Shear flow of cholesterics normal to the helical axis

Abstract

Analytical and numerical calculations of the steady state shear flow of a cholesteric between two plane parallel plates which are normal to the helical axis and at a fixed distance h apart are presented on the basis of Leslie's continuum theory. The material chosen is nematic MBBA in which a twist is assumed to be imposed by the addition of chiralic impurities with no appreciable change in its elastic and viscous properties. The director is assumed to be anchored at the plates in such a way that the twist in the structure is undistorted in the absence of flow. The apparent viscosity η, the, orientation and velocity profiles are studied as functions of pitch p and shear rate s. For very small s, η is analytically shown to be a function of p and h but independent of s, in qualitative agreement with the observations of Candau et al. on the Poiseuille flow of a twisted nematic. When p is varied η exhibits oscillations which are pronounced when p - h. For largep, q asymptoti- cally approaches a lower limit. For p B h, the oscillations are quite negligible and η for different p saturates to almost the same value for low s, again in agreement with the results of Candau et al. For given p and h, numerical calculations show that on increasing s from a low value q decreases from a constant upper limit η, (given exactly by the previous analytical considerations) tending to a lower limit for large s. The shear rate s, at which q starts decreasing from η, is predictably higher for lower p.