**MSC2010** 35J25, 35Q70, 35B06, 35B40, 35C20

### Modeling of interaction of different-sized objects immersed in weal electrolyte

#### A. O. Syromyasov^{1}

Annotation | 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. |
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Keywords | weak electrolyte, linearized Poisson-Boltzmann equation, double electric layer, multipole expansion, asymptotic methods, dummy particle |

^{1}**Aleksei O. Syromyasov**, Associate Professor, Department of Applied Mathematics, Differential Equations and Theoretical Mechanics, National Research Mordovia State University (68/1 Bolshevistskaya St., Saransk 430005, Russia), Ph.D. (Physics and Mathematics), ORCID: http://orcid.org/0000-0001-6520-0204, syal1@yandex.ru

**Citation**: A. O. Syromyasov, "[Modeling of interaction of different-sized objects immersed in weal electrolyte]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,20:4 (2018) 460–472 (In Russian)

**DOI** 10.15507/2079-6900.20.201804.460-472