Analysis of a model microswimmer with applications to blebbing cells and mini-robots

Qixuan Wang, Hans G. Othmer

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


Recent research has shown that motile cells can adapt their mode of propulsion depending on the environment in which they find themselves. One mode is swimming by blebbing or other shape changes, and in this paper we analyze a class of models for movement of cells by blebbing and of nano-robots in a viscous fluid at low Reynolds number. At the level of individuals, the shape changes comprise volume exchanges between connected spheres that can control their separation, which are simple enough that significant analytical results can be obtained. Our goal is to understand how the efficiency of movement depends on the amplitude and period of the volume exchanges when the spheres approach closely during a cycle. Previous analyses were predicated on wide separation, and we show that the speed increases significantly as the separation decreases due to the strong hydrodynamic interactions between spheres in close proximity. The scallop theorem asserts that at least two degrees of freedom are needed to produce net motion in a cyclic sequence of shape changes, and we show that these degrees can reside in different swimmers whose collective motion is studied. We also show that different combinations of mode sharing can lead to significant differences in the translation and performance of pairs of swimmers.

Original languageEnglish (US)
Pages (from-to)1699-1763
Number of pages65
JournalJournal of Mathematical Biology
Issue number7
StatePublished - Jun 1 2018

Bibliographical note

Funding Information:
Supported in part by NSF Grants DMS 0817529 and 1311974, NIH Grants GM29123 and 54-CA-210190, and a grant from the Simons Fdn to H. G. Othmer, and by NIH Grant R01GM107264 and NSF Grant DMS1562176 to Qing Nie.

Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.


  • Amoeboid swimming
  • Low Reynolds number swimming
  • Pushmepullyou
  • Reflection method
  • Robotic swimmers
  • Self-propulsion


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