Nonequilibrium Interfacial Potential

There are four electrokinetic phenomena (electrophoresis, electroosmosis, streaming potential, and sedimentation potential), all of which involve both the theory of the electric double layer and that of liquid flow. Among them electrophoresis has the greatest practical applicability to the study of biomolecules and biocell surface porperties. In this section, the relation between electrophoretic mobility and its related electrokinetic potential C will be discussed. 

If we consider a spherical particle of radius a and electric charge O, moving with a uniform velocity m in a field of unit electrical potential gradient, the electrical force on the particle, OE = Q, will be balanced by the viscous resistance which is assumed to be expressed by Stokes law  

If it is assumed that the particle radius a includes that part of the double layer which moves with the particle, then the zeta potential C can be expressed as the work done in bringing a unit positive charge from infinity to a distance a from the center of the particle. The force, F, on the unit positive charge at any point r from the center of the particle is  

An alternative approach to this problem is to regard the double layer as a parallel plate condenser in which one plate is the particle surface and the other plate is a plane of counterions at a potential located a distance from the surface and moving with a velocity u relative to the particle surface. If the surface charge density is cr, the electrical force per unit area of the particle plate in a field of unit potential gradient will be a and this force will be balanced by the viscous resistance, which for an assumed Newtonian flow, leads to the equation  

The capacitance (C) per unit area of the double layer will be given by  

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In many experimental situations, a steady-state nonequilibrium condition between two phases (A and B) is sustained by electrical work being done on the system. For instance, the net interfacial electron flux Ja b is measured as a function of the difference in the electrochemical potential p Me,B- F " sufficiently small departure from equilibrium, it is observed that the net flux is proportional to the exchange flux and increases with increasing p A Me,B -... 

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