  We present a new simulation scheme based on the Lattice-Boltzmann method to
simulate the dynamics of charged colloids in an electrolyte. In our model we
describe the electrostatics on the level of a Poisson-Boltzmann equation and
the hydrodynamics of the fluid by the linearized Navier-Stokes equations. We
verify our simulation scheme by means of a Chapman-Enskog expansion. Our method
is applied to the calculation of the reduced sedimentation velocity U/U_0 for a
cubic array of charged spheres in an electrolyte. We show that we recover the
analytical solution first derived by Booth (F. Booth, J. Chem. Phys. 22, 1956
(1954)) for a weakly charged, isolated sphere in an unbounded electrolyte. The
present method makes it possible to go beyond the Booth theory, and we discuss
the dependence of the sedimentation velocity on the charge of the spheres.
Finally we compare our results to experimental data.
