J. Phys. II France
Volume 6, Numéro 7, July 1996
Page(s) 985 - 998
DOI: 10.1051/jp2:1996112
J. Phys. II France 6 (1996) 985-998

On the Capillarity of Smectic-A Free Surfaces in Drops and Free Standing Films

J.B. Fournier

Laboratoire de Physique des Solides, Université Paris-Sud, Bât. 510, 91405 Orsay Cedex, France Materials department, University of California at Santa Barbara, CA 93106, USA

(Received 20 October 1995, revised 20 December 1995, accepted 2 April 1996)

Smectic-A free surfaces are discussed in the spirit of capillarity. It is shown that for most practical cases the bulk cannot be treated as a semi infinite medium: the natural length over which a perturbation relaxes along a free surface is just that creating bulk distortions that propagate over the smectic thickness. Hence, the bulk distortions do not simply renormalize the surface tension as in a semi-infinite medium. The relaxation of the layers' distortion within the bulk is fairly linear in most cases: this allows to develop a functional analysis involving only the free surfaces, instead of all the layers. In drops with thickness h, the surface is found to relax exponentially with two capillary lengths $\sim (\lambda h)^{1/2}$, where $\lambda^2=K/B$ is the ratio of the curvature over the dilation elastic constant. This allows to match boundary conditions both on the height and the tangent of the surface extremities. Films have two independent modes: i) an "average" mode describing the film medium layer. It involves a pure curvature-capillary length $\mu=(Kh/\Gamma)^{1/2}$, where $\Gamma$ is the smectic surface tension, and ii) a "differential" mode of behavior similar to the drop one. The effects of added surfactants and applied external fields are discussed together with the possibility of free surface instabilities.

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