Unsteady and inertial dynamics of an active particle in a fluid

Abstract

It is well known that the reversibility of Stokes flow makes it difficult for small microorganisms to swim. Inertial effects break this reversibility, allowing new mechanisms of propulsion and feeding. Therefore it is important to understand the effects of unsteady and fluid inertia on the dynamics of microorganisms in flow. In this work, we show how to translate known inertial effects for non-motile organisms to motile ones, from passive to active particles. The method relies on a principle used earlier by Legendre and Magnaudet (1997) to deduce inertial corrections to the lift force on a bubble from the inertial drag on a solid sphere, using the fact that small inertial effects are determined by the far field of the disturbance flow. The method allows for example to compute the inertial effect of unsteady fluid accelerations on motile organisms, and the inertial forces such organisms experience in steady shear flow. We explain why the method fails to describe the effect of convective fluid inertia.

arXiv comment10 pages, revised version

References in corpus (16)

• Active Particles in Complex and Crowded Environments
• The hydrodynamics of swimming microorganisms
• Flow pattern in the vicinity of self-propelling hot Janus particles
• Rotation of a spheroid in a simple shear at small Reynolds number
• Simple Viscous Flows: from Boundary Layers to the Renormalization Group
• Hydrodynamic interaction of a self-propelling particle with a wall: Comparison between an active Janus particle and a squirmer model
• Continuous breakdown of Purcell's scallop theorem with inertia
• Navigation of micro-swimmers in steady flow: the importance of symmetries
• Unsteady feeding and optimal strokes of model ciliates
• Time-dependent lift and drag on a rigid body in a viscous steady linear flow
• Transition in swimming direction in a model self-propelled inertial swimmer
• Buckling instability causes inertial thrust for spherical swimmers at all scales
• Inertial drag on a sphere settling in a stratified fluid
• Settling of an asymmetric dumbbell in a quiescent fluid
• Angular dynamics of a small particle in turbulence
• Angular velocity of a spheroid log rolling in a simple shear at small Reynolds number

Cited by in corpus (3)

• Designing, Synthesizing and Modeling Active Fluids
• Inertial torque on a squirmer
• Hydrodynamic force on a small squirmer moving with a time-dependent velocity at small Reynolds numbers