Lattice Boltzmann simulations of tracer diffusion in microswimmer suspensions

Abstract: Suspensions of microswimmers are a class of systems inherently out of equilibrium, due to the mechanical work continuously performed by a large number of active agents. Biological examples are plentiful, as many aquatic microorganisms have the ability to propel themselves. A distinct phenomenon displayed by such systems is the increased diffusivity of passive tracer particles, relative to their equilibrium Brownian value. Such enhanced diffusion is known to be of biological importance, from the microscopic level and up to geographical length scales. Active diffusion coefficients have been found to have non trivial dependence on factors such as swimmer concentration and tracer size. The complexities of the topic are especially apparent at high swimmer densities, where the hydrodynamic interactions between bacteria are known to lead to significant non-linear behavior and long-ranged chaotic flows, referred to as active turbulence, and where diffusivity is dramatically increased. Several aspect of experimentally observed enhanced diffusion have been attributed to far-field hydrodynamic advection of tracers by dipolar microswimmers, although many remain unexplained. In this thesis, I seek to explore such phenomena using three-dimensional particle resolved Lattice Boltzmann simulations, where swimmers are modelled as extended force dipoles. Our method allows for the inclusion of large numbers of swimmers (≥10^5), as typically required for adequately reproducing collective behavior. Primarily, I focus on three diffusion-related phenomena. First, I consider the impact of Brownian motion on enhanced tracer diffusion, finding the latter to be suppressed when the Brownian diffusion coefficient is large. However, this effect appears to be negligible for biologically relevant self-propulsion speeds, a finding which is at odds with previous claims in the literature. I then investigate the tracer size dependence of enhanced diffusion, finding a non-monotonic relation qualitatively opposite to previous experimental observations. Lastly, I turn to the phenomenon of anisotropic diffusion of ellipsoidal tracers. I find tracers in pusher-type suspensions to exhibit an increase in the ratio between diffusion coefficients along their major and minor axes, coinciding with the onset of active turbulence. As experimental observations have instead shown a decrease in this ratio with swimmer concentration, we conclude that non-hydrodynamic effects have significant contributions to anisotropic diffusion.