Confined suspensions of active particles show peculiar dynamics characterized by wall accumulation, as well as upstream swimming, centerline depletion and shear-trapping when a pressure-driven flow is imposed. We use theory and numerical simulations to investigate the effects of confinement and non-uniform shear on the dynamics of a dilute suspension of Brownian active swimmers by incorporating a detailed treatment of boundary conditions within a simple kinetic model where the configuration of the suspension is described using a conservation equation for the probability distribution function of particle positions and orientations, and where particle-particle and particle-wall hydrodynamic interactions are neglected. Based on this model, we first investigate the effects of confinement in the absence of flow, in which case the dynamics is governed by a swimming Péclet number, or ratio of the persistence length of particle trajectories over the channel width, and a second swimmer-specific parameter whose inverse measures the strength of propulsion. In the limit of weak and strong propulsion, asymptotic expressions for the full distribution function are derived. For finite propulsion, analytical expressions for the concentration and polarization profiles are also obtained using a truncated moment expansion of the distribution function. In agreement with experimental observations, the existence of a concentration/polarization boundary layer in wide channels is reported and characterized, suggesting that wall accumulation in active suspensions is primarily a kinematic effect which does not require hydrodynamic interactions. Next, we show that application of a pressure-driven Poiseuille flow leads to net upstream swimming of the particles relative to the flow, and an analytical expression for the mean upstream velocity is derived in the weak flow limit. In stronger imposed flows, we also predict the formation of a depletion layer near the channel centerline, due to cross-streamline migration of the swimming particles towards high-shear regions where they become trapped, and an asymptotic analysis in the strong flow limit is used to obtain a scale for the depletion layer thickness and to rationalize the non-monotonic dependence of the intensity of depletion upon flow rate. Our theoretical predictions are all shown to be in excellent agreement with finite-volume numerical simulations of the kinetic model, and are also supported by recent experiments on bacterial suspensions in microfluidic devices.

Suspensions of active particles, such as motile microorganisms and artificial microswimmers, are known to undergo a transition to complex large-scale dynamics at high enough concentrations. While a number of models have demonstrated that hydrodynamicinteractions can in some cases explain these dynamics, collective motion in experiments is typically observed at such high volume fractions that steric interactions between nearby swimmers are significant and cannot be neglected. This raises the question of the respective roles of steric vs hydrodynamic interactions in these dense systems, which we address in this paper using a continuum theory and numerical simulations. The model we propose is based on our previous kinetic theoryfor dilute suspensions, in which a conservation equation for the distribution function of particle configurations is coupled to the Stokes equations for the fluid motion [D. Saintillan and M. J. Shelley,“Instabilities, pattern formation, and mixing in active suspensions,” Phys. Fluids20, 123304 (2008)]10.1063/1.3041776. At high volume fractions,steric interactions are captured by extending classic models for concentrated suspensions of rodlike polymers, in which contacts between nearby particles cause them to align locally. In the absence of hydrodynamic interactions, this local alignment results in a transition from an isotropic base state to a nematic base state when volume fraction is increased. Using a linear stability analysis, we first investigate the hydrodynamic stability of both states. Our analysis shows that suspensions of pushers, or rear-actuated swimmers, typically become unstable in the isotropic state before the transition occurs; suspensions of pullers, or head-actuated swimmers, can also become unstable, though the emergence of unsteady flows in this case occurs at a higher concentration, above the nematic transition. These results are also confirmed using fully nonlinear numerical simulations in a periodic cubic domain, where pusher and puller suspensions are indeed both found to exhibit instabilities at sufficiently high volume fractions; these instabilities lead to unsteady chaotic states characterized by large-scale correlated motions and strong density fluctuations. While the dynamics in suspensions of pushers are similar to those previously reported in the dilute regime, the instability of pullers is novel and typically characterized by slower dynamics and weaker hydrodynamic velocities and active input power than in pusher suspensions at the same volume fraction.

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.

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.

Chemically-powered micromotors offer exciting opportunities in diverse fields, including therapeutic delivery, environmental remediation, and nanoscale manufacturing. However, these nanovehicles require direct addition of high concentration of chemical fuel to the motor solution for their propulsion. We report the efficient vapor-powered propulsion of catalytic micromotors without direct addition of fuel to the micromotor solution. Diffusion of hydrazine vapor from the surrounding atmosphere into the sample solution is instead used to trigger rapid movement of iridium-gold Janus microsphere motors. Such operation creates a new type of remotely-triggered and powered catalytic micro/nanomotors that are responsive to their surrounding environment. This new propulsion mechanism is accompanied by unique phenomena, such as the distinct off-on response to the presence of fuel in the surrounding atmosphere, and spatio-temporal dependence of the motor speed borne out of the concentration gradient evolution within the motor solution. The relationship between the motor speed and the variables affecting the fuel concentration distribution is examined using a theoretical model for hydrazine transport, which is in turn used to explain the observed phenomena. The vapor-powered catalytic micro/nanomotors offer new opportunities in gas sensing, threat detection, and environmental monitoring, and open the door for a new class of environmentally-triggered micromotors.