Comparative study of theories of conversion of electrophoretic mobility into ζ-potential

The conversion of electrophoretic mobility into ζ-potential can be carried out by different theoretical approaches. We have chosen those developed by Dukhin (thin electrical double layer (e.d.l.)), and OʹBrien–White. Both theoretical treatments provide identical dependence of the dimensionless electrophoretic mobility (μ̃e) as a function of the dimensionless ζ-potential (ζ̃) for large electrokinetic radius values (κa>100) and p=0, being p the ratio between of the counter-ion diffusion coefficient near the particle to its value in the bulk solution. Both treatments lead to different results as p increases and they are significantly different for p>0.2 for moderate κa and ζ-potential values. The Dukhin equation may be simplified for p=1 and neglecting the short range polarization potential (capillary osmosis effect). The error derived from this approximation depends on κa and, as a general rule, it is lower than 25% for moderate ζ̃ values. The greater values of ζD−S in comparison to ζo−W are readily explained on the basis that in the first theory, the contribution to polarization from all ions of the diffuse layer is taken into account, whereas OʹBrien–White account for only the ions of the hydrodynamically mobile part of the e.d.l.