S. I. Martynov, L. Yu. Tkach

Surgut State University (Surgut, Russian Federation)

Abstract. Based on the hydrodynamic mechanism, which takes into account the interaction of all particles, a numerical simulation of the formation of a dynamical structure in a viscous fluid was carried out. This structure is a result of the collective dynamics of rotating particles in the fluid. It is supposed that the particles have a magnetic moment and are driven into rotation by an external variable uniform magnetic field. The results of numerical modeling of collective dynamics are presented for three initial structures that can be formed by interacting dipole particles in the absence of an external magnetic field. Such equilibrium structures are a straight chain, a closed chain, and a periodic structure in the form of a flat system of particle chains. The rotation of particles sets the surrounding fluid in motion, whose flow creates hydrodynamic forces and moments that move the particles. The collective dynamics of a system of rotating particles leads to the formation of a new dynamical structure from the original one, and this new structure has its own characteristic features for each case considered. A qualitative comparison of the results of the dynamics for a particles’ system set in motion due to the action of an external moment or an external force is carried out. The proposed hydrodynamic mechanism for the formation of a dynamical structure as a result of the collective dynamics of a rotating particles’ system can be used to control structure formation in a liquid-particle system.

Key Words: collective dynamics, dynamical structure, numerical modeling, viscous fluid, hydrodynamic interaction, rotating particles

For citation: S. I. Martynov, L. Yu. Tkach. Hydrodynamic mechanism for dynamical structure formation of a system of rotating particles. Zhurnal Srednevolzhskogo matematicheskogo obshchestva. 26:2(2024), 175–194. DOI: https://doi.org/10.15507/2079-6900.26.202402.175-194

Information about the authors:

Sergey I. Martynov, Dr.Sci. (Phys.-Math.), Chief Researcher, Surgut State University (1 Lenina A., 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 A., Surgut 628412, Khanty-Mansiysk Autonomous District – Yugra, Russia), ORCID: https://orcid.org/0000-0002-8814-9285, leonilla7777@mail.ru