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Squirmer dynamics near a boundary.

Kenta Ishimoto1, Eamonn A Gaffney2

  • 1Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 4, 2014
PubMed
Summary
This summary is machine-generated.

Microswimmers exhibit stable swimming near no-slip boundaries, with complex behaviors like limit cycles observed. However, stable swimming on free surfaces is not predicted under low capillary numbers, suggesting surface deformation is crucial for such environments.

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Area of Science:

  • Fluid dynamics
  • Microhydrodynamics
  • Biophysics

Background:

  • Microswimmers, such as ciliates and bacteria, are modeled as squirmers.
  • Understanding their boundary behavior is key to micro-robotics and biological fluid dynamics.
  • Previous studies often simplify boundary conditions or swimmer models.

Purpose of the Study:

  • To theoretically investigate the boundary dynamics of axisymmetric microswimming squirmers near no-slip and free surfaces.
  • To analyze the influence of tangential surface deformations and rotlet dipoles on swimmer stability.
  • To explore the conditions for stable microswimming in confined fluid environments.

Main Methods:

  • Theoretical analysis of squirmers in an inertialess Newtonian fluid.
  • Consideration of both no-slip and free surface boundary conditions in the small capillary number limit.
  • Phase plane analysis of swimmer dynamics, incorporating time-reversal duality.

Main Results:

  • Stable swimming and various fixed points (stable/unstable limit cycles) are predicted near no-slip boundaries with varying tangential deformations.
  • Swimmers classified as 'pushers' do not exhibit stable limit cycles near no-slip boundaries.
  • No stable swimming is predicted near free surfaces under the low capillary number assumption, contrary to some observations.

Conclusions:

  • The tangential squirmer model provides a simplified yet effective framework for predicting axisymmetric boundary swimming behaviors.
  • The absence of stable free-surface swimming under low capillary numbers suggests that surface deformation is essential for phenomena like sperm accumulation.
  • Further research should consider surface deformation for accurate modeling of microswimming on free surfaces.