Geothermal Research 68 (1995) 307-323

magmatic suspension is increased, the residence time at each temperature must be sufficient to allow equili-

bration of partial melt and the phenocryst phases.

Murase and McBirney ( 1973) show that the isothermal

viscosity of a supercooled basalt increases steadily with

time; this is due to the slow crystal growth rates in these

experiments at small degrees of supercooling.

Macdonald ( 1953) argued that enhanced crystallis-

ation took place during shearing in some Hawaiian lava

flows. This phenomenon, which has also been noted by

Kouchi et al. ( 1986)) is caused by higher rates of dif-

fusion in the sheared lava. During rheological meas-

urements on crystallising lavas, it may cause an

increase in measured apparent viscosities. Conversely,

Shaw (1969) suggested that one reason for a sudden

drop in shear stress at high shear strain rates in a con-

centric cylinder viscometer could be viscous heating of the lava. For a sheared power law fluid (i.e., a fluid

whose rheological properties can be approximated by

the relationship T= a Lf( T) I”, where a and n are con-

stants characteristic of the fluid), Spera et al. (1988)

calculated the increase in temperature as a result of viscous heating, AT, using the following equation from

Bird et al. (1987):

(2)

where q is the apparent viscosity of the fluid at the shear strain rate under investigation, 0 is the rotation

rate of the spindle, n is the power law exponent, K is

the thermal conductivity of the fluid, and R, and R, are

the radius of the spindle and cup, respectively.

Laboratory measurements should be designed to minimise the effects of viscous heating. During their measurements on rhyolites, Spera et al. (1988) found

that the maximum calculated temperature increase was less than 1°C and consequently this effect could be

could be ignored in their experiments.

2.4. Effect of bubbles

The effects of bubbles on the rheological properties of magma are not fully understood. Comparisons with emulsions and suspensions of bubbles in Newtonian fluids suggests that the effective viscosities of vesicular magmas will be complex functions of bubble size, size- distribution, concentration and shear strain rate (e.g.,

Taylor, 1932; Kraynik, 1988; Pal and Rhodes, 1989; Princen and Kiss, 1989).

During most laboratory rheological measurements (e.g., Shaw, 1969; Ryerson et al., 1988)) care is taken

to minimise the gas contents of the melts. However,

Stein and Spera ( 1992) and Bagdassarov and Dingwell ( 1992) measured the rheological properties of melts

with bubbles and confirmed that the presence of bub-

bles has a stronger influence on rheological properties than similar concentrations of crystals.

Stein and Spera ( 1992) measured the effect of bubbles on the rheology of a GeO, melt. At bubble con-

centrations less than 5 vol.% and low shear strain rates,

their melt was approximately Newtonian, and the

increase in viscosity with gas volume fraction followed

Taylor’s (1932) expression:

77,=77(1+4) (3)

where rls is the viscosity of the suspension, 3 is the viscosity of the fluid and 4 is the vesicularity of the

melt. For low concentrations, a transition to more com-

plex non-Newtonian rheology was recognised once the bubbles deformed. This transition can be calculated

from the capillary number, Cu, given by

where CT is the surface tension between the fluid and

the bubble, rp is the average radius of the bubbles, and

g is the shear strain rate. The critical capillary number

for bubble deformation is 0.4 (Stein and Spera, 1992). Thus, at low shear strain rates, small bubbles increase

the bulk viscosity relative to the fluid viscosity because the bubbles interfere with the flow of the fluid, whereas

at high shear strain rates, viscous forces overcome surface tension, and bubbles deform and align along flowlines, decreasing viscosity. In the concentration range

O-5.5 vol.%, Stein and Spera (1992) have shown that bubble-melt suspensions are pseudoplastic.

Bagdassarov and Dingwell (1992) measured the viscosity of vesicular rhyolitic melts ( > lo9 Pa s) using a parallel plate viscometer and found that the low shear strain rate viscosity of these highly viscous vesicular melts decreased by an order of magnitude as the bubble content increased to 25% and thereafter remained constant with increasing bubble content.

The main limitation of work on the rheological properties of high-temperature vesicular magmas is that the

H. Pinkerton, G. Norton /Joumal of Volcanology and Geothermal Research 68 (1995) 307-323 311

methods of growing bubbles do not permit controlled bubble growth; existing experimental results cannot therefore be used to investigate the separate effects of bubble size, size distribution and concentration. Con- sequently, the rheological effects of bubble growth and coalescence during flow (Sahagian et al., 1989; Herd and Pinkerton, 1993; Manga and Stone, 1994) cannot be calculated from existing experimental data. In addition, Stein and Spera’s ( 1992) measurements were limited to bubble concentrations less than 5.5% and Bagdassarov and Dingwell (1992) published no data in the concentration range 5% to 25%. Also, these results are applicable only to very viscous melts.

2.5. Normal stress effects

Spera et al. (1988) noted that normal stresses i.e., stresses perpendicular to the shearing of a fluid, were characteristic of deforming vesicular melts. The main manifestation of normal stresses in concentric cylinder viscometry is the tendency of fluids to ‘climb’ up the spindle (Weissenberg, 1947). Stein and Spera ( 1992) found that their bubble-fluid emulsion climbed 20 mm up the rod for bubble concentrations of 5.5%, and that the computed normal stress was 2% of the shear stress. In laboratory measurements on basaltic melts, rod climbing has not been observed, though field observations during the 1983 eruption of Mount Etna showed that the proximal channel had a central upward bulge of 0.25 to 0.42 m caused by a negative second normal stress (i.e., the difference between the axial and the vertical normal stresses). This is clear evidence of viscoelastic behaviour (see Spera et al., 1988) of lava in the 1983 channel on Mount Etna.

