Geodesic
Modeling of interaction of different-sized objects immersed in weal electrolyte
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 20 (2018) no. 4, pp. 460-472.

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Author solves problems about interaction of two spherical particles with different radii and also about interaction of a sphere and a plane that are immersed in electrolyte. Double electric layer near the objects' surfaces is supposed to be wide, so Poisson – Boltzmann equation describing the distribution of electric potential in the medium may be linearized. The problems stated are solved by multipole expansion method; the plane is modelled by a dummy particle. Asymptotic expressions are obtained for the coefficients of the expansion. Basing on this solution, forces acting between bodies in electrolyte are found. The particular case when the size of one sphere is much larger than the size of another particle is examined. Author shows that this case can't transform to interaction of a sphere and a plane. The unexpected result of calculation is that under certain conditions the plane may attract spherical particle which has potential of the same sign on its surface, while the interaction between two spheres having potentials of the same sign is always repulsion.
Keywords: weak electrolyte, linearized Poisson-Boltzmann equation, double electric layer, asymptotic methods, dummy particle.
Mots-clés : multipole expansion 
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A. O. Syromyasov. Modeling of interaction of different-sized objects immersed in weal electrolyte. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 20 (2018) no. 4, pp. 460-472. http://geodesic.mathdoc.fr/item/SVMO_2018_20_4_a9/

[1] P. Habdas, E. R. Weeks, “Video microscopy of colloidal suspensions and colloidal crystals”, Current Opinion in Colloid and Interface Science, 7 (2002), 196–203 | DOI

[2] I. F. Efremov, Periodic colloidal structures, Khimiya Publ., Leningrad, 1971, 192 pp. (In Russ.)

[3] M. F. Hsu, E. R. Dufresne, D. A. Weitz, “Charge stabilization in nonpolar solvents”, Langmuir, 21 (2005), 4881–4887 | DOI

[4] G. A. Ostroumov, Interaction of electrical and hydrodynamical fields. Physical foundations of electrohydrodynamics, Nauka Publ., Moscow, 1979, 320 pp. (In Russ.)

[5] E. J. W. Verwey, J. Th. G. Overbeek, Theory of the stability of lyophobic colloids, Elsevier publishing company, Inc., New York-Amsterdam-London-Brussels, 1948, i-xii, 205 pp.

[6] J. Zhu, Min Li, R. Rogers [et al.], “Crystallization of hard-sphere colloids in microgravity”, Nature, 387 (1997), 883–885 | DOI

[7] E. Yariv, “Electro-hydrodynamic particle levitation on electrodes”, Journal of Fluid Mechanics, 645 (2010), 187–210 | DOI | MR | Zbl

[8] M. Wu, A. V. Kuznetsov, W. J. Jasper, “Modeling of particle trajectories in an electrostatically charged channel”, Phys. Fluids, 22:4 (2010) | Zbl

[9] H. Liu, H. H. Bau, “The dielectrophoresis of cylindrical and spherical particles submerged in shells and in semi-infinite media”, Phys. Fluids, 16:5 (2004), 1217–1228 | DOI

[10] A. O. Syromyasov, N. V. Eremkina, “Mathematical modelling of electrostatic interaction among two identical spheres surrounded by double electric layers”, Zhurnal Sredne-Volzhskogo matematicheskogo obshchestva, 17:3 (2015), 100–108. (In Russ.) | Zbl

[11] V. V. Lokhin, L. I. Sedov, “Nonlinear tensor functions depending on several tensor arguments”, Journal of Applied Mathematics and Mechanics, 27:3 (1963), 393–417. (In Russ.) | MR

[12] L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media, Pergamon Press, 1960, 429 pp.

[13] F. H. Stillinger Jr., “Interfacial solutions of the Poisson-Boltzmann equation”, J. Chem. Phys., 35:5 (1961), 1584–1589 | DOI | MR

[14] R. Klein, H. H. von Grünberg, “Charge-stabilized colloidal suspensions. Phase behavior and effects of confinement”, Pure and Applied Chemistry, 73:11 (2001), 1705–1719 | DOI

[15] J. Happel, H. Brenner, Low Reynolds number hydrodynamics, Prentice-Hall, 1965, 553 pp.

[16] V. L. Sennitskii, “Force interaction of a sphere and a viscous fluid in the presence of a wall”, Journal of Applied Mechanics and Technical Physics, 41:1 (2000), 50–54 (In Russ.) | MR

[17] V. E. Baranov, S. I. Martynov, “Simulation of particle dynamics in a viscous fluid near a plane wall”, Computational Mathematics and Mathematical Physics, 50:9 (2010), 1588 – 1604 (In Russ.) | MR | Zbl