Hauptseminar Active Matter SS 2017/Stokes Flow and Life at Low Reynolds Numbers

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Stokes Flow and Life at Low Reynolds Numbers
Patrik Zielinski
Mihail Popescu


Due to their small size, many micro-swimmers within viscous liquids operate within the regime of low-Reynolds hydrodynamics, where inertia is dominated by viscous forces.

This topic aims at discussing the — as Purcell called it [1] — "life at low Reynolds numbers" described by the time-independent Stokes equations (creeping flow) [1,2].

For the incompressible Stokes flows an important result is the so-called Lorentz reciprocal theorem, which is often employed in the studies of micro-swimmers [2].

The Faxen theorem and the Rotne-Prager tensor are introduced and employed as a means of studying hydrodynamic interactions between particles in motion within a fluid [2,3].

Finally, the scallop theorem [1] and the three-sphere swimmer as an example of micro-object escaping the scallop theorem [5,6] are discussed.


  1. E.D. Purcell, Life at Low reynolds, American Journal of Physics, 45,1 (1977).
  2. J. Happel and H. Brenner, Low Reynolds number hydrodynamics (Noordhoff Int. Pub., Leyden, The Netherlands, 1973), Ch. 1, 3.5, 4.1-4.7, 6.1-6.5, 7.
  3. J.M. Rallison, Note on the Faxen relations for a particle in Stokes flow, J. Fluid. Mech. 88, 529 (1978).
  4. J. Rotne and S. Prager, Variational Treatment of Hydrodynamic Interaction in Polymers, J. Chem. Phys. 50, 4831 (1969).
  5. A. Najafi, R. Golestanian, Simple swimmer at low Reynolds number: Three linked spheres, Phys. Rev. E 69, 062901 (2004).
  6. E. Lauga and D. Bartolo, No many-scallop theorem: Collective locomotion of reciprocal swimmers, Phys. Rev. E, 78, 030901 (2008).