Viscous properties of nematic liquid crystals composed of biaxial molecules

This paper presents a further improvement of the mean-field method of obtaining the Leslie viscosity coefficients of biaxial nematic liquid crystals presented in our last paper [M. Fialkowski, Phys. Rev. E 55, 2902 (1997)]. We carry out the calculations without using simplifying procedures employed in the cited paper. The viscosities presented are expressed by suspension parameters such as second- and fourth-rank order parameters, three diffusion constants, temperature, number density, and certain factors depending on the shapes of the molecules. Viscous properties of uniaxial phase composed by biaxial molecules are also considered. We show that our results recover existing formulas for six Leslie viscosities obtained for the uniaxial system. The problem of the rotational diffusion tensor has been investigated within the hydrodynamic approximation. The rotational diffusion coefficients have been expressed by the common shear viscosity eta. As an example, we also present the viscosities calculated numerically for a mean-field model of biaxial nematic liquid crystals.