Flow-induced diffusivity in a packed suspension of swimming microorganisms

Dense suspensions of swimming microorganisms exist extensively in nature, e.g., biofilms and gut flora. In such suspensions, their swimming drives the ambient fluid and enhances mass transport; it is possible to improve the environment to live by activating the transport of nutrition. We described a flow field of a packed suspension of swimming microorganisms by a boundary element method. Flow-induced diffusivity was quantitatively evaluated by the diffusion tensor of material points tracked by the Lagrange manner. It was found that diffusion occurs even in advection-dominated suspension in a long time duration. The flow-induced diffusivity increased with higher microorganisms' volume fraction and the magnitude became about more than 100 times larger than the thermal diffusivity. Moreover, the direction of enhancement depended on their average orientations. We also proposed a flux-based scaling low which can predict flow-induced diffusivity in a heterogeneous flow without solving the mass conservation equation. This scaling is useful as a more general theory because, unlike conventional Taylor dispersion theory, it can predict diffusivity even in the presence of cross-flows.