Boundary conditions in mixture theory and in CFD applications of higher order models

We discuss the importance of and the need for (additional) boundary conditions in Mixture Theory (also known as the Theory of Interacting Continua). Specifically, we will give an overview of the model due to Rajagopal and Massoudi which is appropriate for the flow of a linearly viscous fluid infused with solid particles. The solid particles are modeled as granular materials. In this formulation the need for additional boundary condition arises due to higher gradients of density (or volume fraction). The challenging issue of how to ‘split’ the total stress or the total velocity at the boundary is also discussed.