Effects of crystal shape- and size-modality on magma rheology

Erupting magma often contains crystals over a wide range of sizes and shapes, potentially affecting magma viscosity over many orders of magnitude. A robust relation between viscosity and the modality of crystal sizes and shapes remains lacking, principally because of the dimensional complexity and size of the governing parameter space. We have performed a suite of shear viscosity measurements on liquid-particle suspensions of dynamical similarity to crystal-bearing magma. Our experiments encompass five suspension types, each consisting of unique mixtures of two different particle sizes and shapes. The experiments span two orthogonal subspaces of particle concentration, as well as particle size and shape for each suspension type, thereby providing insight into the topology of parameter space. For each suspension type, we determined the dry maximum packing fraction and measured shear rates across a range of applied shear stresses. The results were fitted using a Herschel-Bulkley model and augment existing predictive capabilities. We demonstrate that our results are consistent with previous work, including friction-based constitutive laws for granular materials. We conclude that predictions for ascent rates of crystal-rich magmas must take the shear-rate dependence of viscosity into account. Shear-rate dependence depends first and foremost on the volume fraction of crystals, relative to the maximum packing fraction, which in turn depends on crystal size and shape distribution.