Particle-laden viscous channel flows: Model regularization and parameter study

We characterize the flow of a viscous suspension in an inclined channel where the flow is maintained in a steady state under the competing influences of gravity and an applied pressure drop. The basic model relies on a diffusive-flux formalism. Such models are common in the literature, yet many of them possess an unphysical singularity at the channel centreline where the shear rate vanishes. We therefore present a regularization of the basic diffusive-flux model that removes this singularity. This introduces an explicit (physical) dependence on the particle size into the model equations. This approach enables us to carry out a detailed parameter study showing in particular the opposing effects of the pressure drop and gravity. Conditions for counter-current flow and complete flow reversal are obtained from numerical solutions of the model equations. These are supplemented by an analytic lower bound on the ratio of the gravitational force to the applied pressure drop necessary to bring about complete flow reversal.