The spatial and orientational distribution in a dilute active suspension of non-Brownian run-and-tumble spherical swimmers confined between two planar hard walls is calculated theoretically. Using a kinetic model based on coupled bulk/surface probability density functions, we demonstrate the existence of a concentration wall boundary layer with thickness scaling with the run length, the absence of polarization throughout the bulk of the channel, and the presence of sharp discontinuities in the bulk orientation distribution in the neighbourhood of orientations parallel to the wall in the near-wall region. Our model is also applied to calculate the swim pressure in the system, which approaches the previously proposed ideal-gas behaviour in wide channels but is found to decrease in narrow channels as a result of confinement. Monte Carlo simulations are also performed for validation and show excellent quantitative agreement with our theoretical predictions.

Recent experimental studies have shown that confinement can profoundly affect selforganization in semi-dilute active suspensions, leading to striking features such as the formation of steady and spontaneous vortices in circular domains and the emergence of unidirectional pumping motions in periodic racetrack geometries. Motivated by these findings, we analyze the two-dimensional dynamics in confined suspensions of active self-propelled swimmers using a mean-field kinetic theory where conservation equations for the particle configurations are coupled to the forced Navier-Stokes equations for the self-generated fluid flow. In circular domains, a systematic exploration of the parameter space casts light on three distinct states: equilibrium with no flow, stable vortex, and chaotic motion, and the transitions between these are explained and predicted quantitatively using a linearized theory. In periodic racetracks, similar transitions from equilibrium to net pumping to traveling waves to chaos are observed in agreement with experimental observations and are also explained theoretically. Our results underscore the subtle effects of geometry on the morphology and dynamics of emerging patterns in active suspensions and pave the way for the control of active collective motion in microfluidic devices.

The transport of self-propelled particles such as bacteria and phoretic swimmers through crowded heterogeneous environments is relevant to many natural and engineering processes, from biofilm formation and contamination processes to transport in soils and biomedical devices. While there has been experimental progress, a theoretical understanding of mean transport properties in these systems has been lacking. In this work, we apply generalized Taylor dispersion theory to analyze the long-time statistics of an active self-propelled Brownian particle transported under an applied flow through the interstices of a periodic lattice that serves as an idealization of a porous medium. Our theoretical model, which we validate against Brownian dynamics simulations, is applied to unravel the roles of motility, fluid flow, and lattice geometry on asymptotic mean velocity and dispersivity. In weak flows, transport is dominated by active dispersion, which results from self-propulsion in the presence of noise and is hindered by the obstacles that act as entropic barriers. In strong flows, shear-induced Taylor dispersion becomes the dominant mechanism for spreading, with pillars now acting as regions of shear production that enhance dispersion. The interplay of these two effects leads to complex and unexpected trends, such as a non-monotonic dependence of axial dispersivity on flow strength and a reduction in dispersion due to swimming activity in strong flows. Brownian dynamics are used to cast light on the pre-asymptotic regime, where tailed distributions are observed in agreement with recent experiments on motile micro-organisms. Our results also highlight the subtle effects of pillar shape, which can be used to control the magnitude of dispersion and to drive a net particle migration in quiescent systems.

We analyze the effective rheology of a dilute suspension of self-propelled slender particles confined between two infinite parallel plates and subject to a pressure-driven flow. We use a continuum kinetic model to describe the configuration of the particles in the system, in which the disturbance flows induced by the swimmers are taken into account, and use it to calculate estimates of the suspension viscosity for a range of channel widths and flow strengths typical of microfluidic experiments. Our results are in agreement with previous bulk models, and in particular, demonstrate that the effect of activity is strongest at low flow rates, where pushers tend to decrease the suspension viscosity whereas pullers enhance it. In stronger flows, dissipative stresses overcome the effects of activity leading to increased viscosities followed by shear-thinning. The effects of confinement and number density are also analyzed, and our results confirm the apparent transition to superfluidity reported in recent experiments on pusher suspensions at intermediate densities. We also derive an approximate analytical expression for the effective viscosity in the limit of weak flows and wide channels, and demonstrate good agreement between theory and numerical calculations.

The rheological behavior of magnetotactic bacterial suspensions is analyzed using a continuum kinetic theory. In both unbounded and confined geometries, the response of these suspensions under simple external flows can be controlled by applying a magnetic field and hinges in a subtle way on the interplay of magnetic alignment, rotation under shear, and wall-induced accumulation under confinement. By tuning magnetic field strength and direction, the apparent viscosity can either be enhanced or reduced, and the mechanisms for these trends are elucidated. In the absence of any applied flow, we further demonstrate the ability of magnetoactive suspensions to internally drive steady unidirectional flows upon application of a magnetic field, thus suggesting novel avenues for the design of microfluidic pumps and flow actuation devices.