2.6. Time-dependent effects

For many fluids, the apparent viscosity varies with time as well as with applied shearing stress. During measurements of the viscosity of a suspension in a rotating viscometer, elongate particles tend to align along the flowlines. This will decrease the bulk viscosity during a measurement, resulting in thixotropic (shear thinning) behaviour. For thixotropic materials, the apparent viscosity returns to the unsheared value when the sample is left undisturbed for a sufficient time for the structure to become re-established.

Measured rheological properties of suspensions during rotation at a constant rate can also change because of particle migration away from the rotor resulting in apparent thixotropic behaviour (e.g., Van Wazer et al., 1963). The critical Reynolds number, RecTit, above which radial motions will occur is given by

(Van Wazer et al., 1963, p. 85). The Reynolds number, Re, for flow of the fluid in the gap between the rotor and the cup is given by:

PR,~ Re=-

rl (6)

where p is the density of the fluid and h is the depth of the rotating fluid in motion. Thus, if the Reynolds number caused by rotation of the spindle in a rotating viscometer is greater than the critical Reynolds number, radial motion of the fluid will occur. Crystals or bubbles will therefore migrate away from the spindle during an experiment, and the bulk viscosity will decrease.

Apparent thixotropic or rheopectic (shear thicken- ing) behaviour of lavas can also be caused by density differences between the melt and the suspended bubble or crystal phases. During rheological measurements, bubbles may float to the top of the melt, and crystals may either float or sink. Clearly, an uneven distribution of particles in the lava will affect its bulk rheology. In all magma rheological studies, crystal and bubble settling and rise rates must be calculated using the method outlined in Kerr and Lister ( 199 1) .

Finally, if crystallisation occurs during an experimental run, the viscosity will tend to increase, leading to apparent rheopectic behaviour. Hence, if rheopexy or thixotropy are noticed during an experiment on a crystal or bubble suspension, care must be taken to distinguish between time-dependent behaviour due to shearing of the suspension and that caused by crystallisation or changes in the melt structure. Thin sections of quenched rheological samples and geochemistry can be used to elucidate the extent of settling, flotation or particle migration due to radial motion at the end of an experiment, but the distribution of crystals and bubbles during a measurement run can be established only by calculation.

312 H. Pinkerton, G. Norton /Journal qf Volcanology and Geothermal Research 68 (1995) 307-323

2.7. The complications of yield strengths in magmas Table I

Previous workers who have measured the rheologi-

cal properties of basaltic lavas in the field (e.g., Shaw

et al., 1968; Gauthier, 1973; Pinkerton and Sparks,

1978) have argued that their data support the presence of a yield strength. A static yield strength is caused by

the formation of a three-dimensional framework of

crystals and/or bubbles in molten lava (Kerr and Lis- ter, 1991; Pinkerton and Stevenson, 1992). If this

threshold stress is exceeded, the lava will shear and the

framework will be damaged, possibly to the extent that,

as the shear strain rate is reduced to zero, the shear

stress-shear strain rate curve will pass through the ori-

gin, indicating that the lava no longer has a yield

strength. In other cases, the shear stress-shear strain rate curve intersects the shear stress axis when the shear

strain rates are slowly reduced to zero, confirming that the lava has a dynamic yield strength and that the frame-

work was not destroyed permanently during flow.

Shear strain rates relevant to magmatic phenomena (based on Spera

et al., 1988)

Flow process

Convection

Magma ascent

Lava flows

characteristics of the system which are relevant to the present measurements.

Because of the potentially important influence, in

many magmatic processes, of a yield strength and other non-newtonian properties (Sparks et al., 1977; Pinker-

ton and Wilson, 1994; Parfitt and Wilson, 1994), controlled laboratory experiments on basaltic lavas at

sub-liquidus temperatures are required to investigate

the rheological effects of crystals and bubbles.

The furnace is 760 mm tall, and the inner tube has an internal diameter of 38 mm. The sample is melted

in a purox re-crystallised alumina crucible with an inner

diameter of 23.8 mm and a height of 88.5 mm, and this sits in a graphite holder. The crucible is prevented from

rotating in the graphite holder by pins made of Inconel 600 (a Ni-Cr-Fe alloy which is corrosion resistant and

maintains its strength at elevated temperatures)

inserted through the graphite into the ceramic. A similar system prevents the graphite holder from rotating in

the furnace inner tube.

3. Laboratory rheological equipment used in the present study

In view of the complex behaviour of magmatic suspensions, any method of measuring their rheological

properties must be capable of measuring shear stresses over a range of shear strain rates. We use rotating vis-

cometers in the laboratory and in the field because they

permit shearing stresses to be measured over a mod-

erate range of shear strain rates. This is important in

view of the wide range of shear strain rates involved in different magmatic processes (Table 1)

A Type R Pt-Pt 13% Rh thermocouple, enclosed in re-crystallised alumina, fits in a recess in the base of

the graphite holder, and the tip of the thermocouple is

5 mm from the base of the melt. Thermocouple readings

are recorded on a Solatron Digital Voltmeter LM 1480.3, and temperatures are calculated using BS Inter- national Thermocouple Reference Tables (BS 4937:

Part 2: 1973). An Ice11 0°C Thermocouple Reference

Chamber (manufactured by Delristor Ltd.) is used as the cold reference junction. Calibration of the thermo-

couple in the temperature range 0°C to 1OO’C confirms

that the precision of the system in this temperature range is + 1°C.

