  The motion of ionic solutes and charged particles under the influence of an
electric field and the ensuing hydrodynamic flow of the underlying solvent is
ubiquitous in aqueous colloidal suspensions. The physics of such systems is
described by a coupled set of differential equations, along with boundary
conditions, collectively referred to as the electrokinetic equations. Capuani
et al. [J. Chem. Phys. 121, 973 (2004)] introduced a lattice-based method for
solving this system of equations, which builds upon the lattice Boltzmann
algorithm for the simulation of hydrodynamic flow and exploits computational
locality. However, thus far, a description of how to incorporate moving
boundary conditions into the Capuani scheme has been lacking. Moving boundary
conditions are needed to simulate multiple arbitrarily-moving colloids. In this
paper, we detail how to introduce such a particle coupling scheme, based on an
analogue to the moving boundary method for the pure LB solver. The key
ingredients in our method are mass and charge conservation for the solute
species and a partial-volume smoothing of the solute fluxes to minimize
discretization artifacts. We demonstrate our algorithm's effectiveness by
simulating the electrophoresis of charged spheres in an external field; for a
single sphere we compare to the equivalent electro-osmotic (co-moving) problem.
Our method's efficiency and ease of implementation should prove beneficial to
future simulations of the dynamics in a wide range of complex nanoscopic and
colloidal systems that was previously inaccessible to lattice-based continuum
algorithms.
