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

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

Abstract
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 , where 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 , where 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.