Eur. Phys. J. Special Topics 166, 83-88 (2009)
https://doi.org/10.1140/epjst/e2009-00883-1

Suction in Darcy and Stokes interfacial flows: Maximum growth rate versus minimum dissipation

Laboratoire de Physique Statistique, École Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex 05, France

Corresponding author: benamar@lps.ens.fr

Abstract

Two-dimensional flows with suction or mass loss are investigated within Darcy's or Stokes' framework. Examples include a Hele-Shaw cell with a lifted plate or extraction of lipids from a lipid bilayer. An initially circular patch ret- racts due to the suction and might undergo an instability whereby it becomes undulating. The selection of the wavelength of undulations is investigated with the help of an extremum principle, the minimization of the generalized dissipation, from which derive the flow equations.