Abstract
SUMMARY 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.
Highlights
The complex interplay between mechanics and thermodynamics in reactive transport processes involving multiple material phases—solids, liquids, and gases—is a common theme in many natural systems, as well as various applied science and engineering contexts
Building a mixture model requires the formulation of conservation statements and thermodynamic principles, along with constitutive relations for transport processes and coefficient closures prescribing the material response to applied forces
We formulate a continuum model for reactive transport in multi-phase aggregates comprising n material phases composed of m thermodynamic components
Summary
The complex interplay between mechanics and thermodynamics in reactive transport processes involving multiple material phases—solids, liquids, and gases—is a common theme in many natural systems, as well as various applied science and engineering contexts. Phases are represented by the volume fraction they occupy in a control volume and their interactions are described by averaged process terms This approach entails that different local phase topologies may result in identical averaged phase fractions, and that local mechanical and thermodynamical phase interactions are reduced to non-unique and often phenomenological constitutive relations and material closures. Building a mixture model requires the formulation of conservation statements and thermodynamic principles, along with constitutive relations for transport processes and coefficient closures prescribing the material response to applied forces. Their constitutive relations and material closures are inherently non-unique and inevitably phenomenological in nature They yield expressions formally resembling their more familiar local-scale, single-phase equivalents and maintain a tractable level of mathematical complexity. We introduce phenomenological closures for material response coefficients coupling fluxes and transfers to their driving forces and discuss how these may be calibrated to recover relevant limiting cases of two- and three-phase flows
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