M.Sc Student M.Sc Thesis Raz Oren Swimming and Pumping at Low Reynolds Number Department of Physics PROFESSOR EMERITUS Joseph Avron PROF. Alexander Leshansky

Abstract

This research is about micro-swimmers, micro-pumps and the relations between them. In order to find the relations between micro-swimmers and micro-pumps, we first study what swimming at low Reynolds number is. This is done by considering some simple examples: the first one is the famous Purcell's three linked swimmer, made of three slender rods, which can control the angles between the rods. Thought this swimmer was invented as "Probably the simplest swimmer" [21], it turns out to be not simple at all. This example demonstrates the non-trivial behavior of even a very simple swimmer at low Reynolds number, and we use a geometric method to give a partial analysis for this swimmer (problems like optimal strokes are not considered). Since this swimmer is very complicated to analyze, we introduce a modification (symmetrization) to this swimmer, making it much simpler to analyze. For this modified Pursell's swimmer, we can carry on many calculations which are too complicated for the Purcell's three linked swimmer, like calculating the fastest stroke or the most efficient stroke.

After understanding what swimming at low Reynolds number is, we connect swimming to pumping and gliding, using the linearity of Stokes equation (which is the governing equation at low Reynolds number) and the Lorenz reciprocity. It turns out that the relations between a swimmer, a glider and the pump one gets by anchoring the swimmer are simple, and can shed light on the properties of both swimmers and pumps. We solve some optimization problems, like optimizing the pitch for a helix as a pump and as a swimmer and what is the best place to anchor a linear swimmer in order to get the best pump. We end up by giving examples for a swimmer that will not pump and a pump that will not swim.