Asymptotic Diffusive Limits for Transport in Markovian Mixtures

We consider the problem of neutral particle transport in a stochastic Markovian mixture consisting of an arbitrary number M of immiscible fluids. The Liouville master equation is used to obtain a model for the ensemble-averaged angular flux. This model consists of M coupled transport equations. If the absorption, internal source, and temporal and spatial gradients are assumed small, this transport description can be reduced to a diffusive description. Depending upon the scaling of the Markovian transition lengths, this diffusive limit consists of either a single diffusion equation or a set of M coupled diffusion equations. The asymptotic analysis is also used to derive appropriate initial and boundary conditions for each diffusion equation.