The hydrodynamic resistance force is evaluated following the Stokes’ law.
The electrophoretic force is evaluated following the Coulomb’s law.
In these equations r  presents the hydrodynamic radius of the colloids,   – the speed of electrophoretic migration,  – the dynamic viscosity of the solutions,   – dielectric constant in vacuum,  is water’s relative dielectric constant at 298 K,  is the zeta potential, E is the electric field. The hydrodynamic radius is the sum of particles’ radiuses and the stationary solvent interface.
By steady state electrophoretic migration of charged colloids the electrophoretic force and the hydrodynamic resistance force are in equilibrium, described by:
:F + F = 0
Those effects influence the electrofiltration of biopolymers, which could be also charged, not only by the hydrodynamic resistance force but also by the electric field force. Focusing on the cathode side reveals that the negatively charged particles are affected by the electric field force, which is opposite to the hydrodynamic resistance force. In this manner the formation of filter cake on this side is impeded or in ideal situation filter cake is not formed at all. In this case the electric field is referred as critical electric field E. As a result of the equilibrium of those forces, liquids subjected to the influence of electric force become charged. In addition to the applied hydraulic pressure ∆pH the process is influenced also by the electro-osmotic pressure P.
Modifying the Darcy’s basic equation, describing filter cake formation, with electro-kinetic effects by integration under assumption of using the constants of electro-osmotic pressure P, the critical electric field E and the electric field E results:
Previous scientific works conducted in the [http://www.bio-ag.de/ Dept. of Bioprocess Engineering, Institute of Engineering in Life Sciences, University of Karlsruhe] demonstrated that electrofiltration is effective for the concentration of charged biopolymers. Very promising results concerning purification of the charged polysaccharide xanthan are already obtained. Figure 2 represents xanthan filter cake.