The linear viscoelastic and diffusional properties of colloidal model dispersions are investigated and possible relations between the (dynamic) shear viscosity and various diffusion coefficients are analyzed. Results are presented for hard sphere and charge-stabilized dispersions with long-range screened Coulomb interactions. Calculations of the dynamic long-time properties are based on a (rescaled) mode coupling theory (MCT). For hard sphere suspensions a simple hydrodynamic rescaling of the MCT results is proposed which leads to good agreement between the theory and experimental data and Brownian dynamics simulation results. The rescaled MCT predicts that the zero-shear limiting viscosity of hard sphere dispersions obeys nearly quantitative generalized Stokes–Einstein (GSE) relations both with regard to the long-time self-diffusion coefficient and the long-time collective diffusion coefficient measured at the principal peak of the static structure factor. In contrast, the MCT predicts that the same GSEs are violated in the case of dispersions of highly charged particles. The corresponding short-time GSEs are found to be partially violated both for charged and uncharged colloidal spheres. A frequency dependent GSE, relating the elastic storage and viscous loss moduli to the particle mean squared displacement, is also investigated, According to MCT, this GSE holds fairly well for concentrated hard spheres, but not for charge-stabilized systems. Remarkably good agreement is obtained, however, with regard to the frequency dependence of the Laplace-transformed reduced shear stress relaxation function and the Laplace-transformed reduced time-dependent self-diffusion coefficient for both charged and uncharged particle dispersions.

Banchio, A. J., Nägele, G., & Bergenholtz, J. (1999). Viscoelasticity and generalized Stokes–Einstein relations of colloidal dispersions. The Journal of Chemical Physics, 111(18), 8721–8740.