Bubble deformation in magma under transient flow conditions

Abstract

We investigate the transient behavior of bubble deformation in magma. Previous studies have used the relationships between capillary number and equilibrium shape for a single bubble under either steady simple shear or steady pure shear to estimate strain rates in pyroclasts and to calculate bubble shapes in a conduit flow. We developed a deformation model for a bubble by adjusting the empirical functions used in an existing model for a droplet to fit experimental data for bubble deformation. The modified model was used to calculate transient large deformations of a single bubble in arbitrary shear flows. In this paper, we demonstrate the significance of the modified model through two different applications. Firstly, using this model, we are able to simulate the entire history of the evolution of bubble shapes in a time dependent flow using the computational code, Conflow. In this simulation, we further include the effect of gas expansion on the bubble shape. From this simulation, we show that bubble deformation in conduit flow is controlled by the history of both capillary number and strain. Secondly, by using this model to analyze bubble shapes observed in natural magma samples, we are able to better estimate the strain rates and deformation durations. We apply this model to certain transient features in the relationship between bubble shape and radius in the published data of obsidian clasts from Newberry Volcano and estimate a deformation duration of 2.7–4.0 min.