Linear stability analysis of multilayer plane Poiseuille flow

Abstract

A linear stability analysis of n‐layer plane Poiseuille flow is performed. Asymptotic solutions are constructed at very small and very large wavenumbers. A numerical analysis is carried out by means of a compound matrix method to identify linearly unstable conditions for wavenumbers of O(1). The governing equations and the boundary conditions are conveniently formulated for n‐layer flow. Neutral stability curves are plotted over a broad range of parameters for three‐layer flows. The investigated parameters include the viscosity ratios, the flow rate ratios, the density ratios, the interfacial tensions, and the Stokes and Reynolds numbers