The Hydrodynamics of Concentrated and Confined Colloidal Dispersions

A method is proposed for computing the low-Reynolds-number hydrodynamic forces on particles comprising a suspension confined by two parallel, no-slip walls. This is constructed via the two dimensional analogue of Hasimoto's solution [Hasimoto, JFM (1959)] for a periodic array of body forces in a viscous, incompressible fluid, and like Hasimoto, the summation of interactions is accelerated by substitution and superposition of “Ewald-like” forcing. This method is akin to the Accelerated Stokesian Dynamics technique [Seirou and Brady, JFM (2001)] and models the suspension dynamics with log-linear computational scaling. The effectiveness of this approach is demonstrated with a calculation of the high frequency dynamic viscosity of a colloidal dispersion as function of suspension volume fraction and channel width. In that same vein, the short-time self-diffusivity for and the sedimentation rate of spherical particles comprising a confined suspension are predicted.