Bubble suspension rheology and implications for conduit flow

Bubbles are ubiquitous in magma during eruption and influence the rheology of the suspension. Despite this, bubblesuspension rheology is routinely ignored in conduit-flow and eruption models, potentially impairing accuracy and resulting in the loss of important phenomenological richness. The omission is due, in part, to a historical confusion in the literature\ud concerning the effect of bubbles on the rheology of a liquid. This confusion has now been largely resolved and recently published studies have identified two viscous regimes: in regime 1, the viscosity of the two-phase (magma–gas) suspension increases as gas volume fraction / increases; in regime 2, the viscosity of the suspension decreases as / increases. The viscous regime for a deforming bubble suspension can be determined by calculating two dimensionless numbers, the capillary number\ud Ca and the dynamic capillary number Cd. We provide a didactic explanation of how to include the effect of bubble-suspension rheology in continuum, conduit-flow models. Bubble-suspension rheology is reviewed and a practical rheological model is presented, followed by an algorithmic,\ud step-by-step guide to including the rheological model in conduit-flow models. Preliminary results from conduit-flow models which have implemented the model presented are discussed and it is concluded that the effect of bubbles on magma rheology may be important in nature and results in a decrease of at least 800 m in calculated agmentation-depth and an increase of between 40% and 250% in calculated eruption-rate compared with the assumption of Newtonian rheology.\ud D 2005 Elsevier B.V. All rights reserved