Fokker-Planck calculations of the viscosities of biaxial fluids

A Fokker-Planck equation for the orientation distribution function is used to calculate the viscosity coefficients of the flow-induced biaxial phase. The results correspond to a special case of proposed phenomenological expressions for biaxial liquid crystals, but with a reduced number of coefficients, apparently due to assumptions on the symmetry of particles. In contrast to a previous calculation, our results satisfy the Onsager relations for the viscosities of biaxial fluids. Sample numerical values indicate that the contribution of flow-induced biaxiality can be significant in the shear viscosities, produce sign changes in the viscosity differences, and thus be important for the interpretation of shear flow data.