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.

We have so far described the fluid dynamics relevant to the propulsion mechanisms of individual microorganisms, with a focus on the physical principles dictating cell locomotion. The length scales involved ranged from tens of nanometres to a few microns. In contrast, the dynamics of cell populations is characterised by much larger length scales, typically hundreds of microns and above. The flow disturbances induced by swimming cells on these large length scales play important biophysical roles, from governing the mixing and transport of nutrients to impacting the physical interactions of cells with their environment and the collective dynamics of populations. In this ninth chapter we address the consequences of the force-free and torque-free swimming constraints of swimming cells on the flows they create. We develop the framework to describe these flow signatures mathematically on length scales larger than that of the organisms, compare them with experimental measurements, explain how to find better approximations near the cells and discuss implications for the hydrodynamic stresses induced by suspensions of swimming microorganisms.