A self-consistent rheological model for bubble and crystal-bearing magmas

Abstract:

Igneous processes involve multiphase magmas that contain crystals (suspensions) and sometimes exsolved volatile bubbles (emulsions). The difference in density between phases has deep implications for magma transport and differentiation. The ascent rate of magmas, and the rate of phase separation is also controlled by the rheology of the multiphase mixture. The rheology of suspensions and emulsions depends strongly on the bubble (or crystal) volume fraction and deformation, dilation and contraction due shearing, and mode alteration in crystal size distribution due breakage. Several experimental studies have been focusing on the rheology of magmatic systems, and they have constrained the impact of all mentioned factors. However, experimentally-based models remain difficult to use because they involve a significant number of free parameters (fitting procedure) that cannot be easily linked to the underlying dynamics in the suspension/emulsion. For example, these fitting parameters show a wide variability when fitted to different datasets. At this stage, we are lacking a unified theory that relates the dependence of the effective viscosity of multiphase magmas on particle volume fraction, strain-rate conditions and finally particle size distribution.

To this end, we study the rheology of crystal-bearing magma from a theoretical perspective, and aim to develop a self-consistent physical model to explain and predict quantitatively the rheology of emulsion and suspension. When compared to published experimental studies, our model can predict the rheology of magmatic systems over a wide range of particle volume fraction. It is based on a stepwise addition of particles and includes a minimal amount of free parameters to constrain the effect of volume fraction, shear rate and breakage of crystals (change in modality). Furthermore, the parameters in our model are related to either geometric or dynamic processes and can easily be constrained independently. The model accounts for both mono-disperse and bi-disperse suspensions/emulsions, and includes the effect of self and mutual crowding. We find an excellent agreement with experimental data while the model requires only constraints on the particle size distribution and particle volume fraction.