Swimming of a sphere in a viscous incompressible fluid with inertia

Abstract

The swimming of a sphere immersed in a viscous incompressible fluid with inertia is studied for surface modulations of small amplitude on the basis of the Navier-Stokes equations. The mean swimming velocity and the mean rate of dissipation are expressed as quadratic forms in term of the surface displacements. With a choice of a basis set of modes the quadratic forms correspond to two hermitian matrices. Optimization of the mean swimming velocity for given rate of dissipation requires the solution of a generalized eigenvalue problem involving the two matrices. It is found for surface modulations of low multipole order that the optimal swimming efficiency depends in intricate fashion on a dimensionless scale number involving the radius of the sphere, the period of the cycle, and the kinematic viscosity of the fluid.

19 pages, 4 figures

References in corpus (5)

• The hydrodynamics of swimming microorganisms
• Optimal translational swimming of a sphere at low Reynolds number
• Stokesian swimmers and active particles
• Effect of inertia on laminar swimming and flying of an assembly of rigid spheres in an incompressible viscous fluid
• Swimming of a deformable slab in a viscous incompressible fluid with inertia

Cited by in corpus (1)

• Swimming of a linear chain with a cargo in an incompressible viscous fluid with inertia