Electrokinetic phenomena refer to the coupling between solvent and charge flows near a charged interface. This includes e.g. the electro-osmotic flow used in microfluidic devices, the electrophoretic mobility of colloidal particles and polyelectrolytes, or the conversion of acoustic waves into electromagnetic signal exploited for underground exploration. Recent experimental advances have extended the range of accessible regimes (e.g. colloidal suspensions at low volume fraction and low salt concentrations) and raised new questions (e.g. by observing individual macromolecules such as DNA in heterogeneous environments , or water droplets in oil stabilized by a charge separation at the liquid/liquid interface ). Modern techniques have allowed to broaden the range of systems of interest. The quantitive understading of electrokinetics in microfluidic devices, the behavior of charged colloidal suspensions of different nature, or the development of new techniques to explore biological materials offer new opprotunities to explore matter and generate new challenges for their modeling and understanding.
The interpretation of experiments relied until recently on analytical theories initiated by the seminal work of Gouy, Debye, Hückel and Onsager) limited in terms of considered geometries and physical conditions (salt concentration, surface charge density, etc). Several simulation approaches have been developped in the last decade, differing primarily on how they represent the solvent and the ions (counterions of the charged surfaces and salt) : explicitly, semi-implicitly as scalar or vector fields, or implicitly lumped into effective hydrodynamic interaction tensors or electrostatic potentials of mean-force.
Atomistic simulations allow to assess the limitations of mean-field theories and analyze the relation between the wall-induced ionic ordering and the effective boundary conditions [3,4]. However, their computational cost prevents their use to investigate the large length and long time scales relevant for colloidal systems or flow in porous media. The traditional approach combines Brownian dynamics with a simplified treatment of hydrodynamics, based on the asymptotic behavior of hydrodynamic interactions (HI) . The long range nature of HI poses analogous problems to those encountered to simulate electrostatics. In this respect, building upon ideas developed for electrostatics, such as Ewald summations and PPPM, algorithms have been introduced to deal with long-range HI , but have not yet been combined with electrostatics to investigate electrokinetic effects. The long range nature of electrostatic interactions in suspensions is normally circumvented by identifying the relevant degrees of freedom and deriving appropriate effective interactions, in particular the potentials of mean force. In general, dealing with both kinds of long range interactions constitutes a challenge that has been faced in the past few years during which partial progress has been made.
The usual assumption of pairwise additivity of HI to account for their long range nature can be avoided at the price of resolving explicitely the dynamics of the fluid in which the electrolyte and charged solutes are suspended. During the last decades several simulation methods have been developed to describe the momentum transfer mediated by the solvent. Particle based approaches treat the solvent at a coarse grained level, as is the case of Dissipative Particle Dynamics (DPD) or Stochastic Rotation Dynamics (SRD). While in the former approach Groot proposed an extension of DPD accounting for electrolyte dynamics, which provided a natural coupling between electrostatics and fluid motion , so far SRD has been not been combined with electrostatics for the study of electrokinetic phenomena. Kinetic approaches, such as the Lattice-Boltzmann (LB) method, offer an alternative to treat electrostatics and hydrodynamics either with explicit counterions or with the electrolyte described in terms of ionic concentration fields. The former approach has been used to study the electrophoresis of colloids and polyelectrolytes , while the latter has been used to investigate a variety of electrokinetic phenomena, such as colloidal sedimentation , DNA translocation through nanopores , transport of charged species through charged porous media and was recently extended to describe ions at an oil/water interface .
All these complementary approaches are discussed in .