Strict simulations of non-equilibrium dynamics of colloids

We review our new direct numerical simulation scheme, called “smoothed profile (SP) method”, which is implemented for a full explicit time-marching simulations of colloidal dispersions. The SP method provides a way to couple continuum fluid dynamics with rigid-body dynamics through smoothed profile of colloidal particle. Our formulation includes extensions to colloids in multi-component solvents such as charged colloids in electrolyte solutions. This method enables us to compute the time evolutions of colloidal particles, ions, and host fluids simultaneously by solving Newton, advection–diffusion, and Navier–Stokes equations so that the electro-hydrodynamic couplings can be fully taken into account. The electrophoretic mobilities of charged spherical particles are calculated in several situations. The comparisons with approximation theories show quantitative agreements for dilute dispersions without any empirical parameters.