Equilibrium Theory of Bidensity Particle-Laden Flows on an Incline

The behaviour of inhomogeneous suspensions in a viscous oil is relevant in the context of oil spill and other oil-related disasters which may lead to the unwanted mixture of sand grains and oil. This warrants the fundamental study of the dynamics of solid particles in a thin film of viscous fluid. Specifically, sheared concentrated suspensions in a viscous fluid are subject to a diffusive mechanism called shear-induced migration that consists of “drift diffusion” and “self or tracer diffusion”. Drift diffusion causes particles to move from high to low concentrations, while tracer diffusion dictates mixing between particles of the same size. The latter mechanism becomes important in polydisperse slurries. In this chapter, we incorporate the effects of shear-induced migration and sedimentation to develop a model for the gravity-driven thin film of bidensity suspensions. We use this mathematical model to validate recent experimental results