Influence of heterogeneity or shape on the locomotion of a caged squirmer

Date

2023-07-12

Authors

Aymen, U.
Palaniappan, D.
Demir, E.
Nganguia, H.

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Abstract

The development of novel drug delivery systems, which are revolutionizing modern medicine, is benefiting from studies on microorganisms’ swimming. In this paper we consider a model microorganism (a squirmer) enclosed in a viscous droplet to investigate the effects of medium heterogeneity or geometry on the propulsion speed of the caged squirmer. We first consider the squirmer and droplet to be spherical (no shape effects) and derive exact solutions for the equations governing the problem. For a squirmer with purely tangential surface velocity, the squirmer is always able to move inside the droplet (even when the latter ceases to move as a result of large fluid resistance of the heterogeneous medium). Adding radial modes to the surface velocity, we establish a new condition for the existence of a co-swimming speed (where squirmer and droplet move at the same speed). Next, to probe the effects of geometry on propulsion, we consider the squirmer and droplet to be in Newtonian fluids. For a squirmer with purely tangential surface velocity, numerical simulations reveal a strong dependence of the squirmer’s speed on shapes, the size of the droplet and the viscosity contrast. We found that the squirmer speed is largest when the droplet size and squirmer’s eccentricity are small, and the viscosity contrast is large. For co-swimming, our results reveal a complex, non-trivial interplay between the various factors that combine to yield the squirmer’s propulsion speed. Taken together, our study provides several considerations for the efficient design of future drug delivery systems.

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Keywords

swimming/flying, multiphase flow

Sponsorship

U.A. and H.N. gratefully acknowledge funding support from the National Science Foundation, grant no. 2211633. H.N. also acknowledges support from a Jess and Mildred Fisher Endowed Professor of Mathematics from the Fisher College of Science and Mathematics at Towson University

Rights:

Attribution 4.0 International

Citation

Aymen, U., Palaniappan, D., Demir, E., & Nganguia, H. (2023). Influence of heterogeneity or shape on the locomotion of a caged squirmer. Journal of Fluid Mechanics, 967, A7. doi:10.1017/jfm.2023.450