Mathematical analysis of the stabilization of lamellar phases by a shear stress

Mathématiques Appliquées de Bordeaux, Université de Bordeaux 1 et UMR 5466 du CNRS, 351 cours de la Libération, 33405 Talence Cedex, France; torri@math.u-bordeaux.fr.

Received: 4 May 2000
Revised: 16 February 2001
Revised: 9 August 2001

Abstract

We consider a 2D mathematical model describing the motion of a solution of surfactants submitted to a high shear stress in a Couette-Taylor system. We are interested in a stabilization process obtained thanks to the shear. We prove that, if the shear stress is large enough, there exists global in time solution for small initial data and that the solution of the linearized system (controlled by a nonconstant parameter) tends to 0 as t goes to infinity. This explains rigorously some experiments.