Electrophoresis of small particles and fluid globules in weak electrolytes

Abstract

The electrical double layer plays an essential role in the electrokinetic behavior of both rigid and fluid spheres. One of the assumptions woven into the formulation of the classical balance laws of electrokinetics is that the ionogenic solutes are fully ionized. In aqueous media, common inorganic electrolytes such as KCl and NaOH dissociate completely into their constituent ions; the high dielectric constant of water favors dissociation by lowering the energy required to ionize a solute. Not all ionic solutions are aqueous, however, and electrokinetic effects are important in these media, too. Less polar liquids have a much lower dielectric constant, and so they are unable to sustain a high degree of solute ionization; in fact ionogenic solutes may dissociate less than a percent. Here we examine the influence of partial ionization on the electrophoresis of small particles and fluid globules, with a view toward understanding how, and under what conditions, dissociation-association alters the electrokinetics. We find generally that mass-action, consistent with Le Chatelier's principle, works to minimize disturbances to the electrical double layer, resisting polarization of the diffuse ion cloud. Thus, dissociation-association processes are quantitatively important in cases where double layer polarization and relaxation would otherwise prevail. Consequently, the predicted impact on the electrophoretic mobility is greatest for drops and bubbles, since their surfaces are fluid and convection within the interface is a factor. Mass-action can reduce the mobility of a conducting drop by an order of magnitude, and sizeable decreases (50% and more) in drop mobility are even found at ζ-potentials below 50 mV. Rigid particles are affected less dramatically and quantitative effects rarely exceed 10%; particles are markedly insensitive to partial solute ionization unless the ζ-potential is high (above ca. 100 mV) and aκ > 1. The computation scheme employed applies strictly to situations in which the magnitude of the forcing-field is small. Nevertheless, the results imply that for electrokinetic phenomena driven by strong forcing-fields, dissociation-association processes involving ionogenic solutes may be significant in apolar liquids.