Long-time dynamics of charged colloidal suspensions: hydrodynamic interaction effects

For charge-stabilized suspensions, we study the influence of hydrodynamic interactions (HI) and electrostatic interactions on the dynamic structure factor S(q,t), and on the long-time self-diffusion coefficient DsL. Both types of interactions give rise to memory effects, which lead to a slower and non-exponential decay of S(q,t), and which cause DsL to be smaller than the short-time self-diffusion coefficient DsS. A global measure of the non-exponential decay of S(q,t) is the non-exponentiality factor Δ(q), which can be determined experimentally by dynamic light scattering. We derive microscopic expressions for the one-particle irreducible memory functions associated with Δ(q) and DsL, based on the generalized Smoluchowski equation and on a projection operator method developed recently by Kawasaki. HI are accounted for by a far-field expansion of the two-body hydrodynamic mobility tensors, by including the leading terms. We calculate Δ(q) and DsL by constructing a novel mode-coupling approximation scheme which accounts for HI, and we extend the theory to moderately polydisperse suspensions. Our results for the measurable non-exponentiality factor compare well with available experimental data. The effect of HI in charge-stabilized colloids is to reduce the non-exponentiality of S(q,t), and to cause an unexpected enhancement of DsL. Our calculations clearly demonstrate the importance of HI at volume fractions even as low as 10−3.