In the absence of advection, confined diffusion characterizes transport in many natural and artificial devices, such as ionic channels, zeolites, and nanopores. While extensive theoretical and numerical studies on this subject have produced many important predictions, experimental verifications of the predictions are rare. Here, we experimentally measure colloidal diffusion times in microchannels with periodically varying width and contrast results with predictions from the Fick-Jacobs theory and Brownian dynamics simulation. While the theory and simulation correctly predict the entropic effect of the varying channel width, they fail to account for hydrodynamic effects, which include both an overall decrease and a spatial variation of diffusivity in channels. Neglecting such hydrodynamic effects, the theory and simulation underestimate the mean and standard deviation of first passage times by 40% in channels with a neck width twice the particle diameter. We further show that the validity of the Fick-Jacobs theory can be restored by reformulating it in terms of the experimentally measured diffusivity. Our work thus shows that hydrodynamic effects play a key role in diffusive transport through narrow channels and should be included in theoretical and numerical models.iffusive transport occurs prevalently in confined geometries (1, 2). Notable examples include the dispersion of tracers in permeable rocks (3), diffusion of chemicals in ramified matrices (4), and the motion of submicrometer corpuscles in living tissues (5, 6). The subject of confined diffusion is of paramount relevance to technological applications and for this reason, has been generating growing interest in the physics (1, 2), mathematics (7), engineering (3), and biology communities (5,6,8).Spatial confinement can fundamentally change equilibrium and dynamical properties of a system via two different effects: limiting the configuration space accessible to its diffusing components (1) and increasing the hydrodynamic drag (9) on them. The former (entropic effect) has been extensively studied analytically and numerically in the case of quasi-1D structures, such as ionic channels (10), zeolites (4), microfluidic channels (11, 12), and nanopores (13). In these systems, transport takes place along a preferred direction, with the spatial constraints varying along it. Focusing on the transport direction, Jacobs (14) and Zwanzig (15), in the absence of advective effects, assumed that the transverse dfs equilibrate fast and proposed to eliminate them adiabatically by means of an approximate perturbation scheme. In first order, they derived a reduced diffusion equation, known as the Fick-Jacobs (FJ) equation, reminiscent of an ordinary 1D Fokker-Planck equation in vacuo, except for two entropic terms (2,(16)(17)(18)(19). Predictions of the FJ equation have been extensively checked against Brownian dynamics (BD) simulations in different types of channels (16,(19)(20)(21)(22)(23)(24)(25)(26)(27). Using the FJ theory and BD simulations, researchers have predicte...

-Bacteria suspension exhibits a wide range of collective phenomena arsing from interactions between individual cells. Here we show Serratia marcescens cells near an air-liquid interface spontaneously aggregate into dynamic clusters through surface-mediated hydrodynamic interactions. These long-lived clusters translate randomly and rotate in the counter-clockwise direction; they continuously evolve, merge with others and split into smaller ones. Measurements indicate that long-ranged hydrodynamic interactions have strong influences on cluster properties. Bacterial clusters change material and fluid transport near the interface and hence may have environmental and biological consequences.Active systems are composed of self-propelled particles that can produce motion by taking in and dissipating energy [1][2][3][4]. Examples exist at different length scales, from bacteria suspension [5][6][7][8][9][10] to flocks of birds [11][12][13]. Being far from thermal equilibrium, active systems are not subject to thermodynamic constraints, such as detailed balance or fluctuation-dissipation theorem [14][15][16]. This renders the physics of active systems much richer than that of thermal systems. For example, collective motion with extended spatio-temporal coherence has been reported in many active systems [5-9, 11-13, 17-19]. Such coherent motion can arise from local interactions that align a particle's motion with its neighbors through biological coordination [11,12] or physical interactions [17,19].Active systems without alignment interactions also exhibit interesting collective behavior. Theoretical models have shown that systems with a density-dependent motility phase separate into dense dynamic clusters and a dilute gas phase [14,15,20]. Numerical simulations of repulsive self-propelled disks confirmed the theoretical prediction of phase separation [21,22]. Effects of motility, attractive interaction, and hydrodynamic forces have been extensively explored in simulations [23][24][25][26]. On the experimental side, dynamic clusters have been observed in Janus particles (platinum-coated [27] and Carbon-coated In this letter, we report experimental results for a new type of bacterial clusters formed near an air-liquid interface in a pure suspension without depletant agents. Fluid dynamic calculation and flow visualization are used to show surface-mediated hydrodynamic interactions can explain the formation of these clusters. We further quantify the statistical and dynamic properties of bacterial clusters and show long-ranged hydrodynamic forces have important influences on cluster properties. We conclude with discussions on related research and on possible technological and environmental implications of our work.Experiments -Our experiments are carried out in drops of wild-type Serratia marcescens (ATCC 274) bacteria, which are propelled by a bundle of a few rotating flagella [32]. For cultivation, small amount of bacteria from frozen stock is put in 4 ml of Luria Broth (LB) growth p-1

We perform experiments on an active chiral fluid system of self-spinning rotors in confining boundary. Along the boundary, actively rotating rotors collectively drives a unidirectional material flow. We systematically vary rotor density and boundary shape; boundary flow robustly emerges under all conditions. Flow strength initially increases then decreases with rotor density (quantified by area fraction φ); peak strength appears around a density φ = 0.65. Boundary curvature plays an important role: flow near a concave boundary is stronger than that near a flat or convex boundary in the same confinements. Our experimental results in all cases can be reproduced by a continuum theory with single free fitting parameter, which describes the frictional property of the boundary.Our results support the idea that boundary flow in active chiral fluid is topologically protected; such robust flow can be used to develop materials with novel functions. *

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