(334b) Upstream Swimming and Taylor Dispersion of Active Brownian Particles

Locomotion of self-propelled particles such as motile bacteria or phoretic swimmers often takes place in the presence of applied flows and confining boundaries. Interactions of these active swimmers with the flow environment are important for the understanding of many biological processes, including infection by motile bacteria and the formation of biofilms. Recent experimental and theoretical work have shown that active particles in a Poiseuille flow exhibit interesting dynamics including accumulation on the wall and upstream swimming. Compared to the well-known Taylor dispersion theory of passive Brownian particles, a theoretical understanding of the transport of active Brownian particles (ABPs) in a pressure-driven flow is less developed. In this paper, employing a small wavenumber expansion of the Smoluchowski equation describing the particle distribution, we explicitly derive an effective advection-diffusion equation for the cross-sectional average of the particle number density. We characterize the effective drift (specifically upstream swimming) and diffusivity of active particles in relation to the flow speed, the intrinsic swimming speed and Brownian motion. In contrast to passive Brownian particles, both the effective drift and diffusivity of ABPs exhibit a non-monotonic variation as a function of the flow speed. In particular, the dispersion of ABPs includes the classical shear-enhanced (Taylor) dispersion and an active contribution called the swim diffusivity. While the pressure-driven flow always enhances particle diffusion through the classical Taylor dispersion process, it has a bidirectional effect on the swim diffusivity. Our continuum theory is corroborated by a direct Brownian dynamics simulation of the Langevin equations governing the motion of each active particle.