Theoretical study of layer alignment in shear flow of smectic A liquid crystals

Abstract

This paper presents a theoretical study of the behaviour of smectic A liquid crystals subject to shear flow. The liquid crystal is assumed to consist of uniform, planar smectic layers, on which no external moments and no external boundary conditions have been imposed. It is shown that of the five viscosity coefficients needed for a full description of dynamical behaviour of the S_A phase, only two, λ₁ and λ₄, enter the expression of the shearing torque. A stability analysis establishes the possible flow alignment configurations of the smectic layers, and the geometrical arrangements of the flow aligned smectic layers are depicted, parametrized by the crucial parameter λ₁/λ₄. Finally, the effective viscosities of the system are derived for some fundamental orientations of the smectic layers with respect to the shear plane, and these allow the derivation of a few inequalities that the viscous coefficients should satisfy.