14 - Hydrodynamics of Collective Locomotion

Summary

In this fourteenth chapter we turn to the collective dynamics of cell populations such as bacterial colonies. Specifically, we use the results from Chapters 9 and 10 on hydrodynamic interactions to adapt the discrete and continuum frameworks introduced in the previous chapter to the case of collective cell locomotion. Swimming cells create flows, which advect and rotate neighbouring organisms, and since the flow induced by each cell depends on its location and orientation, this coupling leads to complex nonlinear swimming dynamics. In the discrete case, we derive a first-principle model of cells interacting in the dilute limit, demonstrate the different ways in which two swimming microorganisms affect each other hydrodynamically, and show how the model can be used to explain clustering instabilities of swimming algae. We then develop a continuum approach coupling the dynamics of the fluid with the distribution in position and orientation of the cell population. After relating the model to alternative phenomenological descriptions based on symmetry arguments, we use this continuum framework to capture collective cell instabilities.