Bubble suspension rheology and implications for conduit flow

Llewellin, E.W.; Manga, M.

Abstract

Bubbles are ubiquitous in magma during eruption and influence the rheology of the suspension. Despite this, bubble-suspension 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 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 phi increases; in regime 2, the viscosity of the suspension decreases as phi increases. The viscous regime for a deforming bubble suspension can be determined by calculating two dimensionless numbers, the capillary number 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, 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 fragmentation-depth and an increase of between 40% and 250% in calculated eruption-rate compared with the assumption of Newtonian rheology.

Citation

Llewellin, E., & Manga, M. (2005). Bubble suspension rheology and implications for conduit flow. Journal of Volcanology and Geothermal Research, 143(1-3), 205-217. https://doi.org/10.1016/j.jvolgeores.2004.09.018

• Journal Article Type: Article
• Publication Date: 2005-05
• Deposit Date: Mar 29, 2007
• Journal: Journal of Volcanology and Geothermal Research
• Print ISSN: 0377-0273
• Electronic ISSN: 1872-6097
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 143
• Issue: 1-3
• Pages: 205-217
• DOI: https://doi.org/10.1016/j.jvolgeores.2004.09.018
• Keywords: Magma rheology, Bubble suspension, Conduit-flow model, Eruption model, Capillary number.
• Public URL: https://durham-repository.worktribe.com/output/1568844