A continuum model of multi-phase reactive transport in igneous systems

Keller, T. and Suckale, J. (2019) A continuum model of multi-phase reactive transport in igneous systems. Geophysical Journal International, 219(1), pp. 185-222. (doi: 10.1093/gji/ggz287)

Abstract

Multiphase reactive transport processes are ubiquitous in igneous systems. A challenging aspect of modelling igneous phenomena is that they range from solid-dominated porous to liquid-dominated suspension flows and therefore entail a wide spectrum of rheological conditions, flow speeds and length scales. Most previous models have been restricted to the two-phase limits of porous melt transport in deforming, partially molten rock and crystal settling in convecting magma bodies. The goal of this paper is to develop a framework that can capture igneous system from source to surface at all phase proportions including not only rock and melt but also an exsolved volatile phase. Here, we derive an n-phase reactive transport model building on the concepts of Mixture Theory, along with principles of Rational Thermodynamics and procedures of Non-equilibrium Thermodynamics. Our model operates at the macroscopic system scale and requires constitutive relations for fluxes within and transfers between phases, which are the processes that together give rise to reactive transport phenomena. We introduce a phase- and process-wise symmetrical formulation for fluxes and transfers of entropy, mass, momentum and volume, and propose phenomenological coefficient closures that determine how fluxes and transfers respond to mechanical and thermodynamic forces. Finally, we demonstrate that the known limits of two-phase porous and suspension flow emerge as special cases of our general model and discuss some ramifications for modelling pertinent two- and three-phase flow problems in igneous systems.

• Item Type: Articles
• Additional Information: TK acknowledges support from the Swiss National Science Foundation Postdoc.Mobility Fellowship 177816, and JS from the US Army Research Office grants W911NF-18-1-0092, and W911NF-12-R-0012-04 (ECASE award).
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Keller, Dr Tobias
• Authors: Keller, T., and Suckale, J.
• College/School: College of Science and Engineering > School of Geographical and Earth Sciences
• Journal Name: Geophysical Journal International
• Publisher: Oxford University Press
• ISSN: 0956-540X
• ISSN (Online): 1365-246X
• Published Online: 25 June 2019
• Copyright Holders: Copyright © 2019 The Authors
• First Published: First published in Geophysical Journal International 219(1): 185-222
• Publisher Policy: Reproduced under a Creative Commons License