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Hydrodynamic force on a small squirmer moving with a time-dependent velocity at small Reynolds numbers

Published online by Cambridge University Press:  13 October 2023

T. Redaelli ,
F. Candelier Open the ORCID record for F. Candelier [Opens in a new window] ,
R. Mehaddi Open the ORCID record for R. Mehaddi [Opens in a new window] ,
C. Eloy Open the ORCID record for C. Eloy [Opens in a new window]  and
B. Mehlig Open the ORCID record for B. Mehlig [Opens in a new window]
T. Redaelli
Affiliation:
Aix Marseille Univ, CNRS, Centrale Marseille, IRPHE, F-13384 Marseille, France
F. Candelier
Affiliation:
Aix Marseille Univ, CNRS, IUSTI, F-13453 Marseille, France
R. Mehaddi
Affiliation:
Université de Lorraine, CNRS, LEMTA, F-54000 Nancy, France
C. Eloy
Affiliation:
Aix Marseille Univ, CNRS, Centrale Marseille, IRPHE, F-13384 Marseille, France
B. Mehlig*
Affiliation:
Department of Physics, Gothenburg University, SE-41296 Gothenburg, Sweden
*
†Email address for correspondence: bernhard.mehlig@physics.gu.se
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Abstract

We calculate the hydrodynamic force on a small spherical, unsteady squirmer moving with a time-dependent velocity in a fluid at rest, taking into account convective and unsteady fluid inertia effects in perturbation theory. Our results generalise those of Lovalenti & Brady (J. Fluid Mech., vol. 256, 1993, pp. 561–605) from passive to active spherical particles. We find that convective inertia changes the history contribution to the hydrodynamic force, as it does for passive particles. We determine how the hydrodynamic force depends on the swimming gait of the unsteady squirmer. Since swimming breaks the spherical symmetry of the problem, the force is not determined completely by the outer solution of the asymptotic matching problem, as it is for passive spheres. There are additional contributions due to the inhomogeneous solution of the inner problem. We also compute the disturbance flow, illustrating convective and unsteady effects when the particle experiences a sudden start followed by a sudden stop.

JFM classification

Biological Fluid Dynamics: Micro-organism dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 973 , 25 October 2023 , A11
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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