A two-fluids model for numerical simulation of shear dominated suspension flows

Suspension flows are ubiquitous in nature and industry. However, these flows are notoriously difficult to model due to the variety of fluid-particle and particle-particle interactions involved. We focus on non-Brownian shear-dominated suspensions, where irreversible phenomena like particle diffusion and migration develop, requiring anisotropic stress models to describe the suspension rheology. On a continuum level, reduced-order models like the suspension balance model (SBM) or the diffusive flux model are commonly used to predict particle migration phenomena. We propose a new method based on the two-fluid model (TFM), where both the phases are considered as interpenetrating continua. Specifically, we show that when an anisotropic stress analogous to that used in the SBM is added to the equilibrium equations for the particle phase, the TFM is able to predict particle migration. Unlike the SBM, the TFM does not require the assumptions of a steady suspension velocity and Stokesian fluid. Thus, the TFM can be easily extended to include buoyancy and even kinetic collisional models.