Swimming of a uniform deformable sphere in a viscous incompressible fluid with inertia

Abstract

The swimming of a deformable uniform sphere is studied in second order perturbation theory in the amplitude of the stroke. The effect of the first order reaction force on the first order center of mass velocity is calculated in linear response theory by use of Newton's equation of motion. The response is characterized by a dipolar admittance, which is shown to be proportional to the translational admittance. As a consequence the mean swimming velocity, calculated in second order perturbation theory, depends on the added mass of the sphere. The mean swimming velocity and the mean rate of dissipation are calculated for several selected strokes.

arXiv comment20 pages, 15 figures

References in corpus (6)

• Propulsion of a two-sphere swimmer
• Optimal translational swimming of a sphere at low Reynolds number
• Effect of fluid inertia on the motion of a collinear swimmer
• Stokesian swimmers and active particles
• Effect of fluid inertia on swimming of a sphere in a viscous incompressible fluid
• Second harmonic generation and vortex shedding by a dipole-quadrupole and a quadrupole-octupole swimmer in a viscous incompressible fluid