Rheological measurements in the present study were performed using Haake Rotovisco viscometers mounted on top of a specially designed vertical tube furnace. Many of the problems associated with the design of a high-temperature rheological system have been discussed by Spera et al. (1988). These are not discussed in detail here. Instead, we describe the main

A water cooling jacket is used to cool the compo- nents at the top of the furnace, and Oxygen-free Nitro-

gen is introduced into the base of the furnace to ensure

that measurements are performed in a reducing environment. Vertical temperature profiles were measured to establish the optimum position of the sample holder.

The centre of the sample is located at a depth of 575 mm below the top of the furnace, where the temperature

profile is 064”C/cm. Special spindles have been developed for sub-liqui-

dus rheological measurements. These ensure that the spindles do not break during measurements and they

Implied shear strain rate

(SK’)

IO-’ (silicic melt) to 1O-6 (basic melt)

IO-’ (basaltic dyke) to lo-’ (silicic dome)

IO-’ (basalt) to 10-j (rhyolite)

H. Pinkerton. G. Norron /Journal of Volcanology and Geothermal Research 68 (I 995) 307-323 313

minimise the problems caused by slippage between the

melt and spindle at high crystal concentrations. For lavas with high crystal contents and high apparent vis-

cosities, a spindle was manufactured from Inconel600.

This is a cylindrical spindle tapered at an angle of 45”

at the top and bottom (i.e., it is an Epprecht spindle for

which the end effects are readily calculated), and in

cross section it is star-shaped with an outer diameter of

15 mm and with twelve 1.8-mm-deep V-shaped

grooves.

The outer furnace tube is positioned accurately so

that its long axis is vertical and passes through the

centre of a precision bearing system which is housed

in a brass water cooling jacket mounted on top of the

furnace. The inner furnace tube is aligned parallel to

the outer tube using graphite spacers around the outside

of the inner tube. The graphite holder and ceramic cru-

cibles are manufactured to sizes that ensure that, in the

temperature range of interest, the gap between the com-

ponents is less than 300 mm. When the spindle is sus-

pended from this bearing using a universal coupling its

centre is located within 0.5 mm of the centre of the

melt.

The pillars and other supports for the Haake viscom-

eter are bolted to the top of the furnace, and they are

also accurately aligned vertically. During the initial

heating stage of a rheological run, the bearing system,

and hence the spindle, are supported 50 mm above their

measuring positions. Thirty minutes before the first

measurement, the system is lowered using a supporting

gantry which is mounted on the central pillar, and the

spindle is positioned accurately in the centre of the melt.

The gantry for the bearing system is removed from the

central pillar and replaced by the Haake measuring head

and drive unit. A precision T-bar, connected to the

accurately located Haake measuring head, is used to

rotate the bearing system and spindle.

On Haake, and many other rotational viscometers,

electrical damping can be used to artificially remove

the fluctuations of noisy torque signals. However, this

type of damping leads to a time delay between the

actual measurement and recording of the torque. This

time delay can produce apparent rheopectic behaviour of the test fluid whilst making a dynamic rheological

measurement i.e., whilst increasing or decreasing the rotation rate, and hence incorrect viscosities are

recorded. Consequently, electrical damping is kept to

a minimum during the dynamic rheological experi-

ments.

4. Methods of analysing rheological data

The data from the laboratory rheological experi-

ments are plotted on a Hewlett-Packard x-y plotter as

instrument torque vs. spindle rotation rate (e.g.,

Fig. 1) . The analytical procedure developed by Krieger

and Elrod ( 1953), Krieger ( 1968), Yang and Krieger ( 1978)) and described by Speraet al. ( 1988), has been

modified to allow yield strengths to be incorporated. The method is used to transform the raw data to a

relationship between shear stress and shear strain rate.

It can readily be shown (e.g., Krieger, 1968) that the rotation rate, 0, of a spindle in a concentric cylinder

viscometer is related to the shear stress T by the rela-

tionship:

(7)

Q-0

where r,, is the shear stress at the spindle and rc is the

shear stress at the cup.

Krieger ( 1968) derived a general expression for the shear strain rate, f( r), by differentiation of Eq. 7 and

subsequent expansion by an Euler-Maclaurin sum-

mation. The resulting equations are valid only for continuous

flow in the gap between the spindle and cup. If the fluid

100

80 -

/

6o;//

/ 40

20

0 .‘.,I....,...’ 0 5 10 15

Rotation rate/x-pm

Fig. 1. Raw torque-rotation rate data from the Haake viscometer for

Sample Etna 83/2 at a temperature of 1105.3T. Small yield

strengths, non-linear relationship between torque and rotation rate

and apparent thixotropic behaviour of the lava at this temperature

are also detected in other runs at temperatures less than I 120°C.


has a yield strength, T,,, and the shear stress at the cup,

r,, does not exceed the yield strength, then only part of

the fluid will be sheared. Beyond the radius, RCtit, at

which r equals rY, the fluid behaves as a rigid body.

The critical radius is readily calculated from:

A4 Rztil = -

7,.2 rrh (8)

where M is the torque required to overcome the yield

strength and h is the effective spindle height. Hence

Eq. 7 is valid for plug flow if T,, is substituted for TV

and, in the subsequent expansion, Rcrit is substituted for R,.

The raw viscometer data are digitised by measuring

the instrument torque at given rotation rate intervals.

The shear stress at the spindle, TV, at a given rotation

rate is calculated using appropriate end corrections for

the spindle (Highgate and Whorlow, 1969).

