# The fluid mechanics of swimming algae

#### by Douglas Brumley

Institution: Department of Applied Mathematics and Theoretical Physics (DAMTP), University of Cambridge
Date: Tue 3rd July 2012
Time: 1:00 PM
Location: Old Geology Theatre 1

Abstract: The colonial alga \textit{Volvox carteri} consists of thousands of cells embedded in a spherical extracellular matrix. Each one of these cells possesses a pair of flagella -- small appendages approximately 10 $\mu$m long that facilitate swimming through executing a breaststroke motion. Using bright-field microscopy and high-speed imaging, we perform a series of experiments in which we directly measure the time-dependent fluid velocity field around a large number of \textit{Volvox} colonies. A ubiquitous feature of the results is the large-scale coordinated motion of beating flagella in the fluid.

We present a model for interacting flagella and show that hydrodynamic interactions robustly lead to symplectic metachronal waves, in agreement with experimental findings. In addition to full fluid dynamical simulations, we present a phase oscillator model in which the hydrodynamic interactions between beating flagella can be represented by effective potentials. These potentials are determined numerically and subsequently used to accurately simulate large ensembles of model flagella with minimal computational effort.