Cluster theory for concentration dependence of shear viscosity for suspensions of interacting spheres. I

摘要

We present a general divergenthyphen;integralhyphen;free cluster theory for the concentration dependence, to any order in concentration, of the shear viscosity of a suspension of interacting colloidal spheres. Treating the solvent as a viscous hydrodynamic continuum, the steady state limit of vanishing shear rate is considered, so the spherendash;sphere interactions enter through the Mayer cluster expansion of the various sphere equilibrium distribution functions. The spheres are taken to move such that the net hydrodynamic forces and torques acting on them identically vanish. We present general formulas for all coefficients in a virial type expansion of the suspension shear viscosity in powers of the concentration for any prescribed spherically symmetric direct interaction potential between the spheres. Previous work has been limited to the twohyphen;sphere contributions only. Every virial coefficient in our complete expansion involves integrals of the sphere equilibrium distribution functions multiplied by functions of hydrodynamic origin. These virial coefficients are perfectly convergent because of the nature of the various equilibrium distribution functions present in the integrals for the virial coefficients.