The Graduate School EFFECTIVE PROPERTIES AND COLLECTIVE DYNAMICS IN BACTERIAL SUSPENSIONS

This dissertation introduces novel computationally efficient PDE models, which are used to investigate the origin of self-organization in bacterial suspensions. The key feature of these models is the incorporation of interbacterial interactions motivated by recent experimental observations suggesting their importance in the emergence of collective swimming. Results on well-posedness, effective properties and the onset of the collective state are established through rigorous asymptotic and numerical analysis. Each problem considered is highly multiscale in that microscopic interactions result in changes in the macroscopic state. This work provides a better understanding of the physical mechanisms governing the transition to collective motion. Throughout this dissertation, novel models are employed where a bacterium is represented as a point force dipole subject to two types of interactions: hydrodynamic interactions and excluded volume type interactions introduced through the use of a short-range Lennard-Jones type repelling potential. The point dipole model accounts for the particle size through this potential and shape via Jeffery’s equations modeling how an ellipsoid interacts with the surrounding fluid. Confirming experimental observation, the mathematical analysis reveals that the alignment of asymmetrical particles and the presence of self-propulsion change the effective rheological properties of the suspension such as a drastic reduction in the effective viscosity. By providing explicit formulas for the effective viscosity as well as the effective normal stress differences, the theory presented herein can describe the complete rheological behavior of an active suspension undergoing planar shear in terms of known physical parameters. The first few chapters (1-4) of this dissertation are concerned with introducing the PDE/ODE model for the suspension allowing for the investigation of this decrease in the effective viscosity. The main challenge is added complexity due to the incorporation of interbacterial interactions, in contrast to previous models