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

Film drainage and the lifetime of bubbles

[1] We present the results of new laboratory experiments that provide constraints on inter bubble film thinning and bubble coalescence as a consequence of liquid expulsion by gravitational and capillary forces. To ensure dynamic similarity to magmatic systems, the experiments are at small Reynolds numbers inline image and cover a wide range of Bond numbers (10−3 ≤ Bo ≤ 102). Results indicate that at Bo < 0.25 film drainage is due to capillary forces, whereas at Bo > 0.25 gravitational forces result in film thinning. The film drainage time scale is given by t ∼ C ln (α) τ and is orders of magnitude faster than often assumed for magmatic systems. Here, C ∼ 10 is an empirical constant and α is the ratio of initial film thickness to film thickness at the time of rupture and τ is the characteristic capillary or buoyancy time scale at values of Bo < 0.25 and Bo > 0.25, respectively

A new bubble dynamics model to study bubble growth, deformation, and coalescence

We propose a new bubble dynamics model to study the evolution of a suspension of bubbles over a wide range of vesicularity, and that accounts for hydrodynamical interactions between bubbles while they grow, deform under shear flow conditions, and exchange mass by diffusion coarsening. The model is based on a lattice Boltzmann method for free surface flows. As such, it assumes an infinite viscosity contrast between the exsolved volatiles and the melt. Our model allows for coalescence when two bubbles approach each other because of growth or deformation. The parameter (disjoining pressure) that controls the coalescence efficiency, i.e., drainage time for the fluid film between the bubbles, can be set arbitrarily in our calculations. We calibrated this parameter by matching the measured time for the drainage of the melt film across a range of Bond numbers (ratio of buoyancy to surface tension stresses) with laboratory experiments of a bubble rising to a free surface. The model is then used successfully to model Ostwald ripening and bubble deformation under simple shear flow conditions. The results we obtain for the deformation of a single bubble are in excellent agreement with previous experimental and theoretical studies. For a suspension, we observe that the collective effect of bubbles is different depending on the relative magnitude of viscous and interfacial stresses (capillary number). At low capillary number, we find that bubbles deform more readily in a suspension than for the case of a single bubble, whereas the opposite is observed at high capillary number