Transport of a dilute active suspension in pressure-driven channel flow

Abstract

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.

Geometric control of active collective motion

“…As first discussed by Ezhilan & Saintillan [30], two interesting limiting cases are found. When Λ → 0 (strong-propulsion limit), the thickness of the layer is set by the balance of swimming and translational diffusion and is given by Ω −1 H ≈ √ 2 d t /V s ; on the other hand, the weak-propulsion limit of Λ → ∞ yields a thickness of Ω −1 H ≈ d t /d r , which is a purely diffusive length scale.…”

“…(22)- (23) at both walls r = r min and r min + 2 but is omitted here for brevity. The solution in a straight channel was also previously calculated by Ezhilan & Saintillan [30].…”

Destabilization of a flow focused suspension of magnetotactic bacteria

“…Upstream swimming occurs naturally in pressure-driven flows of bacteria in the absence of any field [24], but an interesting aspect of externally driven systems is that they could serve as conceptual building blocks for remotely controllable microsurgeons or cargos that would be piloted through blood vessel networks [25]. In that perspective, shifting the focused microswimmers beam towards the channel side where the flow slows down could be a strategy for achieving upstream swimming against high-speed blood flow.…”

Population splitting of rodlike swimmers in Couette flow

“…In the context of continuum models, Ezhilan and Saintillan [76] have conducted a thorough study on the response of a confined suspension of active rodlike particles to imposed Poiseuille flow, using a kinetic model in which the active suspension is described by a joint position-orientation probability distribution function (PDF) governed by a non-interacting Smoluchowski equation. Without considering hydrodynamic inter-particle and surface-particle interactions, they have been able to observe many of the important effects arising from confinement and imposed flow coupled with self-propulsion.…”