Potential Causes for the Non-Newtonian Rheology of Crystal-bearing Magmas

Experimental studies indicate that crystal-bearing magmas exhibit non-Newtonian behavior at high strain rates and solid fractions. With a zero-dimensional (0D) inversion model we re-evaluate laboratory data of Caricchi et al. [EPSL, 2007] and retrieve aggregate viscosity, elastic shear modulus and adiabatic temperature increase. Parameter estimates from these laboratory experiments indicate non-Newtonian behavior with power law coefficients of up to n = 13.5. The physical causes for the non-Newtonian rheology remain unclear. It has been speculated that finite strain effects (microstructural reordering of crystals), shear heating, power law melt rheology, or plasticity might be responsible for the non-linear behavior. Here, we use 2D direct numerical simulations to study the relative importance of each of these mechanisms. We resolve individual crystals and use a visco-elasto-plastic rheology including shear heating. Simulations are performed for spherically, elliptically and naturally shaped crystals. Numerical simulations with comparable parameters to laboratory experiments performed by Caricchi et al. [EPSL, 2007] demonstrate that shear heating has little effect on aggregate rheologies. Finite strain effects result in strain weakening or hardening, but the power law coefficient for the strain weakening is modest (maximum n = 1.3). For simulations with spherical crystals the strain weakening and hardening behavior is related to rearrangement of crystals rather than strain rate related weakening. For naturally shaped crystals finite strain effects play a minor role. Power law melt rheology is likely to occur as locally enhanced strain rates may trigger a change from Newtonian to non-Newtonian rheology. Numerical simulations show large differential stresses and large fluid pressures in the melt, this makes it likely that crystals fail plastically during deformation. Numerical experiments in which plastic failure is taken into account show high power law coefficients (n ≈ 50 in some simulations). The contribution to the non-Newtonian rheology of finite strain effects and shear heating is insufficient to induce power law coefficients comparable to laboratory experiments of Caricchi et al. [2007], while it is possible to have high power law coefficients due to plastic failure of crystals. We conclude that a combination of shear heating, finite strain effects, power law melt rheology and plastic failure of crystals, of which plasticity is the most important factor, causes the non-Newtonian rheology of crystal-bearing magmas.