Curvature effects on the surface viscosity of nematic liquid crystals

Abstract

We analyse the flow of a nematic liquid crystal close to a cylindrical surface. As a first result, we show that it is not possible to decouple the motion equations for the director and the macroscopic velocity. Nevertheless, we derive an expression for an effective viscosity, which can be used in the dynamic boundary condition linking the time derivative and the gradient of the director angle on the surface. The effective viscosity so obtained may be greater or smaller than its planar counterpart, depending on both the concavity of the surface and the sign of the Leslie coefficients α 2 and α 3. In particular, in materials that align in shear, the correction to the surface viscosity changes sign depending on whether the angle between the director and the surface normal exceeds or not a critical value.