Poisson -- Boltzmann Brownian Dynamics of Charged Colloids in Suspension
  We describe a method to simulate the dynamics of charged colloidal particles suspended in a liquid containing dissociated ions and salt ions. Regimes of prime current interest are those of large volume fraction of colloids, highly charged particles and low salt concentrations. A description which is tractable under these conditions is obtained by treating the small dissociated and salt ions as continuous fields, while keeping the colloidal macroions as discrete particles. For each spatial configuration of the macroions, the electrostatic potential arising from all charges in the system is determined by solving the nonlinear Poisson--Boltzmann equation. From the electrostatic potential, the forces acting on the macroions are calculated and used in a Brownian dynamics simulation to obtain the motion of the latter. The method is validated by comparison to known results in a parameter regime where the effective interaction between the macroions is of a pairwise Yukawa form. 
J. Dobnikar, D. Halo\v{z}an, M. Brumen, H.-H. von Gr\"unberg, and R.   Rzehak