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Unsteady and inertial dynamics of a small active particle in a fluid

T. Redaelli1, F. Candelier2, R. Mehaddi3, and B. Mehlig4

  • 1Aix Marseille Univ., CNRS, Centrale Marseille, IRPHE, F-13384 Marseille, France
  • 2Aix-Marseille Univ., CNRS, IUSTI, F-13453 Marseille, France
  • 3Université de Lorraine, CNRS, LEMTA, F-54000 Nancy, France
  • 4Department of Physics, Gothenburg University, SE-41296 Gothenburg, Sweden

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Phys. Rev. Fluids 7, 044304 – Published 22 April, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.044304

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 nonmotile 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 us, 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.

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Phys. Rev. Fluids 7, 044304– Published 22 April, 2022
  • Received 4 May 2021
  • Accepted 19 January 2022
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