Radial flow in a cholesteric subjected to a rotary (torsional) shear about the helical axis

Abstract

A planar cholesteric sample sandwiched between two infinite plane parallel discs, one of which is rotating in its own plane relative to the other at constant angular velocity Ω, is investigated on the baais of the continuum theory. For low shears (or low Ω) the Leslie equations are linearised for small distortions and the mode involving antisymmetric angular velocity ω is studied. It is assumed that ω is a function of z alone in the form of an infinite antisymmetric series ∑X_iz²ⁱ⁺¹ , and, taking the pitch to be small compared to the sample thickness, the elastic and viscous responses of the system are replaced by their averages over one pitch. Further, the perturbations are assumed to be independent of ψ the azimuthal coordinate. By applying boundary conditions on the radial (secondary) velocity v_l, axial velocity v₃ and the twist distortion angle φ, a compatibility condition is obtained from which it should be possible in principle to determine the constants of the theory, though not uniquely. However, the following conclusions can be drawn unambiguously: (i) when the handedness of the helix is reversed, the flow pattern remains unaltered if v_l and v₃ change sign, and (ii) when ω (or equivalently X_i) is reversed, v_l, v₃ and φ change sign. The theory appears to provide a possible explanation of an interesting phenomenon reported recently by Janossy. Using the same experimental geometry as the one discussed here, he observed that for one sense of rotation dust particles in the cholesteric sample drifted towards the centre of the discs, whilst for the opposite sense of rotation they drifted away from the centre.