ON THE CAPILLARITY OF SMECTIC-A FREE SURFACES IN DROPS AND FREE STANDING FILMS

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 r elaxes along a free surface is just that creating bulk distortions tha t propagate over the smectic thickness. Hence, the bulk distortions do not simply renormalize the surface tension as in a semi-infinite medi um. The relaxation of the layers' distortion within the bulk is fairly linear in most cases: this allows to develop a functional analysis in volving only the free surfaces, instead of all the layers. In drops wi th thickness h, the surface is found to relax exponentially with two c apillary lengths similar to (lambda h)(1/2), where lambda(2) = K/B is the ratio of the curvature over the dilation elastic constant. This al lows to match boundary conditions both on the height and the tangent o f the surface extremities. Films have two independent modes: i) an ''a verage'' mode describing the film medium layer. It involves a pure cur vature-capillary length mu = (Kh/Gamma)(1/2), where Gamma is the smect ic surface tension, and ii) a ''differential'' mode of behavior simila r to the drop one. The effects of added surfactants and applied extern al fields are discussed together with the possibility of free surface instabilities.