1and driven systems [2][3][4][5] . It is commonly held that potential interactions 6 , depletion forces 7 , or sensing 8 are the only mechanisms which can create long-lived compact structures. Here we show that persistent motile structures can form spontaneously from hydrodynamic interactions alone, with no sensing or potential interactions. We study this structure formation in a system of colloidal rollers suspended and translating above a floor, using both experiments and large-scale three-dimensional simulations. In this system, clusters originate from a previously unreported fingering instability, where fingers pinch o from an unstable front to form autonomous 'critters', whose size is selected by the height of the particles above the floor. These critters are a stable state of the system, move much faster than individual particles, and quickly respond to a changing drive. With speed and direction set by a rotating magnetic field, these active structures o er interesting possibilities for guided transport, flow generation, and mixing at the microscale.We have identified a new instability in one of the most basic systems of low-Reynolds-number (steady Stokes or overdamped) flow, a collection of spheres rotating near a wall. This system has been well studied analytically and numerically 9,10 , since it is considered a base model for understanding many microbial and colloidal flows. The instability visually resembles wet paint dripping down a wall or individual droplets sliding down a windshield 11 -examples of Rayleigh-Taylor instabilities 12 . However, in those and other clustering phenomena, what holds things together is surface tension or other forces deriving from an interaction potential.Here we use a model system to explore whether hydrodynamic interactions alone, without particle collisions, attractions or sense/response redirection, can lead to stable finite clusters.The experimental system consists of polymer colloids with radius a = 0.66 µm which have a small permanent magnetic moment (|m| ∼ 5 × 10 −16 A m −2 ) from an embedded haematite cube 13 (see schematic in Fig. 1a). Inter-particle magnetic interactions are small compared to thermal energy (< 0.1k B T ). A rotating magnetic field (B = B 0 cos(ωt)x + sin(ωt)ẑ ) with magnitude B 0 and frequency f = ω/2π is applied, causing all the particles to rotate about the y-axis at the same rate ω. The particles rotate synchronously with the field for ω < ω c , where ω c is the critical frequency above which the applied magnetic torque is not enough to balance the viscous torque on the particle (see Supplementary Section I for details of the rotation mechanism). In all of our experiments, ω < ω c . In contrast with recent experiments on Quincke rollers 14 , the rotation direction is prescribed and does not arise from the system dynamics.Hydrodynamics is the dominant inter-particle interaction in this system, which is distinctly different from many other systems of rotating magnetic particles, where dynamics is found to be a strong function of inter-particle ...

A drop impacting a solid surface with sufficient velocity will emit many small droplets creating a splash. However, splashing is completely suppressed if the surrounding gas pressure is lowered. The mechanism by which the gas affects splashing remains unknown. We use high-speed interference imaging to measure the air beneath all regions of a spreading viscous drop as well as optical absorption to measure the drop thickness. Although an initial air bubble is created on impact, no significant air layer persists until the time a splash is created. This suggests that splashing in our experimentally accessible range of viscosities is initiated at the edge of the drop as it encroaches into the surrounding gas.

A liquid drop impacting a solid surface may splash either by emitting a thin liquid sheet that subsequently breaks apart or by promptly ejecting droplets from the advancing liquid-solid contact line. Using high-speed imaging, we show that surface roughness and air pressure influence both mechanisms. Roughness inhibits thin-sheet formation even though it also increases prompt splashing at the advancing contact line. If the air pressure is lowered, droplet ejection is suppressed not only during thin-sheet formation but for prompt splashing as well.PACS numbers: 47.20.Cq, 47.20.Gv, 47.20.Ma,Will a drop hitting a dry surface splash? Different criteria [1][2][3][4][5] have been proposed to predict when such a drop will splash by comparing the roughness of the solid surface with hydrodynamic length scales, which depend on parameters such as the drop velocity, radius, viscosity and surface tension. Several years ago Xu et al. [6,7] found that these criteria ignore a crucial parameter: the ambient gas pressure, P . When a drop splashes on a smooth surface it spreads smoothly forming a lamella before ejecting a thin sheet that subsequently breaks up into secondary droplets. As P is reduced below a threshold pressure, the drop no longer splashes [6][7][8][9][10]. On the other hand, when splashing occurs on a rough surface, no thin sheet is formed and droplets are ejected directly from the advancing liquid-substrate contact line via a "prompt" splash [1][2][3][4]8].It has been suggested that thin-sheet splashes depend on air pressure while prompt splashes do not and depend only on surface roughness [8]. Here we show that the situation is more complex in that both types of splashing depend, albeit in opposite ways, on surface roughness. In particular, we observe four distinct regimes. In agreement with earlier results [4], we observe a thin-sheet splash on very smooth surfaces and a prompt splash on very rough ones. However, at intermediate roughness, we identify two new regimes: at low viscosities both prompt and thin-sheet splashes occur during a single impact, while at high viscosities neither splash is formed. In addition, as found for thin-sheet splashing [6], we find that a drop deposits smoothly on a rough surface if P is low enough. Clearly, the role of both air pressure and substrate roughness must be considered in all cases.The experiments were conducted with silicone oil (PDMS, Clearco Products) with kinematic viscosity ν ranging from 5 cSt to 14.4 cSt and surface tension σ between 19.7 dyn/cm and 20.8 dyn/cm. The basic results were replicated using water/glycerin mixtures with a similar viscosity range but higher surface tension: σ=67 dyn/cm. Low-viscosity impacts were studied with ethanol. Drops with reproducible diameter D=3.1 mm were produced using a syringe pump (Razel Scientific, Model R99-E) and released in a chamber from a height above a substrate. This height set the impact velocity u 0 which was varied between 2.7 m/s and 4.1 m/s. These parameters determine the Reynolds number Re=Du 0 /ν giving the rati...

