Flow of a binary mixture of linearly incompressible viscous fluids between two horizontal parallel plates

In this paper, we use the classical Mixture Theory and present exact solutions to the equations of motion for the steady flow of two linearly viscous fluids between two horizontal plates. We show that for a saturated mixture and under very special conditions, namely when the body forces are assumed negligible, the only interaction force is due to relative velocity (drag force), and if the two velocities are assumed to be related to each other in a linear fashion, then it is possible to integrate the coupled ordinary differential equations and obtain analytical expressions for the velocities and the volume fraction.