Modelling the transport of active particles in a dilute suspension #

Lloyd Fung, R N Bearon, Y Hwang

10:50 Wednesday in 4Q56.

Part of the Asymptotics in active matter session.

Abstract #

Active Brownian Particle (ABP) is a class of models for particles whose trajectories depend on their noise orientation. It is a particularly popular model for swimming microorganisms such as bacterial, motile and sinking phytoplanktons. In a dilute suspension where these particles only interact hydrodynamically through their disturbance to the fluid bulk, they can be modelled as a continuum phase through the Fokker-Planck equation, which governs the probability distribution of the particles in both the orientational and physical space. However, the two-way coupling between the Fokker-Planck equation and the momentum equation governing the flow, i.e. the Navier-Stokes equation, remains a difficult problem, largely owing to the high number of dimensions in the Fokker-Planck equation.

I am going to present a new model to reduce the high-dimensional Fokker-Planck equation into a low-dimensional transport equation for the number density of the particles. This model is based on a novel transformation of the Fokker-Planck equation, which, even without any approximation, can reveal physical insight into how the orientational motility of ABPs affects their macro-transport. We will also compare this new model with the more restrictive generalised Taylor dispersion model.