Permeative and hydroelastic flow in smectic A liquid crystals

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Abstract
We compute the coupled flow and elastic distortion of an ideal smectic A liquid crystal normally squeezed between two oscillating plates parallel to the layers. At low frequency, permeation occurs within the boundary layers as already predicted. At high frequency, permeation vanishes. The flow is a pure hydroelastic distortion, with the smectic layers « frozen » inside the matter. The elastic part of the mechanical impedance of the smectic slab undergoes a relaxation, increasing by 20 % above the purely elastic low frequency regime. Surface tension will suppress the permeation boundary layers at low frequency