Evaluation of translational friction coefficients of micro-sized spherical probes in nematic liquid crystals

We study the translational friction coefficients of a spherical micrometric probe moving in nematic liquid crystalline fluids, by solving numerically the constitutive hydrodynamic equations of uncompressible isothermal nematic fluids (Leslie–Ericksen equations). The nematic medium is described by a vector field, which specifies the director orientation at each point and by the velocity vector field. Simulations of director dynamics surrounding the moving probe are presented, and the dependence of translational diffusion upon liquid crystal viscoelastic parameters is discussed. The time evolution of director field is studied in the presence of an orienting magnetic field in two characteristic situations, i.e. direction of motion parallel and perpendicular to field. In particular, a detailed analysis is given for the case of a spherical probe in rectilinear motion in nematic MBBA (4-methoxibenzylidene-4′-n-butylaniline), together with a comparison with other nematogens.