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.