Effect of surfactants on the stability of two-layer channel flow
M. G. BLYTH a1andC. POZRIKIDIS a2 a1 School of Mathematics, University of East Anglia, Norwich, NR4 7TJ, UK M.Blyth@uea.ac.uk a2 Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA 92093-0411, USA email@example.com
The effect of an insoluble surfactant on the stability of two-layer viscous flow in an inclined channel confined by two parallel walls is considered. A lubrication-flow model applicable to long waves and low-Reynolds-number-flow is developed, and pertinent nonlinear evolution equations for the interface position and surfactant concentration are derived. Linear stability analysis based on the lubrication-flow model and the inclusive equations of Stokes flow confirm the recent findings of Frenkel & Halpern (2002) and Halpern & Frenkel (2003) that the presence of an insoluble surfactant induces a Marangoni instability in certain regions of parameter space defined by the layer thickness and viscosity ratios. Numerical simulations based on both approaches show that the interfacial waves may grow and saturate into steep profiles. The lubrication-flow model is adequate in capturing the essential features of the instability for small and moderate wavenumbers.
(Received January 31 2003) (Revised October 28 2003)