Evaluation of translational friction coefficients of macroscopic probes in nematic liquid crystals

We present a study of the translational friction coefficients of spherical and ellipsoidal probes in nematic liquid crystalline fluids, based on the numerical treatment of Leslie-Ericksen equations [Q. J. Mech. Appl. Math. 19, 357 (1966); Adv. Liq. Cryst. 4, (1979); Trans. Soc. Rheol. 5, 23 (1961); Adv. Liq. Cryst. 2, 233 (1976)] for incompressible nematic fluids. Simulations of director dynamics in a local environment surrounding the moving probe are presented, and the dependence of translational diffusion on liquid crystal viscoelastic parameters is discussed. The time evolution of the director field is studied in the presence of an orienting magnetic field in two characteristic situations: Directors of motion parallel and perpendicular with respect to the field. In the particular case under investigation, a detailed analysis is given for the case of spherical, prolate, and oblate ellipsoidal probes in rectilinear motion in nematic (4-methoxibenzylidene-4'-n-butylaniline), together with a comparison with other nematogens, namely, 4,4'-dimethoxuazoxy benzene and (4'-n-pentyl-4-cyanobiphenil). A discussion of the general methodology presented in this work is given for the case of colloidal dispersions in nematic liquid crystals, which are considered as model systems of dispersions of particles in host media with anisotropic physical properties.