Bubble growth in visco-elastic magma: implications to magma fragmentation and bubble nucleation

Abstract

We present a visco-elastic bubble growth model, accounting for viscous and elastic deformations and for volatile mass transfer between bubbles and melt. We define the borders between previous bubble growth models accounting for incompressible viscous melt, and our new model accounting also for elastic deformation; this is done by a set of end-member analytical solutions and numerical simulations. Elastic deformation is most prominent for magma of small vesicularity, where the growth regime depends on the shear modulus. For high shear modulus, bubble growth is slow and follows an exponential law in a viscous growth regime, while for low shear modulus bubbles quickly follow a square-root diffusive solution. Our model provides all the elastic components (stresses, strains and strain rates) required for defining criteria for failure and magma fragmentation. We suggest two failure criteria, a stress related one based on the internal friction and the Mohr-Coulomb failure theory, and a strain related one based on fibre elongation experiments. We argue that both criteria are equivalent if we consider their shear modulus dependency and its effect on magma rheology. Last, we apply our model to the process of bubble nucleation. In the incompressible case, following nucleation, growth is slow and leads to long incubation times during which bubbles may be dissolved back into the melt. The elastic response in magmas with low shear modulus results in a short incubation time, increasing the probability of survival. The above effects emphasize the significance of visco-elasticity for the dynamic processes occurring in magmas during volcanic activity.