Fast equilibration dynamics of viscous particle-laden flow in an inclined channel

A viscous suspension of negatively buoyant particles released into a wide, open channel on an incline will stratify in the normal direction as it flows. We model the early dynamics of this stratification under the effects of sedimentation and shear-induced migration. Prior work focuses on the behaviour after equilibration where the bulk suspension either separates into two distinct fronts (settled) or forms a single, particle-laden front (ridged), depending on whether the initial concentration of particles exceeds a critical threshold. From past experiments, it is also clear that this equilibration time scale grows considerably near the critical concentration. This paper models the approach to equilibrium. We present a theory of the dramatic growth in this equilibration time when the mixture concentration is near the critical value, where the balance between settling and shear-induced resuspension reverses.