Following Krieger ( 1968) and Spera et al. ( 1988), the evaluation of the shear strain rate function f(~~)

requires the first, second and third derivatives of a graph

of In ragainst In 0. A polynomial is fitted to this graph

and the 12 value is computed initially for a first-order

polynomial: if? is greater than 0.95, this is considered statistically significant; if 2 is less than 0.95, the proc-

ess is repeated for a higher order polynomial curves until ? is greater than 0.95. The resulting polynomial

is differentiated and the results are substituted into the

Euler-Maclaurin expansion and hence the shear strain

rate at each shear stress can be plotted. This gives a general flow curve as the calculation does not assume

a flow model at any point during the analysis. Flow models are fitted to the general flow curve to derive

rheological parameters such as the viscosity at unit

shear strain rate.

4.1. Assessment of errors

In addition to the problems noted earlier, significant

errors in some rotational viscometers can be caused by friction within the bearings and measuring head. ‘This has been assessed in the present study by measuring the torque as the spindle is rotated in air. During all calibration runs, the maximum recorded frictional torque was less than 1% of the maximum possible

torque for the measuring heads. Moreover, if a spindle is not perfectly straight, or if the system is not designed to ensure central alignment of the spindle, it will not

rotate on the concentric axis of the measuring system,

resulting in fluctuating torque readings. Our system has

been designed to minimise these problems, and total errors are estimated to be less than 5% for all rheological measurements.

4.2. Equipment calibration

The RV3 Haake rotoviscometer was calibrated at

low temperatures using standard viscosity silicone oils

and at high temperatures by measuring the viscosity of

a standard soda-lime-silica float glass supplied by Pilk- ington, PLC. The measured viscosities were within 5%

of the supplied values at all measured temperatures.

The Type R Pt-Pt 13% Rh thermocouple used in the

furnace was calibrated against two other thermocouples

of the same type connected to an independent digital voltmeter. In all cases, temperatures were within * 2°C.

5. Laboratory rheological measurements on a Mount Etna lava

Results presented here are based on two sets of measurements on lava collected during the 1983 eruption of Mount Etna (Guest et al., 1987). The lava was col-

lected from an overflow from the main channel at an

altitude of 2400 m. It was air-quenched from the erup-

tive temperature of 1095°C.

5.1. Sample preparation

Samples of lava were crushed and ground in a Tema Mill. Controlled degassing in the laboratory was

achieved by heating the powdered basalt in the furnace at a temperature of 1145°C. The lavas in two sets of measurements (Etna83/ 1 andEtna 83/2) weremelted at the same temperature. This ensured that the loss of

volatiles and evolution of bubbles and crystals in both measurements would be similar.

5.2, Etna 83/l measurements

All the Etna 83/l rheological measurements were made using a Haake RV3 viscometer. The MK500 measuring head, which has a maximum torque of 5 X 10m6 kg m, was used for all measurements above


Table 2 Time-temperature evolution of Etna 83/ 1 rheological measurements. Measurement runs took between 20 and 26 minutes.

Run Measurement run duration (min)

Time between measurement runs (min)

Temperature

(“0

9 0

21 5 32 2 31 60 31 1 31 65 31 2 31 61 31 1

1084 1084 1084 1093 1093 1101 1101 1116 1116

1 lOO”C, whereas the MK5000, which has a maximum torque of 50 X 10e6 kg m, was used at lower temperatures. The degassed sample was heated at a rate of 10°C min- ’ to a temperature of 1084’C. Thermal equi- librium of the melt in all samples was attained by keep- ing the temperature constant at the required temperature for periods of 60 to 67 minutes (Table 2) before making any measurement. Three sets of measurements were made at 1084”C, and two were made at each of 1093”C, 1101°C and 1116°C (Table 2). The sample was quenched from 1116°C by turning off the furnace and flushing with Oxygen-free Nitrogen. Each set of measurements involved recording the torque-rotational rate relationship as the spindle rotation rate was firstly increased slowly to 10 t-pm and then decreased at the same rate to zero. The star-shaped spindle described earlier was used for all measurements.

No yield strengths were detected during any of the 83/l measurements. A repeat set of experiments was performed on an identical sample to check the repro- ducibility of measurements. We also wished to deter- mine whether the apparent absence of a yield strength during the 8311 measurements was because the measuring head used at lower temperatures was insuffi- ciently sensitive to detect a small yield strength.

5.3. Etm 83/2 measurements

During this set of measurements, we replicated the 8311 measurements during a similar heating cycle. We

measured the rheological properties of the lava at lower temperatures than in the 83/l measurement and we established the chemical and rheological changes that developed when lava was left at an elevated tempera-

ture for different times. Finally, we measured the rheological properties as the temperature was reduced at a similar rate to that used during the heating cycles.

Sixteen sets of measurements were made at temperatures in the range 1090 to 1125°C. The Haake RV3 viscometer was used in conjunction with the MK500 measuring head at all temperatures, except for one of the runs at 1118°C when a Haake RV20 viscometer with an Ml0 measuring head was used. Measurements were also made as the temperature was decreased to 1089.9”C (Table 3).

During the first measurement at 1095”C, measured torques were highly variable as the rotation rate was increased. However, when the rotation rate was reduced to zero, the torque-rotation rate trace was stable. The trace was non-linear, and it did not pass through the origin. Since the instrument was zeroed precisely before each experiment, the lava thus had a well defined dynamic yield strength. A duplicate run confirmed that the lava had similar properties. The second run also confirmed that the lava exhibited apparent thixotropy. The temperature was then raised in 10°C steps to 112X, and rheological measurements made at each intermediate temperature.

The furnace temperature was reduced to 1118°C and left for 12 hours at this temperature. While the shear stress-shear strain rate relationships before and after this period were similar, the small yield strength which the lava possessed before the 12-hour gap had doubled (Table 3). The temperature was then decreased to 1089.9”C. At this temperature, the maximum rotation rate was kept constant for 5 minutes and the lava showed rheopectic properties.


