Swimming at small Reynolds number of a collinear assembly of spheres in an incompressible viscous fluid
Abstract
Swimming at small Reynolds number of a linear assembly of identical spheres immersed in a 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 swimming velocity is deduced from the momentum balance equation for the assembly of spheres, and the mean power required during a period is calculated from an instantaneous power equation. Expressions are derived for the mean swimming velocity and the mean power, valid to second order in the amplitude of displacements from the relative equilibrium positions. Hence these quantities can be evaluated in terms of prescribed periodic displacements. Explicit calculations are performed for a linear chain of three identical spheres.
 Publication:

arXiv eprints
 Pub Date:
 October 2016
 DOI:
 10.48550/arXiv.1610.06029
 arXiv:
 arXiv:1610.06029
 Bibcode:
 2016arXiv161006029F
 Keywords:

 Physics  Fluid Dynamics
 EPrint:
 12 pages, 1 figure