The Dukhin-Deryaguin equation for the electrophoretic mobility in monovalent electrolytes with arbitrary ion...

The Dukhin-Deryaguin equation, used in the modern theory of electrophoresis for the calculation of electrophoretic mobility (EPM) in the region of double layer polarization, is known from literature [4-6] in its form (DD1) valid for the equal mobilities of the cation and anion in solutions of symmetrical electrolytes. Here we describe the other version of this equation (DD2), for arbitrary ion mobilities in 1:1 electrolytes. The EPMs calculated from this latter version are in good agreement with an exact computer solution [12]. The use of DD2 is illustrated in a series of EMP vs. IgC curves, calculated for selected examples of negatively charged lipid membranes. In addition, we describe two simplified versions of DD2, which are valid, respectively, for the high zeta potentials and when the electroosmotic component of ions' fluxes at the charged surface is neglected. Comparing DD2 with DD1 shows that the latter equation results in an error which may exceed the experimental dispersion of EPM values in the absence of specific ion binding. This error is reduced if the counter-ion binding is not small; hence, DD1 may also be used in some cases for solutions with arbitrary ion mobilities.