Basic Equations of Electrokinetic Processes

The basic eqnations of electrokinetic processes establish the connection between zeta-potential valnes and the parameters of the electrokinetic processes the velocity 

The equations of the electrokinetic processes were derived in 1903 by the Polish physicist Maryan Ritter von Smoluchowski on the basis of ideas concerning the function of EDL in these processes that had been developed by H. Helmholtz in 1879. These equations are often called the Helmholtz-Smoluchowski equations. 

The charge density (2s)t the zeta potential, and the thickness 5q are interrelated by the plate-capacitor relation 

The linear velocity of the liquid developing under the effect of this force is zero directly at the solid surface, and increases to some maximum value v at the distance X = 8o from the surface. Solution regions farther out lack the excess charges that could come under the effect of the external electric field hence, there is no further increase in liquid velocity (Fig. 31.4). When the layer (Sg) is much thinner than the capillary radius, 5g r, the assumption can be made that the bulk of the solution moves with a uniform velocity v. 

The velocity v of liquid motion can be found from the condition that the electric force should be compensated by the viscous friction force /f. The latter is proportional to the velocity gradient in the layer of slipping charges  

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