We consider two systems of active swimmers moving close to a solid surface, one being a living population of wild-type E. coli and the other being an assembly of self-propelled Au-Pt rods. In both situations, we have identified two different types of motion at the surface and evaluated the fraction of the population that displayed ballistic trajectories (active swimmers) with respect to those showing randomlike behavior. We studied the effect of this complex swimming activity on the diffusivity of passive tracers also present at the surface. We found that the tracer diffusivity is enhanced with respect to standard Brownian motion and increases linearly with the activity of the fluid, defined as the product of the fraction of active swimmers and their mean velocity. This result can be understood in terms of series of elementary encounters between the active swimmers and the tracers.

The viscosity of an active suspension of E-Coli bacteria is determined experimentally in the dilute and semi dilute regime using a Y shaped micro-fluidic channel. From the position of the interface between the pure suspending fluid and the suspension, we identify rheo-thickening and rheo-thinning regimes as well as situations at low shear rate where the viscosity of the bacteria suspension can be lower than the viscosity of the suspending fluid. In addition, bacteria concentration and velocity profiles in the bulk are directly measured in the micro-channel.PACS numbers: 47.57.Qk,The fluid mechanics of microscopic swimmers in suspension have been widely studied in recent years. Bacteria [1, 2], algae [3,4] or artificial swimmers [5] dispersed in a fluid display properties that differ strongly from those of passive suspensions [6]. The physical relationships governing momentum and energy transfer as well as constitutive equations vary drastically for these suspensions [7,8]. Unique physical phenomena caused by the activity of swimmers were recently identified such as enhanced Brownian diffusivity [1,[8][9][10]] uncommon viscosity [4,12,13], active transport and mixing [11] or the extraction of work from isothermal fluctuations [13,16]. The presence of living and cooperative species may also induce collective motion and organization at the mesoscopic or macroscopic level [17,18] impacting the constitutive relationships in the semi-diluted or dense regimes. The E.Coli bacterium possesses a quite sophisticated propulsion apparatus consisting of a collection of flagella (7-10 µm length) organized in a bundle and rotating counter-clockwise [20]. In a fluid at rest, the wild-type strain used here has the ability to change direction by unwinding some flagella and moving them in order to alter its swimming direction (a tumble) approximately once every second [21]. In spite of the inherent complexity of the propulsion features, low Reynolds number hydrodynamics impose a long range flow field which can be modeled as an effective force dipole. Due to the thrust coming from the rear, E.coli are described as "pushers", hence defining a sign for the force dipole which has a crucial importance on the rheology of active suspensions [7]. For a dilute suspension of force dipoles, Haines et al [22] and Saintillan [24] derived an explicit relation relating viscosity and shear rate. They obtained an effective viscosity similar in form to the classical Einstein relation for dilute suspensions : η = η 0 (1 + Kφ) (η 0 being the suspending fluid viscosity and φ the volume fraction). These theories predict a negative value for the coefficient K for pushers at low shear rates, meaning the suspension can exhibit a lower viscosity than the suspending fluid. The theoretical assessment of shear viscosity relies on an assumed statistical representation of the orientations of the bacteria, captured by a Fokker-Plank equation and a kinematic model for the swimming trajectories [25,26].Despite the large number of theoretical studies, few experimen...

The induced diffusion of tracers in a bacterial suspension is studied theoretically and experimentally at low bacterial concentrations. Considering the swimmer-tracer hydrodynamic interactions at low-Reynolds number and using a kinetic theory approach, it is shown that the induced diffusion coefficient is proportional to the swimmer concentration, their mean velocity and a coefficient β, as observed experimentally. The coefficient β scales as the tracer-swimmer cross section times the mean square displacement produced by single scatterings. The displacements depend on the swimmer propulsion forces. Considering simple swimmer models (acting on the fluid as two monopoles or as a force dipole) it is shown that β increases for decreasing swimming efficiencies. Close to solid surfaces the swimming efficiency degrades and, consequently, the induced diffusion increase. Experiments on W wild-type Escherichia coli in a Hele-Shaw cell under buoyant conditions are performed to measure the induced diffusion on tracers near surfaces. The modification of the suspension pH vary the swimmers' velocity in a wide range allowing to extract the β coefficient with precision. It is found that the solid surfaces modify the induced diffusion: decreasing the confinement height of the cell, β increases by a factor 4. The theoretical model reproduces this increase although there are quantitative differences, probably attributed to the simplicity of the swimmer models.

