Swimming at small Reynolds number of a planar assembly of spheres in an incompressible viscous fluid with inertia
Abstract
Translational and rotational swimming at small Reynolds numbers of a planar assembly of identical spheres immersed in an incompressible viscous fluid is studied on the basis of a set of equations of motion for the individual spheres. The motion of the spheres is caused by actuating forces and forces derived from a direct interaction potential, as well as hydrodynamic forces exerted by the fluid as frictional and added mass hydrodynamic interactions. The translational and rotational swimming velocities of the assembly are deduced from momentum and angular momentum balance equations. The mean power required during a period is calculated from an instantaneous power equation. Expressions are derived for the mean swimming velocities and the mean power, valid to second order in the amplitude of displacements from the relative equilibrium positions. Hence these quantities can be evaluated for prescribed periodic displacements. Explicit calculations are performed for three spheres interacting such that they form an equilateral triangle in the rest frame of the configuration.
 Publication:

Physics of Fluids
 Pub Date:
 September 2017
 DOI:
 10.1063/1.5001970
 arXiv:
 arXiv:1611.00643
 Bibcode:
 2017PhFl...29i1901F
 Keywords:

 Physics  Fluid Dynamics
 EPrint:
 20 pages, 4 figures. arXiv admin note: text overlap with arXiv:1610.06029