Fluid transport by individual microswimmers

Dmitri O. Pushkin, Henry Shum, Julia M. Yeomans

Research output: Contribution to journalArticlepeer-review


We discuss the path of a tracer particle as a microswimmer moves past on an infinite, straight trajectory. If the tracer is sufficiently far from the path of the swimmer it moves in a closed loop. As the initial distance between the tracer and the path of the swimmer ρ decreases, the tracer is displaced a small distance backwards (relative to the direction of the swimmer velocity). For much smaller tracer–swimmer separations, however, the tracer displacement becomes positive and diverges as ρ→0. To quantify this behaviour we calculate the Darwin drift, the total volume swept out by a material sheet of tracers, initially perpendicular to the swimmer path, during the swimmer motion. We find that the drift can be written as the sum of a universal term which depends on the quadrupolar flow field of the swimmer, together with a non-universal contribution given by the sum of the volumes of the swimmer and its wake. The formula is compared to exact results for the squirmer model and to numerical calculations for a more realistic model swimmer.
Original languageEnglish
Pages (from-to)5-25
Number of pages21
JournalJournal of Fluid Mechanics
Early online date30 May 2013
Publication statusPublished - Jul 2013


  • Biological fluid dynamics
  • low-Reynolds-number flows
  • Mixing

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