Permeative flows in cholesterics: shear and Poiseuille flows

By using a lattice Boltzmann scheme that solves the Beris-Edwards equations of motion describing liquid-crystal hydrodynamics, we study the response of cholesterics to shear and Poiseuille flows. The geometry we focus on is a flow along the direction of the helical axis, which is known to give rise to permeation. For both shear and Poiseuille flow we find that the boundary conditions on the director field are crucial in determining the rheological properties of the liquid crystal. For helices pinned at the boundaries, a small forcing leads to a large viscosity increase whereas a stronger forcing induces a sharp decrease towards the Newtonian value. This shear thinning behavior is in agreement with experiments and previous analytic results. If, on the other hand, the director is free to rotate at the walls, different behaviors are found depending on the symmetry of the steady-state primary flow. Some of the cases considered are compared to a similar imposed flow but with the helix lying perpendicular to the plates, for which no viscosity increase is observed.