Motion at low Reynolds number

Abstract

The work described in this thesis centers on inertialess motion at low Reynolds numbers at the crossroad between biofluids and microfluids. Here we address questions regarding locomotion of micro-swimmers, transport of nutrient around micro-organisms as well as mixing and heat exchange inside micro-droplets of water. A general framework for the investigation of optimal locomotion strategies for slender swimmers has been developed and applied to different systems. Here we exclusively study the hydrodynamical aspects of locomotion without further consideration for the swimmers internal dynamics. The first system studied is the "three-link" swimmer, first introduced and discussed by Nobel prize laureate E.M. Purcell in his famous lecture "Life at low Reynolds number" [121]. For this simple swimmer, we find and later discuss optimal stroke kinematics and swimmer geometries. We then further investigate flagellated swimmers and verify the convergence of the optimization procedure in the case of a single flagellum, for which the optimal stroke kinematics are known analytically. Optimal stroke kinematics and geometries for unifiagellates are also computed and found to be relevant in the context of biological microorganisms.

(cont.) We then turn our attention to stroke kinematics of biflagellates and demonstrate that all the different strokes, which are experimentally observed to be performed by biflagellated organisms such as green algae chlamydomonas, are found to be local hydrodynamical optima. These observations strongly suggest the central role of hydrodynamics in the internal dynamical organization of the stroke patterns. Finally, we present experimental results on convective transport and mixing inside small droplets of water sitting on superhydrophobic substrates. We demonstrate by a scaling analysis, that the regular convection pattern is due to a thermocapillary driven Marangoni flow at the surface of the droplet. We develop an analytical solution for the temperature and flow field inside the droplet, which is found to be in agreement with our experimentally recorded data.