STABILITY IN A 2-DIMENSIONAL HAGEN-POISEUILLE RESUSPENSION FLOW

A linear stability analysis of a viscous resuspension flow, which develops from an initially well-mixed suspension flowing along a two-dimensional channel, is described. The analysis is based on a two-fluid model in which the non-uniformity of the particle concentration distribution within the suspended layer is ignored. Numerical solutions to the relevant Orr-Sommerfeld equations for both temporal and spatial disturbance modes are obtained for the special case of a suspension of spherical particles in water and flowing in a duct with vertical spacing 0.02 m. It is found that the resuspension flow is convectively unstable and that the largest amplification occurs in the range of moderate stability Reynolds numbers. It is also shown that a reduction in the particle concentration in the feed suspension and/or an increase in the relative density ratio of the solid particles to that of the suspending fluid will enhance the instability of the interfacial mode.