Undulation instability under shear: A model to explain the different orientations of a lamellar phase under shear?
A.S. Wunenburger1 - A. Colin1 - T. Colin2 - D. Roux1
1 Centre de Recherche Paul Pascal, CNRS, Av. Dr. Schweitzer,
33600 Pessac, France
2 Mathématiques Appliquées de
Bordeaux, Université Bordeaux I, CNRS ESA 5466, 351 Cours de la
Libération, 33405 Talence cedex, France
colin@crpp.u-bordeaux.fr
Received 18 October 1999
Abstract
We study the effects of a dilation on a sheared smectic
A phase. Through a linear analysis, we show that undulation may
grow in the direction of the flow and of the vorticity as found in
previous works. At higher shear rates, we evidence that the
undulation along the flow disappears whereas it persists in the
vorticity direction. We determine the stable or unstable zone as a
function of the shear rate and of the lamellar spacing. This allows
us to draw a theoretical shear diagram of the instability. Finally
we compare our results with the orientations found experimentally
in a lyotropic lamellar phase under shear. Our diagram describes
qualitatively and quantitatively the transition observed at high
shear rate.
PACS
47.20.-k Hydrodynamic stability
- 83.00 Rheology
- 83.50.Ax Steady shear flows
Copyright EDP Sciences, Società Italiana di Fisica, Springer-Verlag
