Influence of a shear flow on the phase transition liquid-solid

A generalized Fokker-Planck equation for the bond-orientational distribution function is formulated. Torques are taken into account which stem from a mean field proportional to a fourth rank anisotropy tensor specifying a state with cubic symmetry and from the gradient of a flow velocity field. Expansion of the distribution function leads to coupled relaxation equations for the expansion coefficients. The general form of these equations is stated for an expansion with respect to spherical harmonics, the detailed analysis is carried out for symmetry adapted functions, viz. for an expansion with respect to cubic harmonics. After a discussion of the equilibrium phase transition liquid-solid (cubic symmetry), the effects of steady-flow are studied: the distortion of the bond-orientational order and the lowering of the transition temperature.