Table 3

Yield strengths for Etna 83/2 6. Discussion of the rheological results

Run Time between runs Temperature Yield strength

(min) (“C) (Pa)

lu

Id

2u

2d

3U

3d

4u

4d

SU

Sd

6u

6d

7u

ld

8u

8d

9u

9d

IOU

10d

IIU

IId

12U

12d

13u

14u

15u

16~

16d

53

37

44

22

715

15

50

40

40

48

24

15

41

1095.0 n/d

1095.0 51

1095.0 51

1095.0 51

1105.3 0

1105.3 0

1105.3 0

1105.3 17

1115.5 0

I 115.5 0

1125.0 0

1125.0 0

1118.0 17

1118.0 17

I 118.0 34.5

I1 18.0 31.0

1118.0 0

1118.0 0

1112.0 0

1112.0 0

1100.9 17

1100.9 17

1089.9 17

1089.9 17

1086.5 78.3

1089.9 78.3

1089.9 78.3

1097.5 n/d

1097.5 26.0

A measurement was attempted at a temperature of

1078°C. However, at this temperature there was con- siderable elastic rebound of the spindle during insertion

into the melt due to the viscoelastic properties of the

melt and, as the spindle rotated in the lava, erratic torques were measured because the high viscosity and

yield strength of the lava caused a cavity to be formed during spindle insertion. This cavity did not refill on

the time scale of a measurement. Thus, as the spindle rotated, it sheared varying amounts of lava, giving erratic torque readings. This behaviour is reminiscent of that of the Hawaiian lava used by Shaw at 1120°C (Shaw, 1969). Finally, the temperature was increased to 1097.5”C, the last rheological measurements were made, and the sample was quenched from this temperature.

Data from the laboratory rheological experiments are

recorded as graphs of instrument torque vs. spindle

rotation rate (Fig. 1) . Using the analytical procedure

described earlier, the raw data are transformed to shear

stress - shear strain rate relationships. The rheological

data collected during the Etna 83/l and 8312 heating

cycles are similar.

The measurements, which have been analysed for

shear strain rates in the range 0.3 to 5.0 s-‘, confirm

that the 1983 Etna lava is Newtonian at temperatures

greater than 1120°C. When the shear strain rate was

very slowly reduced to zero, measurements confirmed

that the Etna lavas at temperatures less than 1120°C

had dynamic yield strengths which varied systemati-

cally with temperature (Fig. 2). The maximum yield

strength recorded in the laboratory was 78 Pa at a tem-

perature of 1087°C. While the lavas are therefore Her-

schel-Bulkley fluids, their yield strengths are so low

that they can be approximated as power law fluids

(r* > 0.95) at temperatures less than 1120°C (Fig. 3).

The exponent in the power law equation decreases sys- tematically from 1.00 at temperatures greater than

1120°C to 0.46 at 1084°C. The variation of unit shear

strain rate viscosity as a function of temperature is

shown in Fig. 4. From Fig. 4, the activation energy, E, for a shear strain rate of 1 s- ’ is 1485 kJ mol- ’ K- ’

Temperature /“C 1156 1116 1078

40°4

0.00070 0.00071 0.00072 0.00073 0.00074

Inverse Temperature /(l/K)

Fig. 2. Yield strength of the 1983 Etna lavas measured in the labo-

ratory as a function of temperature.

H. Pinkerton, G. Norton /Journal of Volcanology and Geothermal Research 68 (I 995) 307-323 317

Temperature / “C 1156 1116 1078

1 I I

1

1.0 -

0.8 -

0.6 -

0.4 I I I 0.00070 0.00071 0.00072 0.00073 0.00074


Fig. 3. Power law exponent as a function of temperature for the 1983

Etna lavas. Data for lavas with a high crystallinity are represented

by open squares; data for lavas with a lower crystal content are

represented by filled diamonds.

Temperature PC 1156 1116 1078

CA o! I I . f 8100

5 0.00070 0.00071 0.00072 0.00073 0.00074


Fig. 4. Laboratory measurements of apparent viscosity (at unit shear

strain rate) as a function of temperature for the 1983 Etna lavas. The

symbols are the same as those in Fig. 3.

as the temperature is increased, and 942 kJ mol- ’ K- ’ as the temperature is reduced.

Our measurements also indicate that, as previously

found for hawaiian lavas (Shaw et al., 1968; Shaw,

1969), the lavas are thixotropic at all measured temperatures. During the time interval between rheological

measurements at the same temperature, the static yield strength increased, and the magnitude of the regained

yield strength was dependent on the time at rest. Because crystal growth rates are considerably slower

than rates at which crystals dissolve, the crystal content

on melting a lava at a given heating rate will generally

be greater than in a sample which has been cooled to

the same temperature at the same relatively rapid rate. This explains why the apparent viscosities of crystal-

lising Etna lavas were larger in samples that have been

heated than in those which have cooled (Fig. 4).

