Electrokinetic phenomena in a dilute suspension of charged mercury drops

Fundamental equations are derived which govern the electrokinetic phenomena in a dilute suspension of charged spherical mercury drops in an electrolyte solution. General expressions for the electrophoretic mobility, the conductivity and the sedimentation velocity and potential in the suspension are derived. Numerical results are displayed as functions of the ζ-potential and κa(where κ is the Debye–Huckel parameter and a is the drop radius). There are remarkable differences between the results for mercury drops and those for spherical rigid particles. In particular, the electrophoretic mobility and sedimentation potential (the same quantity when suitably scaled, a consequence of an Onsager relation) of mercury drops are much larger than those of rigid particles for large κa, and their maxima (occurring when κa≳ 1) are shifted to low ζ-potentials (ca. 75 mV in a KCl solution). Some approximate analytic formulae are also derived. It is shown that the theory of Levich and Frumkin for the electrophoresis and sedimentation of mercury drops is valid only for very small ζ and κa≫ 1 and only when all the ionic species have the same drag coefficient.