After impact onto a smooth dry surface, a drop of viscous liquid initially spreads in the form of a thick lamella. If the drop splashes, it first emits a thin fluid sheet that can ultimately break up into droplets causing the splash. Ambient gas is crucial for creating this thin sheet. The time for sheet ejection, t{ejt}, depends on impact velocity, liquid viscosity, gas pressure, and molecular weight. A central air bubble is trapped below the drop at pressures even below that necessary for this sheet formation. In addition, air bubbles are entrained underneath the spreading lamella when the ejected sheet is present. Air entrainment ceases at a lamella velocity that is independent of drop impact velocity as well as ambient gas pressure.

We perform detailed computational and experimental measurements of the driven dynamics of a dense, uniform suspension of sedimented microrollers driven by a magnetic field rotating around an axis parallel to...

In this review article, we focus on collective motion in externally driven colloidal suspensions, as well as how these collective effects can be harnessed for use in microfluidic applications. We highlight the leading role of hydrodynamic interactions in the self-assembly, emergent behavior, transport, and mixing properties of colloidal suspensions. A special emphasis is given to recent numerical methods to simulate driven colloidal suspensions at large scales. In combination with experiments, they help us to understand emergent dynamics and to identify control parameters for both individual and collective motion in colloidal suspensions.

We investigate how material rigidity acts as a key control parameter for the failure of solids under stress. In both experiments and simulations, we demonstrate that material failure can be continuously tuned by varying the underlying rigidity of the material while holding the amount of disorder constant. As the rigidity transition is approached, failure due to the application of uniaxial stress evolves from brittle cracking to system-spanning diffuse breaking. This evolution in failure behavior can be parameterized by the width of the crack. As a system becomes more and more floppy, this crack width increases until it saturates at the system size. Thus, the spatial extent of the failure zone can be used as a direct probe for material rigidity.failure | metamaterials | jamming | cracks | glasses

We combine experiments, large scale simulations and continuum models to study the emergence of coherent structures in a suspension of magnetically driven microrollers sedimented near a floor. Collective hydrodynamic effects are predominant in this system, leading to strong density-velocity coupling. We characterize a uniform suspension and show that density waves propagate freely in all directions in a dispersive fashion. When sharp density gradients are introduced in the suspension, we observe the formation of a shock. Unlike Burgers' shock-like structures observed in other active and driven confined hydrodynamic systems, the shock front in our system has a well-defined finite width and moves rapidly compared to the mean suspension velocity. We introduce a continuum model demonstrating that the finite width of the front is due to far-field nonlocal hydrodynamic interactions and governed by a geometric parameter: the average particle height above the floor. Large-scale structures can emerge naturally from the dynamics of driven and active systems [1]. These structures result from the collective, coherent motion of many * delmotte@courant.nyu.edu † mdriscoll@nyu.edu ‡ chaikin@nyu.edu § donev@courant.nyu.edu individual units, and although similar phenomena are seen in widely disparate systems [2][3][4], the interactions that result in collective and coherent motion strongly depend on the specifics of the system being considered. Colloidal suspensions, for example, are always in the Stokes (overdamped) limit due to their small scale. In this limit, the interactions between the colloidal particles are longranged and strongly depend on the presence of nearby boundaries. Despite the linearity of the equations for the fluid flow in the Stokes regime, elucidating the precise role of hydrodynamic interactions in confined or bounded systems is still an open and challenging problem.Under strong in-plane confinement, i.e. in a Hele-Shaw cell, active suspensions exhibit coherent motion at large scales and phase transitions to polar and ordered states. For example, recent experiments [5] and models [6][7][8][9][10][11] have shown that hydrodynamic and steric interactions lead to the emergence of collective motion and structure formation in the form of swirls and vortices [7,9], asters [7,9], or polarized density waves [6,7,12,13]. In addition to using motile particles, a background flow can also be used to drive a suspension, leading to a rich and diverse array of structure formation: long-ranged orientational correlations [14], density fluctuations at all scales [15], and the formation of Burgers-like shocks [7,12,16,17]. In all of these strongly-confined driven suspensions, despite the difference in propulsion mechanism/driving, the local flow field around a particle is always quasi-twodimensional (q2D) and can be modeled as a potential dipole [6,18,19]. Here we show that related but quite different structure formation can emerge from a fundamentally different system, with a different particle-induced flow field and a diffe...