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A regularised force-doublet framework for self-propelled microswimmers

Published online by Cambridge University Press:  11 April 2025

Alexander Peter Hoover Open the ORCID record for Alexander Peter Hoover [Opens in a new window] ,
Priya Shilpa Boindala Open the ORCID record for Priya Shilpa Boindala [Opens in a new window]  and
Ricardo Cortez Open the ORCID record for Ricardo Cortez [Opens in a new window]
Alexander Peter Hoover*
Affiliation:
Department of Mathematics and Statistics, Cleveland State University, Cleveland, OH 44115, USA
Priya Shilpa Boindala
Affiliation:
Department of Mathematics and Statistics, Georgia Gwinnett College, Lawrenceville, GA 30043, USA
Ricardo Cortez
Affiliation:
Department of Mathematics, Tulane University, New Orleans, LA 70118, USA
*
Corresponding author: Alexander Peter Hoover, [email protected]
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Abstract

A single particle representation of a self-propelled microorganism in a viscous incompressible fluid is derived based on regularised Stokeslets in three dimensions. The formulation is developed from a limiting process in which two regularised Stokeslets of equal and opposite strength but with different size regularisation parameters approach each other. A parameter that captures the size difference in regularisation provides the asymmetry needed for propulsion. We show that the resulting limit is the superposition of a regularised stresslet and a potential dipole. The model framework is then explored relative to the model parameters to provide insight into their selection. The particular case of two identical particles swimming next to each other is presented and their stability is investigated. Additional flow characteristics are incorporated into the modelling framework with in the addition of a rotlet double to characterise rotational flows present during swimming. Lastly, we show the versatility of deriving the model in the method of regularised Stokeslets framework to model wall effects of an infinite plane wall using the method of images.

JFM classification

Biological Fluid Dynamics: Propulsion Biological Fluid Dynamics: Collective behaviour
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1009 , 25 April 2025 , A1
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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