Effectiveness of nonequilibrium closures for the many body forces in concentrated colloidal dispersions

Here we present a theory for predicting the effect of interparticle interactions on the nonequilibrium dynamics of concentrated colloidal dispersions. A configuration-space conservation equation for the pair density P2 provides a fundamental basis for calculating the nonequilibrium microstructure; however, it includes pairwise additive three-body couplings. The resulting forces depend on the three-particle distribution function, necessitating an additional equation to completely specify P2. In this paper nonequilibrium Percus–Yevick and hypernetted chain closures complete the formulation by relating these forces to the interparticle force and pair distribution function. A computational algorithm exploiting Fast Fourier Transforms solves the resulting integro-differential equations for weak perturbations from equilibrium, yielding the perturbed pair density as a function of the volume fraction φ and the interparticle potential. The advantage of a fundamental approach is that clearly defined approximations lead from the characteristics of the individual colloidal particles to the nonequilibrium structure and macroscopic properties. The calculation of all dynamic properties, both rheological stresses and diffusion coefficients, is accomplished with the same approximations. Detailed predictions of the structure provide an additional comparison with simulation and experiment lacking in theories that calculate only bulk properties. The numerical methods demonstrated here allow efficient solution of a class of models more sophisticated than previously attempted. To test the merits of nonequilibrium closures we present predictions of the low-shear viscosity and long-time self-diffusion coefficient as a function of volume fraction for various repulsive potentials without hydrodynamic interactions. Comparison with results available from computer simulations demonstrates that the closures capture the trends in the transport properties with volume fraction and interparticle potential and yield realistic predictions for the nonequilibrium structure. The hypernetted chain closure yields the best agreement with the available data for bulk properties at moderate volume fractions (φ<0.4), but significant quantitative deviations appear at φ⩾0.45.