The colonization of surfaces by bacteria is a widespread phenomenon with consequences on environmental processes and human health. While much is known about the molecular mechanisms of surface colonization, the influence of the physical environment remains poorly understood. Here we show that the colonization of non-planar surfaces by motile bacteria is largely controlled by flow. Using microfluidic experiments with Pseudomonas aeruginosa and Escherichia coli, we demonstrate that the velocity gradients created by a curved surface drive preferential attachment to specific regions of the collecting surface, namely the leeward side of cylinders and immediately downstream of apexes on corrugated surfaces, in stark contrast to where nonmotile cells attach. Attachment location and rate depend on the local hydrodynamics and, as revealed by a mathematical model benchmarked on the observations, on cell morphology and swimming traits. These results highlight the importance of flow on the magnitude and location of bacterial colonization of surfaces.

We quantitatively study the transport of E. coli near the walls of confined microfluidic channels, and in more detail along the edges formed by the interception of two perpendicular walls. Our experiments establish the connection between bacteria motion at the flat surface and at the edges and demonstrate the robustness of the upstream motion at the edges. Upstream migration of E. coli at the edges is possible at much larger flow rates compared to motion at the flat surfaces. Interestingly, the bacteria speed at the edges mainly results from collisions between bacteria moving along this single line. We show that upstream motion not only takes place at the edge but also in an "edge boundary layer" whose size varies with the applied flow rate. We quantify the bacteria fluxes along the bottom walls and the edges and show that they result from both the transport velocity of bacteria and the decrease of surface concentration with increasing flow rate due to erosion processes. We rationalize our findings as a function of the local variations of the shear rate in the rectangular channels and hydrodynamic attractive forces between bacteria and walls.

Dispersion and migration of bacteria under flow in tortuous and confined structures such as porous or fractured materials is related to a large spectrum of practical interest, but is still poorly understood.Here, we address the question of transport and dispersion of an E. coli suspension flowing through a micro-fluidic channel with a funnel-like constriction in its center. We show a counter-intuitive symmetry breaking of the bacterial concentration, which increases significantly past the funnel. This concentration

This paper describes our findings regarding the accumulation of motile bacteria at the rear of a confined obstacle and the physical description of the mechanisms at play. We found that the modification of flow due to the presence of the obstacle produces vorticity that favor the diffusion of bacteria towards the downstream stagnation point. By testing different flow rates, we determined the range in which bacteria accumulate. More interestingly, we observe that hydrodynamic interaction between the bacteria and the top and bottom surface of the microfluidic chip maintain the bacteria in the region where the flow velocity is lower than their own velocity. In the case of non-motile bacteria, this effect is not observed because bacteria follow the streamlines as passive tracers do.

We present a simple model for bacteria like Escherichia coli swimming near solid surfaces. It consists of two spheres of different radii connected by a dragless rod. The effect of the flagella is taken into account by imposing a force on the tail sphere and opposite torques exerted by the rod over the spheres. The hydrodynamic forces and torques on the spheres are computed by considering separately the interaction of a single sphere with the surface and with the flow produced by the other sphere. Numerically, we solve the linear system which contains the geometrical constraints and the force-free and torque-free conditions. The dynamics of this swimmer near a solid boundary is very rich, showing three different behaviors depending on the initial conditions: (1) swimming in circles in contact with the wall, (2) swimming in circles at a finite distance from the wall, and (3) swimming away from it. Furthermore, the order of magnitude of the radius of curvature for the circular motion is in the range 8 − 50 µm, close to values observed experimentally.