  We use Stokesian Dynamics simulations to study the microscopic motion of
particles suspended in fluids passing through porous media. We construct model
porous media with fixed spherical particles, and allow mobile ones to move
through this fixed bed under the action of an ambient velocity field. We first
consider the pore scale motion of individual suspended particles at pore
junctions. The relative particle flux into different possible directions
exiting from a single pore, for two and three dimensional model porous media is
found to approximately equal the corresponding fractional channel width or
area. Next we consider the waiting time distribution for particles which are
delayed in a junction, due to a stagnation point caused by a flow bifurcation.
The waiting times are found to be controlled by two-particle interactions, and
the distributions take the same form in model porous media as in two-particle
systems. A simple theoretical estimate of the waiting time is consistent with
the simulations. We also find that perturbing such a slow-moving particle by
another nearby one leads to rather complicated behavior. We study the stability
of geometrically trapped particles. For simple model traps, we find that
particles passing nearby can ``relaunch'' the trapped particle through its
hydrodynamic interaction, although the conditions for relaunching depend
sensitively on the details of the trap and its surroundings.
