Multiphase rheology
Naturally-occurring magmas and lavas consist of a suspension of gas bubbles and solid crystals in a liquid silicate melt. Crystal volumes range from 0% up to the critical point of maximum packing (~60%). Particle sizes range widely, from large lithic fragments down to micron-sized microlites. The bulk of crystals grown in-situ within the magma are typically in the range 1mm-10mm. They can be rounded (e.g. olivine) or angular (e.g. feldspar) with possibly very high aspect ratios. Bubble volumes in magmas cover an even wider range than crystal volumes because, being deformable, there is no maximum packing fraction. Bubble volumes around 60%-80% are not uncommon and >90% can be attained (e.g. basaltic reticulate). Our ability accurately to predict natural flow processes and the resultant geohazards rests on an understanding of the effects of such inclusions on the fundamental flow behaviour, or 'rheology', of the mixture. For example, the rheology is needed to quantify convection and crystal settling in magma chambers; volatile exsolution, bubble growth rates and the resultant explosivity, magnitudes and dimensions of eruptions; and effusion rates and flow dynamics of lavas.
Our aim with this project is to establish the rheological effect of adding appreciable amounts of bubbles and crystals to magmas. We will be using several volcanic field settings in the West Indies to provide case studies to which we will apply the results, specificaly St Kitts (Mount Liamuiga, left photo), Montserrat (Soufriere Hills Volcano, middle photo) and St Vincent (La Soufriere Volcano, right photo). The primary aim of rheological studies is to produce a constitutive equation that relates the rate of deformation (shear strain-rate) to the imposed stress (shear stress). Such an equation allows the dynamic shear viscosity of the mixture to be determined from its fundamental physico-chemical properties (e.g. particle content, surface tension, viscosity of the liquid etc.). Knowledge of the constitutive equation for a fluid allows its flow to be modelled via the Navier-Stokes equations. The simplest constitutive equation is that of a 'Newtonian' fluid for which the stress is proportional to the strain-rate. The constant of proportionality is the 'viscosity' of the fluid. Pure silicate melts are known to be Newtonian for a broad range of conditions.
The results of an earlier (also NERC-funded) project on bubble suspensions enabled us to understand the rheological impact of adding bubbles to Newtonian liquids. In that project, we generated bubble suspensions in an analogue (i.e. non-magmatic), strictly Newtonian liquid (golden syrup) and used rotational rheometric techniques to observe the viscoelasticity of the suspensions. A semi-empirical constitutive equation was generated by combining these data with a physical analysis of the response of deformable inclusions to imposed stresses (see Llewellin et al (2002a) and Llewellin et al (2002b)). In this project we are extending this approach to particle suspensions.
A problem that has been a major stumbling block for all previous studies of the effect of adding solid particles to liquids is that the rheology is strongly-dependent on the internal arrangement of the particles. For example, yield strength, shear thickening and shear dilatancy all result from interactions between particles. Previous researchers have not been able to observe the dynamic arrangement of the particles in tandem with a rheological measurement. As a result, the standard view has been that the rheology is dependent on sample 'history'; the internal arrangement of particles and hence the rheology was altered during a measurement and the only way to reproduce the rheology was to reproduce the entire process. In the last few years there has been a major advance in technology with the company HAAKE producing the first combined Rheometer/Microscope, called the HAAKE MARS Rheoscope (see photo). We are using this instrument to try to link the rheology directly with the fundamental internal particle dynamics and hence bypass the problem of sample 'history'.
Dr Sebastian Mueller is primarily interested in understanding the effect of adding solid particles to magmas. As a case study, he will consider the rheological effect of the evolution of crystal content during magma ascent at Soufriere Hills Volcano on Montserrat. Also, Deborah Robertson has now joined the group and will be studying the effect of three-phase magmas (i.e. magmas containing bubbles and crystals) with St Kitts as a case study. She is based at the University of the West Indies (UWI) and is co-supervised by Dr Jocelyn Knight (Department of Physics, UWI) & Dr Nicolas Fournier (Seismic Research Unit, UWI).
Related publication:
- Llewellin EW, Mader HM & Wilson SDR (2002)'The constitutive equation and flow dynamics of bubbly magmas.' Geophysical Research Letters, 29(24), 2170, 2002. Llewellin EW, Mader HM & Wilson SDR (2002) 'The rheology of a bubbly liquid.' Proceedings of the Royal Society, Series A, 458, 987-1016, 2002.