Rheological behavior of bubble-bearing magmas

The vesiculation of the rising magma in a volcanic conduit results in a large change in the viscosity of magma. Understanding the effect of bubbles on the viscous behavior of bubble–melt mixtures over a wide range of bubble volume fractions is essential for accurate modeling of the volcanic processes. In this study, new equations for the relative viscosity of concentrated bubble-bearing suspensions are developed using a differential scheme along with the solution of an infinitely dilute suspension of bubbles. Out of the four models developed in the paper, two models predict the relative viscosity to be a function of only two variables: capillary number and volume fraction of bubbles. There are no adjustable parameters in these models. The remaining two models include an additional parameter, that is, the maximum packing volume fraction of bubbles. The proposed models are evaluated using published numerical and experimental data on the relative viscosity of concentrated suspensions of bubbles. The viscosity models for bubble-bearing suspensions developed in this study are useful in modeling of the volcanic processes.