  A model is presented for the solution of electrokinetic phenomena of
colloidal suspensions in fluid mixtures. We solve the discrete Boltzmann
equation with a BGK collision operator using the lattice Boltzmann method to
simulate binary fluid flows. Solvent-solvent and solvent-solute interactions
are implemented using a pseudopotential model. The Nernst-Planck equation,
describing the kinetics of dissolved ion species, is solved using a finite
difference discretization based on the link-flux method. The colloids are
resolved on the lattice and coupled to the hydrodynamics and electrokinetics
through appropriate boundary conditions. We present the first full integration
of these three elements. The model is validated by comparing with known
analytic solutions of ionic distributions at fluid interfaces, dielectric
droplet deformations and the electrophoretic mobility of colloidal suspensions.
Its possibilities are explored by considering various physical systems, such as
breakup of charged and neutral droplets and colloidal dynamics at either planar
or spherical fluid interfaces.
