Microorganisms can swim in a variety of environments, interacting with chemicals and other proteins in the fluid. In this talk, we will highlight recent computational methods and results for swimming efficiency and hydrodynamic interactions of swimmers in different fluid environments. Sperm are modeled via a centerline representation where forces are solved for using elastic rod theory. The method of regularized Stokeslets is used to solve the fluid-structure interaction where emergent swimming speeds can be compared to asymptotic analysis. In the case of fluids with extra proteins or cells that may act as friction, swimming speeds may be enhanced, and attraction may not occur. We will also highlight how parameter estimation techniques can be utilized to infer fluid and/or swimmer properties.

The Smoluchowski equation has often been used as the starting point of many continuum models of active suspensions. However, its six-dimensional nature depending on time, space and orientation requires a huge computational cost, fundamentally limiting its use for large-scale problems, such as mixing and transport of active fluids in turbulent flows. Despite the singular nature in strain-dominant flows, the generalised Taylor dispersion (GTD) theory (Frankel & Brenner 1991, J. Fluid Mech. 230:147-181) has been understood to be one of the most promising ways to reduce the Smoluchowski equation into an advection-diffusion equation, the mean drift and diffusion tensor of which rely on ‘local’ flow information only. In this talk, we will introduce an exact transformation of the Smoluchowski equation into such an advection-diffusion equation requiring only local flow information. Based on this transformation, a new advection-diffusion equation will subsequently be proposed by taking an asymptotic analysis in the limit of small particle velocity. With several examples, it will be demonstrated that the new advection-diffusion model, non-singular in strain-dominant flows, outperforms the GTD theory.