Bulletin of Mathematical Biology

, Volume 72, Issue 1, pp 148–183 | Cite as

A Model of Hydrodynamic Interaction Between Swimming Bacteria

  • Vitaliy Gyrya
  • Igor S. Aranson
  • Leonid V. Berlyand
  • Dmitry Karpeev
Original Article


We study the dynamics and interaction of two swimming bacteria, modeled by self-propelled dumbbell-type structures. We focus on alignment dynamics of a coplanar pair of elongated swimmers, which propel themselves either by “pushing” or “pulling” both in three- and quasi-two-dimensional geometries of space. We derive asymptotic expressions for the dynamics of the pair, which complemented by numerical experiments, indicate that the tendency of bacteria to swim in or swim off depends strongly on the position of the propulsion force. In particular, we observe that positioning of the effective propulsion force inside the dumbbell results in qualitative agreement with the dynamics observed in experiments, such as mutual alignment of converging bacteria.


Bacteria Hydrodynamic interaction Self-propulsion Low Reynolds Stokes 


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Copyright information

© Society for Mathematical Biology 2009

Authors and Affiliations

  • Vitaliy Gyrya
    • 1
  • Igor S. Aranson
    • 2
  • Leonid V. Berlyand
    • 3
  • Dmitry Karpeev
    • 4
  1. 1.Department of MathematicsPennsylvania State UniversityUniversity ParkUSA
  2. 2.Materials Science DivisionArgonne National LaboratoryArgonneUSA
  3. 3.Department of MathematicsPennsylvania State UniversityUniversity ParkUSA
  4. 4.Mathematics and Computer Science DivisionArgonne National LaboratoryArgonneUSA

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