Stability in a fully-developed two-dimensional resuspension flow

A linear stability analysis examining the stability of a fully-developed, t wo-dimensional Hagen-Poiseuille resuspension flow is presented. Whilst the analysis includes the non-uniformity of the particle concentration distribu tion, the inclusion of any concentration fluctuations is ignored. Numerical solutions to the relevant Orr-Sommerfeld equations for temporal disturbanc e modes are obtained with the aid of ortho-normalization for a variety of d ifferent parameters by means of a classical shooting technique. It is found that interfacial instabilities result from long wavelength disturbances ev en in a small Reynolds number range. The growth rates of disturbances are s hown to increase with decreasing initial feed concentration, whilst increas ing density stratification is shown to stabilize the resuspension flow. It is also shown that the neglect of fluctuations in the particle concentratio n severely limits the validity of the stability analysis performed, especia lly for flows in which the particle concentration in the interfacial region varies rapidly. (C) 1999 Elsevier Science Ltd. All rights reserved.