On one model of the dynamics of self-propelled aggregates of particles in a viscous fluid

The model of an aggregate of spherical particles connected by rods and moving in a viscous fluid is considered. The motion of the aggregate is due to the action of hydrodynamic forces from the vortex flow of the viscous fluid. The fluid flow is generated by rotation in opposite directions of two particles of the aggregate. The rotation of the particles is caused by the action of moments of the internal forces whose sum is equal to zero. Other particles of the aggregate are subject to constraints preventing their rotation. To calculate the dynamics of the aggregate, a system of equations of the viscous fluid is jointly solved in the approximation of small Reynolds numbers with appropriate boundary conditions and equations of motion of the particles under the action of applied external and internal forces and torques. The hydrodynamic interaction of the particles is taken into account. It is assumed that the rods do not interact with the fluid and do not allow the particles to change the distance between them. Computer simulation of the dynamics of three different aggregates of 5 particles is tested by special software. The forces in the rods and the speed of movement for each aggregate are calculated. It was found that one aggregate moves faster than others. This means that the shape of the aggregate is more adapted for such movement as compared to the other two. This approach can be used as a basis to create a model of self-propelled aggregates of different geometric shape with two or more pairs of rotating particles. Examples of constructions of aggregates and their dynamics in viscous fluid are also studied by computer simulation.