Friction drag on a particle moving in a nematic liquid crystal

The flow of a liquid crystal around a particle not only depends on its shape and the viscosity coefficients but also on the direction of the molecules. We studied the resulting drag force on a sphere moving in a nematic liquid crystal MBBA (4-methoxybenzlidene-$4^{\prime }$-n-butylaniline) in a low Reynold’s number approach for a fixed director field (low Ericksen number regime) using the computational artificial compressibility method. Taking the necessary disclination loop around the sphere into account, the value of the drag force anisotropy (${\mathit{F}}_{\mathrm{\perp }}$/${\mathit{F}}_{\mathrm{\parallel }}$=1.50) for an exactly computed field is in good agreement with experiments (∼1.5) done by conductivity diffusion measurements. We also present data for weak anchoring of the molecules on the particle surface and of trial fields, which show to be sufficiently good for most applications. Furthermore, the behavior of the friction close to the nematic to isotropic transition point and for a rodlike and a disklike liquid crystal will be given. © 1996 The American Physical Society.