S. I. Martynov, L. Yu. Tkach

Surgut State University (Surgut, Russian Federation)

Abstract. The dynamics of this process is modeled based on experiments on the capture and movement of a load by a system of self-organizing particles in a magnetic field. The transport system of particles is a structure in the form of one closed chain (two-dimensional case) or two parallel closed chains (three-dimensional case). As a result of the action of the external field, the particles are set in rotation and move translationally. Hydrodynamic interaction between all particles and the load, which does not interact with the external field, is taken into account. The mathematical model includes equations of viscous fluid hydrodynamics and particle dynamics in the approximation of small Reynolds numbers. Numerical modeling and visualization of the obtained results are performed using a specially developed software package. The performed numerical calculations confirmed the possibility of capture and transfer of the load in the case of location of the particle system and the load in the same plane. In the three-dimensional case, the capture of cargo and its movement by the transport structure in the form of parallel chains of particles does not lead to the capture of cargo. The obtained results are in qualitative agreement with the experiments. The proposed model can be used to calculate the dynamics of a system of particles self-organizing into closed chains in a liquid in the presence of foreign bodies.

Key Words: collective dynamics, dynamic structure, numerical modeling, viscous fluid, hydrodynamic interaction, cargo capture, cargo transfer, external field, control

For citation: S. I. Martynov, L. Yu. Tkach. Modeling the trapping and transporting of cargo in a fluid by a system of self-assembled magnetic particles controlled by an external field. Zhurnal Srednevolzhskogo matematicheskogo obshchestva. 27:3(2025), 364–379. DOI: https://doi.org/10.15507/2079-6900.27.202503.364-379

Information about the authors:

Sergey I. Martynov, D. Sci. (Phys. and Math.), Chief Researcher, Surgut State University (1 Lenina av., Surgut, 628412, Khanty-Mansiysk Autonomous District - Yugra, Russia), ORCID: https://orcid.org/0000-0001-6420-3315, martynovsi@mail.ru

Leonilla Yu. Tkach, Researcher, Surgut State University (1 Lenina av., Surgut, 628412, Khanty-Mansiysk Autonomous District - Yugra, Russia), ORCID: https://orcid.org/0000- 0002-8814-9285, leonilla7777@mail.ru