Electrokinetics and the movement of charge-selective micro-granules in an electrolyte solution under the influence of an external electric field are investigated theoretically. Straightforward perturbation analysis is applied to a thin electric double layer and a weak external field, while a numerical solution is used for moderate electric fields. The asymptotic solution enables the determination of the salt concentration, electric charge distribution, and electro-osmotic velocity fields. It may also be used to obtain a simple analytical formula for the electrophoretic velocity in the case of quasi-equilibrium electrophoresis (electrophoresis of the first kind). This formula differs from the famous Helmholtz-Smoluchowski relation, which applies to dielectric microparticles, but not to ion-selective granules. Numerical calculations are used to validate the derived formula for weak external electric fields, but for moderate fields, nonlinear effects lead to a significant increase in electrophoretic mobility and to a transition from quasi-equilibrium electrophoresis of the first kind to nonequilibrium electrophoresis of the second kind. Theoretical results are successfully compared with experimental data.
Nonequilibrium electrophoresis of an ion-selective microgranule for weak and moderate external electric fields
E. A. Frants, G. S. Ganchenko, V. S. Shelistov, S. Amiroudine, E. A. Demekhin; Nonequilibrium electrophoresis of an ion-selective microgranule for weak and moderate external electric fields. Physics of Fluids 1 February 2018; 30 (2): 022001. https://doi.org/10.1063/1.5010084
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