Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-25T17:24:44.145Z Has data issue: false hasContentIssue false
  • English
  • Français

Effect of surfactants on the stability of two-layer channel flow

Published online by Cambridge University Press:  21 April 2004

M. G. BLYTH  and
C. POZRIKIDIS
M. G. BLYTH
Affiliation:
School of Mathematics, University of East Anglia, Norwich, NR4 7TJ, [email protected]
C. POZRIKIDIS
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA 92093-0411, [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 505 , 25 April 2004 , pp. 59 - 86
Copyright
© 2004 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)