Self-consistent solution for the generalized hydrodynamics model of suspension dynamics: Comparison of theory with rheological and optical measurements

A self-consistent theory for the dynamics and rheology of suspensions of Brownian colloids is presented completely in terms of physicochemical suspension properties. The theory uses the Rogers-Young closure [Phys. Rev. A 30, 999 (1984)] of the Ornstein-Zernike equation for the equilibrium structure and the generated hydrodynamics theory developed by Hess and Klein [Adv. Phys. 33, 173 (1983)] for the dynamic properties. Direct hydrodynamic interactions are neglected. Mode-mode coupling is used to close the generalized hydrodynamics equations and provide a self-consistent set of equations for the dynamics. Two closures for the three-particle vertex function, a two-body approximation and convolution, are derived and compared. All accessible linear viscoelastic properties of the suspension are then calculated from the dynamics of the intermediate-scattering function. Numerical solutions are obtained for Yukawa particles through the viscoelastic approximation. Comparisons with dynamic-light-scattering measurements of the cumulants and the intermediate-scattering function of dilute but strongly correlated suspensions demonstrate the accuracy of the self-consistent solution with the two-body approximation for low particle concentrations. Comparisons of the mechanical properties of concentrated, strongly correlated suspensions demonstrate the accuracy of the self-consistent solutions with the convolution approximation. The results are interpreted in terms of the cage-melting model for colloid dynamics.