Stokes flows near boundaries: bacteria, corners, and pumps

Change log
Dauparas, Justas 

We investigate flows generated by bacteria near boundaries which are ubiquitous in biological systems. A bacterium such as \textit{Escherichia coli} is equipped with a number of rotary motors on its surface. Every motor has a helical flagellum attached to it and by rotating these motors the bacterium can move the fluid. We consider these flows in four different systems.

Firstly, we explore a chiral flow which is always in the clockwise direction (when viewed from above) ahead of a dense suspension of bacteria on a moist surface. We quantitatively test a hypothesis that this flow is due to the action of cells stalled at the edge of a colony which extend their flagella outwards, moving fluid over a substrate. The model provides insight on the flagella orientations and their spatial distributions.

Secondly, inspired by experiments which proposed to use confined bacteria in order to generate flows near surfaces, we develop a theoretical model of this fluid transport using a superposition of fundamental flow singularities. The rotation of a helical bacterial flagellum induces both a force and a torque on the surrounding fluid, both of which lead to a net flow along the surface. We investigate the optimal helical shapes to be used as micropumps near surfaces and show that bacterial flagella are nearly optimal.

Thirdly, we build a theoretical model on a reorientation of peritrichous bacteria at the edge of a liquid drop on a Petri dish. Bacteria are more likely to turn clockwise because of the interaction between counterclockwise rotating flagella and boundaries which causes them to self-organise and circle clockwise (when viewed from above) around the outer edge of the colony.

Finally, motivated by problems in biological physics occurring near corners, we derive the asymptotic behaviour for the Stokeslet (a flow due to a point force at low Reynolds number) both near and far from a corner geometry by using complex analysis on a known double integral solution for corner flows. We analyse flows in acute, obtuse and salient three-dimensional corners. We also use experiments on beads sedimenting in corn syrup to qualitatively test our results.

The fundamental understanding of Stokes flows near boundaries is important for future developments in biophysics and bioengineering including applications to bacterial micropumps, steering microswimmers near corners, and preventing biofilm formation.

Lauga, Eric
Stokes, corner, boundaries, fluid, bacteria, biophysics, pumping, flows, eddies
Doctor of Philosophy (PhD)
Awarding Institution
University of Cambridge