7. Reasons for the non-Newtonian behaviour of l

Etna lavas at temperatures below 1120°C

Apparent non-Newtonian behaviour in suspensions

can be caused by factors such as crystal settling or

bubble rise during measurement, thixotropy of the melt,

alignment of crystals during shearing, particle migra-

tion away from the spindle, viscous heating and shear-

induced crystallisation. As noted earlier, some of these

effects can be artefacts of the measuring system or measurement procedure. Before we can have any con-

fidence that the measurements made here reflect the

rheological properties of flowing Etna lava, we need to investigate the possible reasons for the non-Newtonian

properties of the lavas examined during the present

study. Geochemical analyses of the quenched Etna 8312

rheological sample show that the composition is not

significantly different from that of the original lava or

from the Etna 83 / 1 quenched lava (Table 4). In addition, the composition of the top of the sample is virtu-

ally identical to the composition of the bottom, suggesting that crystal settling was not important on

the time scale of these experiments. A modal analysis

of thin sections cut perpendicular to the axis of rotation of the fluid at the mid point of the Etna 83/2 sample

show that there were 5-10 vol.% and < 20 vol.% bub-

bles less than 0.5 mm diameter in the lava at 1116°C and 1097.X, respectively. The sample quenched from

1097S”C contained 30-35 vol.% crystals of plagio-

clase, augite and olivine of less than 0.2 mm equivalent

diameter. The crystals were generally subhedral,

although some of the pyroxenes were acicular. The radial distribution of crystals and bubbles in the Etna

8312 thin section was uniform, and there was no evidence of heterogeneous crystallisation or bubble nucleation at the spindle or cup. An examination of a thin section parallel to the long axis of the sample showed that the axial distribution of particles did not vary, confirming the lack of crystal settling. The crystal

Table 4 Petrography and geochemistry of Etna lava (Sample number GPW832). Major-element geochemistry of Etna 83/ 1 (column 4) and post-rheological measurement geochemistry of Etna 83/2. Anal- yses of the Ema 8312 samples were carried out at the Grant Institute of Geology, Edinburgh University; pellets and discs were kindly prepared by Stuart Black and Ricky Herd at Lancaster University. Etna 83/l and 83/2 are very similar, both chemically and mineralogically, to the lavas erupted during the 1991-93 eruption of Etna (Armienti et al., 1994)

Etna 83/2: Bottom

Major elements (wt.%) SiO, 41.32 Al@, 16.73 Fe@, 11.24 MgO 5.78 CaO 10.32 Na,O 3.80 GO 1.87 TiO, 1.70 MnO 0.18 pzo5 0.55 Total 99.49 L.O.1 0.50

Etna 83/2: Top Etna 83/ 1

47.20 46.79 16.91 16.56 11.30 10.29 5.61 5.65

10.35 10.38 3.84 3.21 1.90 1 .I5 1.74 1.70 0.18 0.18 0.55 0.55

99.48 97.12 0.00 0.00

Trace elements (ppm) SC 27 Ba 696 V 330 La 58 Ce 124 Nd 43 Cr 821 Ni 3290 cu 125 Zn 105 Pb 7 Th 9 Rb 43 Sr 1171 Y 28 Zr 228 Nb 53

29 704 316

70 125 51

854 3276

119 100

6 9

44 1196

28 231

55

sizes and concentrations in the Etna 8312 quenched samples were larger than those in the Etna 83/l quenched sample, which is understandable considering the lower quench temperature used in the Etna 8312

case. The effects of radial motion can be further. investi-

gated by calculating the critical Reynolds number for radial flow using Eqs. 5 and 6. Substituting Rb = 7.5 mm and R,= 16 mm in Eq. 5, the critical Reynolds


number for secondary motion in the crucible is 56.6.

By contrast, the maximum Reynolds number of the

tangential flow caused by rotation of the spindle is 6~ 10-s (substituting r=2700 kg rnp3, 0=2

rad s-‘, q=200 Pas and h=28 mm in Eq. 6). This

confirms that particle migration will not be important,

even at the highest rotation rates and lowest viscosities

encountered during these measurements. The observed

thixotropy is therefore not caused by bubble or crystal migration, but is probably due to crystal alignment par-

allel to the flowlines. The effect of viscous heating of the melt at high shear

strain rates can be calculated for the worst case using

Eq.2withr)=3000Pas,R=2rads-1,R,=7.5mm, R,=16 mm and ~=3.0 W m-r K-‘. For n=0.4,

AT= 0.02 K and for n = 1 .O, A T = 0.03 K; hence the

observed non-Newtonian behaviour during many runs

was not caused by viscous heating.

Another factor which can cause pseudoplastic

behaviour is bubble deformation at high shear strain

rates. The critical shear strain rates which cause bubble

deformation are readily calculated from Eq. 4, using

u = 0.3 N m _ ‘, Ca = 0.4 and rp = 0.4 mm. The results

suggest that critical shear strain rates of 3 s- ’ and 0.1

S -' are required to deform bubbles in melts with a

viscosity of 100 Pa s and 3000 Pa s, respectively. The

calculated shear strain rates for the rheological exper-

imentsareupto5s-‘, so bubbles will deform at the

higher rotation rates of the spindle, especially at the

lower temperatures. These calculations are supported by a thin section of the Etna 83/l sample which was

quenched from 1116°C. This revealed that the sample

had less than 20 vol.% crystals measuring < 0.01 mm along their longest dimension, and 5-10 vol.% vesicles

measuring up to 0.2 mm along their longest dimension.

Many of the bubbles in the quenched specimen were distorted along the line of shear, supporting our view

that they contributed to the observed pseudoplastic behaviour in some of the measurements. The other fac-

tor causing pseudoplastic behaviour in the low-temperature runs at all strain rates is an interaction effect between crystals at high crystal concentrations (Pin- kerton and Stevenson, 1992).

