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

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- Date
- 2017-04-19
- Time
- 17:30
- Topic
- Stokes Flow and Life at Low Reynolds Numbers
- Speaker
- Patrik Zielinski
- Tutor
- Mihail Popescu
- Handout
- [1]

## Contents

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.

## Literature

- E.D. Purcell, Life at Low reynolds, American Journal of Physics, 45,1 (1977).
- 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.
- J.M. Rallison, Note on the Faxen relations for a particle in Stokes flow, J. Fluid. Mech. 88, 529 (1978).
- J. Rotne and S. Prager, Variational Treatment of Hydrodynamic Interaction in Polymers, J. Chem. Phys. 50, 4831 (1969).
- A. Najafi, R. Golestanian, Simple swimmer at low Reynolds number: Three linked spheres, Phys. Rev. E 69, 062901 (2004).
- E. Lauga and D. Bartolo, No many-scallop theorem: Collective locomotion of reciprocal swimmers, Phys. Rev. E, 78, 030901 (2008).