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.
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February 2018
Research Article|
February 07 2018
Nonequilibrium electrophoresis of an ion-selective microgranule for weak and moderate external electric fields
E. A. Frants
;
E. A. Frants
a)
1
Department of Mathematics and Computer Science, Financial University
, Krasnodar 350051, Russian Federation
2
Department of Applied Mathematics, Kuban State University
, Krasnodar 350040, Russian Federation
3
Institut de Mécanique et d’Ingénierie–TREFLE, UMR CNRS 5295, University of Bordeaux
, 16 Avenue Pey-Berland, Pessac Cedex, France
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G. S. Ganchenko
;
G. S. Ganchenko
4
Laboratory of Micro- and Nanoscale Electro- and Hydrodynamics, Financial University
, Krasnodar 350051, Russian Federation
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V. S. Shelistov;
V. S. Shelistov
4
Laboratory of Micro- and Nanoscale Electro- and Hydrodynamics, Financial University
, Krasnodar 350051, Russian Federation
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S. Amiroudine;
S. Amiroudine
3
Institut de Mécanique et d’Ingénierie–TREFLE, UMR CNRS 5295, University of Bordeaux
, 16 Avenue Pey-Berland, Pessac Cedex, France
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E. A. Demekhin
E. A. Demekhin
1
Department of Mathematics and Computer Science, Financial University
, Krasnodar 350051, Russian Federation
4
Laboratory of Micro- and Nanoscale Electro- and Hydrodynamics, Financial University
, Krasnodar 350051, Russian Federation
5
Laboratory of General Aeromechanics, Institute of Mechanics, Moscow State University
, Moscow 119192, Russian Federation
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a)
Electronic mail: eafrants@gmail.com
Physics of Fluids 30, 022001 (2018)
Article history
Received:
October 23 2017
Accepted:
January 19 2018
Citation
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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