During some runs, the viscosity increased on shearing. An explanation for this anomalous behaviour is, as noted earlier, that prolonged shearing in a magma can cause crystallisation and hence increase apparent viscositv (Kouchi et al.. 1986). These effects will be , \


greater at lower temperatures. This is supported by the

observation that the rheopectic behaviour in runs at

1084°C was greater than at 1093°C. In summary, the non-Newtonian properties of the

Etna lavas that we measured cannot be explained by

crystal settling, secondary fluid motion in the lava or

viscous heating. The deformation of bubbles and inter-

action effects between crystals are considered to be the

main factors causing the pseudoplastic behaviour of the lavas. The alignment of the long axes of the crystals

parallel to the flowlines is considered to be the main

factor causing the thixotropic behaviour of the lavas,

and the rheopectic behaviour results from shear-

induced crystallisation. Since these processes also take

place during the flow of lava in the field, our measurement system mimics the flow behaviour of lava in

active flows.

8. Field measurements of the rheological properties of lavas

Field rheological measurements were made on a

small overflow from the main channel of the 1983 eruption of Mount Etna (Guest et al., 1987), 200 metres

10 , I

0 10000 20000

Shear stress /Pa 3oooo

Fig. 5. Raw field data using a rotating vane viscometer: (a) with a

Newtonian model ( 7) = I385 Pa s) fitted to the data (the dotted line);

and (b) with a Bingham model ( Q = 1260 Pa s; rY = 370 Pa) fitted

to the raw data (the solid line). The raw rotation rate-torque data

are analysed by solving the equation f2= l/r),{ [(r- $)/2] - [e/2

In( T/I/I) ) ) (Pinkerton, unpubl. calculations) using graphical itera-

tion where r and R are the measured torques and corresponding

rotation rates, and I,+ and qr, are the best-tit yield strengths and Bing-

ham viscosities. Note that data for Bingham models are non-linear

on plots of rotation rate against torque.

from the main effusive source, where the measured

temperature was 109W.

A pre-heated vane was inserted into the lava and rotated at different rates by hand. The shear stresses

required to shear the lava at different shear strain rates

were calculated from the measured torque and rotation

rates using the methods described earlier.

The results of these measurements are shown in

Fig. 5. Since the measurements were made over a limited range of rotation rates, a unique rheological model cannot be applied to the data. If the lava is assumed to

behave as a Newtonian fluid, it has a Newtonian vis-

cosity of 1385 Pa s (Fig. 5, dashed line). If a Bingham

model is applied, and if we assume a maximum yield

strength of 370 Pa, the apparent viscosity at unit shear

strain rate is 1630 Pa s, and the Bingham viscosity is

1260 Pa s (Fig. 5, solid line). Pinkerton and Sparks ( 1978) used a shear vane vis-

cometer and a penetrometer to measure the rheological

properties of the interior of the 1975 Mount Etna lava

flow. They fitted a Herschel-Bulkley model to their

measurements at 1086°C to give a viscosity of approximately 9200 Pa s at a shear strain rate of 0.1 s- ‘, and

a yield strength of 370 Pa. Extrapolating these values

to a shear strain rate of 1 s - ‘, the apparent viscosity of

the 1975 Etna lava is 8625 Pa s.

Clearly, there is a need for better constrained meas-

urements of the rheological properties of lavas in the field. Nevertheless, the range of rheological properties

based on field measurements during 1983 are compat-

ible with those inferred from laboratory measurements

(Figs. 2 and 4). The unit strain rate apparent viscosity

of the 1975 lava was three times that of the 1983 lava at comparable temperatures. This difference is attrib-

uted mainly to the high crystal content (45 vol.%) and

vesicularity of the lava in the field in 1975 compared with the highest values attained in our laboratory meas-

urements.

9. Comparison of measured and calculated rheological properties

The viscosities measured in this study (lines OX and OY, Fig. 6) are significantly higher than values calculated using the method of Shaw ( 1969) (line AOB, Fig. 6). This difference is due to the changing chemistry of the melt during crystallisation, together with

320 H. Pinkerton, G. Norton /Journal of Volcanology and Geothermal Research 68 (I995) 307-323

TemDerature /“C 1156

1 1116 1078

: 9 I I . 8100

A 0.00070 0.00071 0.00072 0.00073 0.00074


Fig. 6. A comparison of the measured and calculated unit shear strain rate viscosities of the 1983 Etna lavas as a function of temperature. The lowest line (A-B) is calculated using the method of Shaw ( 1972); the dotted line (0-C) is the calculated viscosity of the residual glass assuming 40% crystallisation at a temperature of 1084°C; lines P-Q and R-S represent the calculated viscosities for 20% and 40% crystallisation, based on the method described by Pinkerton and Stevenson ( 1992). The values for shape, size distribution and maximum packing concentration used here are identical to those used by Pinkerton and Stevenson ( 1992) for the 1975 Etna lava. Lines O-X and O-Y correspond to the trends measured during the heating and cooling cycles in the laboratory, and they represent different crystal contents of the lava at different temperatures. Line O-B represents the changing rheological properties resulting from supercooling of the melt. Activation energies change from 227 k.J mol- ’ K- ’ for the supercooled melt to 413 kJ mol-’ K-’ for the residual glass to 942 kJ mol-’ K-’ for lavas with a low crystal content and 1485 kJ mol-’ K-l for lavas with a higher crystal content. The symbols are the same as those in Figs. 3 and 4.

the hydrodynamic interaction effects caused by bubbles and crystals in the experimental sample. The factors

controlling the development of a non-Newtonian rhe-

ology in crystallising melts have been reviewed by

Pinkerton and Stevenson ( 1992), and it is accepted that basic melts can be approximated as Newtonian

fluids at crystal concentrations less than 25 vol.%. At

higher concentrations, lavas behave as pseudoplastic

materials with a yield strength, and their shear stress - shear strain rate relationships can be calculated from the crystal sizes, shapes and size distributions.

