Julia Yeomans OBE FRS

Abstract:

We numerically solve the hydrodynamic equations of motion for a cholesteric liquid crystal under an imposed Poiseuille flow, by means of lattice Boltzmann simulations. The elasticity of the cholesteric helix couples to the external flow to give rise to a highly viscoelastic flow. This is a technically difficult problem for standard flow solvers due to its fully two-dimensional nature. We consider a helix with axis parallel to the boundaries, and at the same time to either the primary flow or the vorticity direction (we identify these two flow modes as permeation and vorticity mode respectively). We quantify the large difference found in the steady state director and velocity profiles, and in the apparent viscosities obtained in the two cases.

Abstract:

We present an investigation of the phase diagram of cholesteric liquid crystals within the framework of Landau-de Gennes theory. The free energy is modified to incorporate all three Frank elastic constants and to allow for a temperature dependent pitch in the cholesteric phase. It is found that the region of stability of the cubic blue phases depends significantly on the value of the elastic constants, being reduced when the bend elastic constant is larger than splay and when twist is smaller than the other two. Most dramatically we find a large increase in the region of stability of blue phase I, and a qualitative change in the phase diagram, in a system where the cholesteric phase displays helix inversion.