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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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Squirming with a backward-propelling cage
A squirmer enclosed in a droplet represents a minimal model for some drug delivery systems. In the case of a spherical squirmer swimming with a spherical cage in a Newtonian fluid [Reigh et al., “Swimming with a cage: Low-Reynolds-number locomotion inside a droplet,” Soft Matter 13, 3161 (2017)], it was found that the squirmer and droplet always propelled in the same direction albeit at different speeds. We expand the model to include particles' shape and medium's heterogeneity, two biologically relevant features. Our results reveal a novel behavior: a configuration that consists of a spherical squirmer and a spheroidal droplet in highly heterogeneous media yields a backward motion of the droplet.
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- Award ID(s):
- 2211633
- PAR ID:
- 10412908
- Date Published:
- Journal Name:
- Physics of Fluids
- Volume:
- 35
- Issue:
- 5
- ISSN:
- 1070-6631
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1063/5.0152711
