  We present a hybrid method for the simulation of colloidal systems, that
combines molecular dynamics (MD) with the Lattice-Boltzmann (LB) scheme. The LB
method is used as a model for the solvent in order to take into account the
hydrodynamic mass and momentum transport through the solvent. The colloidal
particles are propagated via MD and they are coupled to the LB fluid by viscous
forces. With respect to the LB fluid, the colloids are represented by uniformly
distributed points on a sphere. Each such point (with a velocity V(r) at any
off-lattice position r is interacting with the neighboring eight LB nodes by a
frictional force F=\xi_0(V(r)-u(r)) with \xi_0 being a friction force and u(r)
being the velocity of the fluid at the position r. Thermal fluctuations are
introduced in the framework of fluctuating hydrodynamics. This coupling scheme
has been proposed recently for polymer systems by Ahlrichs and D"unweg [J.
Chem. Phys. 111, 8225 (1999)]. We investigate several properties of a single
colloidal particle in a LB fluid, namely the effective Stokes friction and long
time tails in the autocorrelation functions for the translational and
rotational velocity. Moreover, a charged colloidal system is considered
consisting of a macroion, counterions and coions that are coupled to a LB
fluid. We study the behavior of the ions in a constant electric field. In
particular, an estimate of the effective charge of the macroion is yielded from
the number of counterions that move with the macroion in the direction of the
electric field.
