  A new computational method is presented for study suspensions of charged soft
particles undergoing fluctuating hydrodynamic and electrostatic interactions.
The proposed model is appropriate for polymers, proteins and porous particles
embedded in a continuum electrolyte. A self-consistent Langevin description of
the particles is adopted in which hydrodynamic and electrostatic interactions
are included through a Green's function formalism. An Ewald-like split is
adopted in order to satisfy arbitrary boundary conditions for the Stokeslet and
Poisson Green functions, thereby providing a formalism that is applicable to
any geometry and that can be extended to deformable objects. The
convection-diffusion equation for the continuum ions is solved simultaneously
considering Nernst-Planck diffusion. The method can be applied to systems at
equilibrium and far from equilibrium. Its applicability is demonstrated in the
context of electrokinetic motion, where it is shown that the ionic clouds
associated with individual particles can be severely altered by the flow and
concentration, leading to intriguing cooperative effects.
