A Mixture Theory formulation for hydraulic or pneumatic transport of solid particles

In this paper, we discuss the importance of constitutive modeling of the stress tensors in certain engineering issues, related to the pressure drop and skin friction, encountered in solids transport. To study this problem, we first give a brief account of the formulation of a two-component mixture based on the theory proposed by Massoudi, Rajagopal and co-workers. The mixture consists of a linearly viscous fluid infused with solid particles. The solids particles are modeled as a granular media and it is assumed that the mixture is dense enough so that we can use the theory of interacting continua. The subsequent boundary value problem, flow between two flat plates, is then solved numerically and results for various dimensionless numbers are presented for velocities and volume fraction profiles. The engineering quantities of interests discussed are related to the pressure drop and skin friction at the walls.