Modeling simple locomotors in Stokes flow

Alex Kanevsky, Michael Shelley, Anna Karin Tornberg

Research output: Contribution to journalArticle

Abstract

Motivated by the locomotion of flagellated micro-organisms and by recent experiments of chemically driven nanomachines, we study the dynamics of bodies of simple geometric shape that are propelled by specified tangential surface stresses. We develop a mathematical description of the body dynamics based on a mixed-type boundary integral formulation. We also derive analytic axisymmetric solutions for the case of a single locomoting sphere and ellipsoid based on spherical and ellipsoidal harmonics, and compare our numerical results to these. The hydrodynamic interactions between two spherical and ellipsoidal swimmers in an infinite fluid are then simulated using second-order accurate spatial and temporal discretizations. We find that the near-field interactions result in complex and interesting changes in the locomotors' orientations and trajectories. Stable as well as unstable pairwise swimming motions are observed, similar to the recent findings of Pooley et al. [C.M. Pooley, G.P. Alexander, J.M. Yeomans, Hydrodynamic interaction between two swimmers at low Reynolds number, Phys. Rev. Lett. 99 (2007) 228103].

Original languageEnglish (US)
Pages (from-to)958-977
Number of pages20
JournalJournal of Computational Physics
Volume229
Issue number4
DOIs
StatePublished - Feb 20 2010

Fingerprint

Stokes flow
Hydrodynamics
hydrodynamics
Reynolds number
locomotion
Trajectories
low Reynolds number
interactions
spherical harmonics
ellipsoids
organisms
Fluids
near fields
trajectories
harmonics
formulations
fluids
Experiments
Swimming

Keywords

  • Boundary integral formulation
  • Locomotors
  • Nystrom collocation
  • Stokes equations

ASJC Scopus subject areas

  • Computer Science Applications
  • Physics and Astronomy (miscellaneous)

Cite this

Modeling simple locomotors in Stokes flow. / Kanevsky, Alex; Shelley, Michael; Tornberg, Anna Karin.

In: Journal of Computational Physics, Vol. 229, No. 4, 20.02.2010, p. 958-977.

Research output: Contribution to journalArticle

Kanevsky, A, Shelley, M & Tornberg, AK 2010, 'Modeling simple locomotors in Stokes flow', Journal of Computational Physics, vol. 229, no. 4, pp. 958-977. https://doi.org/10.1016/j.jcp.2009.05.030
Kanevsky, Alex ; Shelley, Michael ; Tornberg, Anna Karin. / Modeling simple locomotors in Stokes flow. In: Journal of Computational Physics. 2010 ; Vol. 229, No. 4. pp. 958-977.
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