MSC2010 76D07, 76D09, 76D17
Model of dynamics of a self-moving chain of particles in a viscous fluid
S.I. Martynov1, L.U.Tkach2
|We consider a model of a chain consisting of spherical particles interconnected by rods. This chain moves in a viscous fluid by forming around itself such a vortex flow that creates a hydrodynamic force that propels the chain in a given direction. The vortex flow of a fluid is formed by the rotation of chain particles under the action of moments of internal forces; their sum is zero. To calculate the dynamics of the chain, the system of equations is solved that includes equations of creeping flow, boundary conditions and equations of particle dynamics. The hydrodynamic interaction of all particles is taken into account. It is assumed that the rods don’t interact with the fluid, and their role is to keep the connected particles at the same distance. Computer simulation of the dynamics of three chains is carried out. These chains differ in the particle size. The forces in the rods and the movement speed for each chain are calculated. It is found that one of the models considered moves faster. Basing on the proposed approach, it is possible to create models of self-propelled chains of different length.
|numerical modeling, viscous fluid, self-propelled chains of particles, hydrodynamic interaction, internal forces of interaction.
1Sergey I. Martynov, Professor of the Institute of Information Systems and Technological Complexes, Ugra State University (16 Chekhova st., Khanty-Mansiysk, 628000, Khanty-Mansi Autonomous District - Yugra, Russia), Doctor of Physical and Mathematical Sciences, ORCID: https://orcid.org/0000-0001-6420-3315, email@example.com
2Lionilla U. Tkach, Senior Lecturer of the Institute of Information Systems and Technological Complexes, Ugra State University (16 Chekhova st., Khanty-Mansiysk, 628000, Khanty-Mansi Autonomous District - Yugra, Russia), ORCID: https://orcid.org/0000-0002-8814-9285, Leonilla7777@mail.ru
Citation: S.I. Martynov, L.U.Tkach, "[Model of dynamics of a self-moving chain of particles in a viscous fluid]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,19:4 (2017) 45–54 (In Russian)