Suspension flow modelling in particle migration and microfiltration

We review existing mixture models for shear-induced migration (SIM) in flowing viscous, concentrated particle suspensions via an analysis of the models from the perspective of a two-fluid formulation. Our analysis shows that particle suspensions in strong non-linear shear fields are a prime example of a driven soft matter system. The driving forces for particle migration can be expressed in terms of non-equilibrium osmotic pressure and chemical potential. Using the linear scaling of the effective temperature with the shear stress, we show that the osmotic pressure and shear-induced diffusion coefficients can be written in identical equations. This is similar to the equations for Brownian motion with the temperature replaced by the effective temperature. As a guiding application we have taken crossflow microfiltration, where the driving is very strong and there is formation of a jammed state, cake layer, coexisting with the fluid state. The question whether the SIM mixture models holds for this aplication is investigated. Another questions is how SIM models can be extended for bidisperse suspensions, which is relevant for microfiltration applications involving particle fractionation. Analysis of existing closures of SIM mixture models from the two-fluid perspective learns us that the theory seems to be extendable towards bidisperse suspensions by means of the effective medium theory.