Understanding the properties of active matter is a challenge which is currently driving a rapid growth in soft- and bio-physics. Some of the most important examples of active matter are at the microscale, and include active colloids and suspensions of microorganisms, both as a simple active fluid (single species) and as mixed suspensions of active and passive elements. In this last class of systems, recent experimental and theoretical work has started to provide a window into new phenomena including activity-induced depletion interactions, phase separation, and the possibility to extract net work from active suspensions. Here I will present our work on a paradigmatic example of mixed active-passive system, where the activity is provided by swimming microalgae. Macro- and micro-scopic experiments reveal that microorganism-colloid interactions are dominated by rare close encounters leading to large displacements through direct entrainment. Simulations and theoretical modelling show that the ensuing particle dynamics can be understood in terms of a simple jump-diffusion process, combining standard diffusion with Poisson-distributed jumps. Entrainment length can be understood within the framework of Taylor dispersion as a competition between advection by the no-slip surface of the cell body and microparticle diffusion. Building on these results, we then ask how external control of the dynamics of the active component (e.g. induced microswimmer anisotropy/inhomogeneity) can be used to alter the transport of passive cargo. As a first step in this direction, we study the behaviour of mixed active-passive systems in confinement. The resulting spatial inhomogeneity in swimmers’ distribution and orientation has a dramatic effect on the spatial distribution of passive particles, with the colloids accumulating either towards the boundaries or towards the bulk of the sample depending on the size of the container. We show that this can be used to induce the system to de-mix spontaneously.

Understanding the transport of microorganisms and self-propelled particles in porous media has important consequences in human health as well as for microbial ecology. In this work, we explore models for the dispersion of active particles in both periodic and random porous media. In a first problem, we analyze the long-time transport properties in a dilute system of active Brownian particles swimming in a periodic lattice in the presence of an external flow. Using generalized Taylor dispersion theory, we calculate the mean transport velocity and dispersion dyadic and explain their dependence on flow strength, swimming activity and geometry. In a second approach, we address the case of run-and-tumble particles swimming through unstructured porous media composed of randomly distributed circular pillars. There, we show that the long-time dispersion is described by a universal hindrance function that depends on the medium porosity and ratio of the swimmer run length to the pillar size. An asymptotic expression for the hindrance function is derived in dilute media, and its extension to semi-dilute and dense media is obtained using stochastic simulations. We conclude by discussing the role of hydrodynamic interactions and swimmer concentration effects.

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.