Continuum models for active suspension
Date:
Active suspensions, which consist of suspended self-propelling particles such as swimming microorganisms, often exhibit non-trivial transport properties. Continuum models are frequently employed to elucidate phenomena in active suspensions, such as shear trapping of bacteria, bacterial turbulence, and bioconvection patterns in suspensions of algae. Yet, these models are often empirically derived and may not always agree with the individual-based description of active particles. Here we establish a more rigorous foundation for macroscopic continuum modelling based on the respective microscopic dynamics and fully develop a continuum model through coarse-graining. All the assumptions needed to reach popular continuum models from a multi-particle Fokker-Planck equation, which governs the probability of the full configuration space, are explicitly presented. In the dilute limit, this approach leads to the mean-field model (a.k.a. Doi-Saintillan-Shelley model). We then introduce various methods to further reduce the high-dimensional Fokker-Planck equation into a particle density equation, which allows tractable numerical modelling of the various phenomena.