In Fig. 6, we show the calculated apparent viscosity

of a supercooled Etna lava (line OB); the apparent viscosity of the residual melt during crystallisation

(line OC); and the calculated trends (using the Pin- kerton and Stevenson ( 1992) model) for 20% and 40% crystal content (lines PQ and RS). Modelled crystal

contents are similar to those of quenched samples

heated to 1116°C and 1098”C, respectively. Calculated yield strengths increase from 64 Pa for a crystal content,

@,of0.2to138Pafor@=0.4,and478Pafor@=0.47.

The close agreement between theoretical and measured

values of apparent viscosity and yield strength in the field and in the laboratory (Figs. 4 and 6) supports the usefulness of the model developed by Pinkerton and

Stevenson ( 1992) to calculate the rheological properties of lavas at sub-liquidus temperatures.

10. Discussion of the rheological properties of Etna laws

At temperatures less than 112O”C, the 1983 Etna lava

is a pseudoplastic fluid with a yield strength which increases with decreasing temperature. However, even

at the lowest temperatures measured in the laboratory,

yield strengths are so small that the lavas can be approximated as power law fluids in the temperature range

1084 to 1120°C. At higher temperatures, the bulk viscosity decreases according to an Arrhenius relation-

ship, and the lava becomes Newtonian at temperatures

above 1120°C. Viscous heating and crystal settling were negligible for the time scales and shear strain rates

used in these experiments, and migration of crystals

and bubbles away from the spindle due to radial motion

of the lava on shearing did not occur.

On cooling the lava, the activation energy for Row increased as a function of decreasing temperature and

inferred increasing crystal content. Our measurements

suggest that the Etna lavas are thixotropic at tempera-

tures less than 1120°C. They also support previous observations (Kouchi et al., 1986) that stirring induces

crystallisation, especially at high degrees of supercooling, leading to rheopectic behaviour, a dramatic

increase in viscosity, and the development of a yield

strength. Our measurements also suggest that, if a magma is

left at rest for a sufficient length of time, the static yield strength will increase, with the magnitude of the regained yield strength depending partly on the time at rest. For most magmatic situations, it is the dynamic yield strengths that are important, as a magma will usually have been sheared to some extent, destroying any structure that gives the magma a static yield strength. However, the static yield strength will control


some phenomena, such as crystal settling, bubble growth and episodic eruptions from a high-level magma chamber. Most measurements of yield strengths on active lava flows record the dynamic yield strength, and only in situations such as a stationary flow lobe or after a time at rest in a rotating cylinder viscometer will static yield strengths be measured. Thus, for quoted values of magmatic yield strengths in the liter- ature, it is important to assess the shearing history of the fluid.

In all of our quenched samples, the bubbles were distorted by shearing. According to results from experiments on rhyolitic lavas (Spera et al., 1988)) up to 10 vol.% bubbles generated a five-fold increase in the viscosity of the bubble-free fluid. By contrast, our measurements indicate that the unit strain rate apparent viscosities at different temperatures can be explained in terms of crystal interactions. However, we accept that bubble interaction and deformation at high strain rates could accentuate the observed large departures from Newtonian behaviour at lower temperatures. We also accept that bubbles have an important influence in the field rheological measurements, but it is conceiva- ble that their effects were buffered by the higher volatile concentrations of lavas in the field. Clearly, additional investigations on the separate effects of crystals, bubbles and volatiles are required.

11. Conclusions

Our measurements have shown that the 1983 Etna lavas are Newtonian at temperatures above 1120°C. At lower temperatures, the lava is a thixotropic, pseudoplastic fluid with a maximum yield strength of 78 Pa at a temperature of 1087°C. Apparent viscosities at unit shear strain rates increase from 150 Pa s at 1125°C to 3000 Pa s at 1084°C. These values are compatible with apparent viscosities measured on the same lavas in the field, which range from 1385 Pa s to 1630 Pas at a temperature of 1095”C, and with those calculated using the model developed by Pinkerton and Stevenson ( 1992). The measurements in this paper clearly doc- ument the wide range of rheological properties of lava that can be erupted from the source vents on Etna.

In view of the limited compositional variations of historic lavas erupted from Mount Etna, the results can be used to infer the rheological properties of lavas

erupted during future eruptions on Etna, although it has to be recognised that some historic Etna lavas have had higher crystallinities than those encountered during the present study. As mentioned earlier, the 1975 sub-ter- minal lavas on Etna had higher crystal and bubble contents and consequently they had apparent unit strain rate viscosities three times higher than those measured at the same temperature in the present study. The results also give an insight into the rheological behaviour of basaltic lavas from other volcanoes at subliquidus temperatures.

This is the first stage in a programme which is designed to investigate the rheological properties of lavas in the field. Further measurements are planned using a co-axial cylinder field viscometer. The results from all of this work will help to constrain the appropriate rheological parameters to use in future finite element models of lava flows.

Acknowledgements

This paper is dedicated to Rob Williams who was responsible for much of the development work on the high-temperature rheology system, and who tragically died in an air crash in March, 1993. The authors wish to thank Harry Vasey and Robert Sumner from Lan- caster University for the outstanding engineering skills they displayed while constructing the high-temperature systems described in this paper. They also wish to thank John Guest and the Royal Society for their assistance during the 1983 eruption of Mount Etna and GEN thanks NERC for a studentship. The paper has improved considerably thanks to the careful reviews by Steve Self and Eric Grosfils and helpful editorial comments by Lionel Wilson. This study was completed with the assistance of a grant from the commission of the European Communities, DG XII, Environment Pro- gramme, Climatology and Natural Hazards Unit, in the framework of the contract EVSV CT92-0190.

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Rheological properties of basaltic lavas at sub-liquidus temperatures: laboratory and field measurements on lavas from Mount Etna