  Multi-phase 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.
