ISSN 2079-6900 (Print) 
ISSN 2587-7496 (Online)

Middle Volga Mathematical Society Journal

DOI 10.15507/2079-6900.25.202302.53-61

Original article

ISSN 2079-6900 (Print)

ISSN 2587-7496 (Online)

MSC2020 76D07, 76D09, 76D17

Anisotropic Transport of Dielectric Particles by a Uniform Electric Field in an Inhomogeneously Heated Viscous Fluid

S. I. Martynov

Surgut State University (Surgut, Russian Federation)

Abstract. The anisotropic transfer of dielectric particles by a uniform electric field in a nonuniformly heated fluid is modeled. The transport anisotropy is determined by the mechanism of interaction between particles whose permittivity depends on temperature. The temperature distribution in the particles and in the fluid is determined by their thermal diffusivity and does not depend on the motion of the fluid, thus corresponding to small Peclet numbers. The fluid flow is considered in the approximation of small Reynolds numbers. The transfer of particles is due to the action of an anisotropic force exerted by applied uniform electric field and friction forces exerted by the fluid. The interaction of particles is taken into account. Numerical modeling of anisotropic transport dynamics of two dielectric particles is carried out. The process mentioned depends on the mutual orientation of electric field vector, temperature gradient, and initial orientation of the vector connecting the particle centers. For the case of a large number of particles, an anisotropic equilibrium distribution of the particle concentration in an external electric field is found taking into account the mechanisms of their diffusion and interaction.

Key Words: dielectric particles, electric field, temperature gradient, interaction, displacement anisotropy

For citation: S. I. Martynov. Anisotropic Transport of Dielectric Particles by a Uniform Electric Field in an Inhomogeneously Heated Viscous Fluid. Zhurnal Srednevolzhskogo matematicheskogo obshchestva. 25:2(2023), 53–61. DOI:

Submitted: 01.03.2023; Revised: 12.05.2023; Accepted: 25.05.2023

Information about the author:

Sergey I. Martynov, Chief Researcher, Surgut State University (1 Lenina Av., Surgut 628412, Russia), Dr.Sci. (Phys.-Math.), ORCID:,

The author have read and approved the final manuscript.

Conflict of interest: The author declare no conflict of interest.

Creative Commons Attribution 4.0 International License This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International License.