Hydrodynamics of Microorganism Motility: Flagellar Shapes and Boundary Effects

Mathematics Department  

School of Engineering, Brown University

In one of the most common means of microorganism propulsion, bacteria propel themselves through fluids by passing either helical waves (typically prokaryotes) or planar waves (typically eukaryotes) along a slender flagellum. Both from a biological and an engineering perspective, it is of great interest to understand the role of the waveform shape in determining an organism's locomotive kinematics, as well as its hydrodynamic efficiency. We will begin by discussing polymorphism in bacterial flagella, and show by examination of experimental data and numerical simulation that fluid mechanical forces may have played a role in the evolution of the flagellum. For eukaryotic flagella, we will see how the optimal waveform is degenerate under the most common efficiency measure, and how that solution is regularized when energetic costs of internal bending and axonemal sliding are taken into account. Finally, we will study the hydrodynamic effects of nearby boundaries on swimming organisms from a generalized framework, through which a number of recent surprising observations of natural systems might be explained.