  Electrohydrodynamics is crucial in many nanofluidic and biotechnological
applications. In such small scales, the complexity due to the coupling of fluid
dynamics with the dynamics of ions is increased by the relevance of thermal
fluctuations. Here, we present a mesoscale method based on the Dissipative
Particle Dynamics (DPD) model of the fluid. Two scalar quantities,
corresponding to the number of positive and negative ions carried by each DPD
particle, are added to the standard DPD formulation. We introduced a general
framework that, given the definition of the free-energy of the DPD particle,
allows to derive a fluctuation-dissipation relation and the expression for
ionic fluxes between the DPD particles. This provides a link between the
dynamics of the system and its equilibrium properties. The model is then
validated simulating a planar electroosmotic flow for the cases of overlapping
and non overlapping electric double layers. It is shown that using a Van der
Waals equation of state the effect of ionic finite size can be accounted,
leading to significant effects on the concentration and velocity profiles with
respect to the ideal solution case.
