Effect of inertia on laminar swimming and flying of an assembly of rigid spheres in an incompressible viscous fluid

Abstract

A mechanical model of swimming and flying in an incompressible viscous fluid in the absence of gravity is studied on the basis of assumed equations of motion. The system is modeled as an assembly of rigid spheres subject to elastic direct interactions and to periodic actuating forces which sum to zero. Hydrodynamic interactions are taken into account in the virtual mass matrix and in the friction matrix of the assembly. An equation of motion is derived for the velocity of the geometric center of the assembly. The mean power is calculated as the mean rate of dissipation. The full range of viscosity is covered, so that the theory can be applied to the flying of birds, as well as to the swimming of fish or bacteria. As an example a system of three equal spheres moving along a common axis is studied.

19 pages, 11 figures

References in corpus (3)

• The hydrodynamics of swimming microorganisms
• Analytic results for the three-sphere swimmer at low Reynolds number
• Optimization of flagellar swimming by a model sperm

Cited by in corpus (10)

• Effect of fluid inertia on the motion of a collinear swimmer
• Retarded hydrodynamic interaction between two spheres immersed in a viscous incompressible fluid
• Swimming of a deformable slab in a viscous incompressible fluid with inertia
• Swimming of a linear chain with a cargo in an incompressible viscous fluid with inertia
• Swimming at small Reynolds number of a planar assembly of spheres in an incompressible viscous fluid with inertia
• Collinear velocity relaxation of two spheres in a viscous incompressible fluid
• Swimming of a sphere in a viscous incompressible fluid with inertia
• Optimizing the Mean Swimming Velocity of a Model Two-sphere Swimmer
• Dynamics of cruising swimming by a deformable sphere for two simple models
• Swimming at small Reynolds number of a collinear assembly of spheres in an incompressible viscous fluid