The stability of plane Poiseuille flow of a dusty gas

Abstract

In this paper some approximate results are presented for the problem of the stability of plane Poiseuille flow of a dusty gas, following a formulation given recently by Saffman (1962). It is assumed that the mass concentration of the dust, f, is small, and results are obtained by making a perturbation of the curve of neutral stability for a clean gas, using the approximate solutions given by Stuart (1954). The perturbation equation is expressed in terms of integrals by introducing the adjoint wave function, the calculation of which is described. The integral coefficients were evaluated by numerical integration using a Mercury computer, and the results are illustrated for f = 0.05 by a set of perturbed neutral stability curves at different values of the time relaxation parameter SR varying from 0 to 500. These results, whilst not of great numerical accuracy, are sufficient to show qualitatively how the curve of neutral stability is modified by the presence of the dust.