  The influence of hydrodynamic interactions on lane formation of oppositely
charged driven colloidal suspensions is investigated using Brownian dynamics
computer simulations performed on the Rotne-Prager level of the mobility
tensor. Two cases are considered, namely sedimentation and electrophoresis. In
the latter case the Oseen contribution to the mobility tensor is screened due
to the opposite motion of counterions. The simulation results are compared to
that resulting from simple Brownian dynamics where hydrodynamic interactions
are neglected. For sedimentation, we find that hydrodynamic interactions
strongly disfavor laning. In the steady-state of lanes, a macroscopic phase
separation of lanes is observed. This is in marked contrast to the simple
Brownian case where a finite size of lanes was obtained in the steady-state.
For strong Coulomb interactions between the colloidal particles a lateral
square lattice of oppositely driven lanes is stable similar to the simple
Brownian dynamics. In an electric field, on the other hand, the behavior is
found in qualitative and quantitative accordance with the case of neglected
hydrodynamics.
