Clogging of noncohesive suspensions through constrictions using an efficient discrete particle solver with unresolved fluid flow.

When objects are forced to flow through constrictions their transport can be frustrated temporarily or permanently due to the formation of arches in the region of the bottleneck. While such systems have been intensively studied in the case of solid particles in a gas phase being forced by gravitational forces, the case of solid particles suspended in a liquid phase, forced by the liquid itself, has received much less attention. In this case, the influence of the liquid flow on the transport efficiency is not well understood yet, leading to several apparently trivial but yet unanswered questions, e.g., would an increase of the liquid flow improve the transport of particles or worsen it? Although some experimental data are already available, they lack enough detail to give a complete answer to such a question. Numerical models would be needed to scrutinize the system deeper. In this paper, we study this system making use of an advanced discrete particle solver (mercurydpm) and an approximated numerical model for the liquid drag and compare the results with experimental data.

Self-organization of agitated microspheres on various substrates.

The vibration dynamics of relatively large granular grains is extensively treated in the literature, but comparable studies on the self-assembly of smaller agitated beads are lacking. In this work, we investigate how the particle properties and the properties of the underlying substrate surface affect the dynamics and self-organization of horizontally agitated monodisperse microspheres with diameters between 3 and 10 µm. Upon agitation, the agglomerated hydrophilic silica particles locally leave traces of particle monolayers as they move across the flat uncoated and fluorocarbon-coated silicon substrates. However, on the micromachined silicon tray with relatively large surface roughness, the agitated silica agglomerates form segregated bands reminiscent of earlier studies on granular suspensions or Faraday heaps. On the other hand, the less agglomerated hydrophobic polystyrene particles form densely occupied monolayer arrangements regardless of the underlying substrate. We explain the observations by considering the relevant adhesion and friction forces between particles and underlying substrates as well as those among the particles themselves. Interestingly, for both types of microspheres, large areas of the fluorocarbon-coated substrates are covered with densely occupied particle monolayers. By qualitatively examining the morphology of the self-organized particle monolayers using the Voronoi approach, it is understood that these monolayers are highly disordered, i.e., multiple symmetries coexist in the self-organized monolayers. However, more structured symmetries are identified in the monolayers of the agitated polystyrene microspheres on all the substrates, albeit not all precisely positioned on a hexagonal lattice. On the other hand, both the silica and polystyrene monolayers on the bare silicon substrates transition into less disordered structures as time progresses. Using Kelvin probe force microscopy measurements, we show that due to the tribocharging phenomenon, the formation of particle monolayers is promoted on the fluorocarbon surface, i.e., a local electrostatic attraction exists between the particle and the substrate.

Impact of a microfluidic jet on a pendant droplet.

High speed microfluidic jets can be generated by a thermocavitation process: from the evaporation of the liquid inside a microfluidic channel, a rapidly expanding bubble is formed and generates a jet through a flow focusing effect. Here, we study the impact and traversing of such jets on a pendant liquid droplet. Upon impact, an expanding cavity is created, and, above a critical impact velocity, the jet traverses the entire droplet. We predict the critical traversing velocity (i) from a simple energy balance and (ii) by comparing the Young-Laplace and dynamic pressures in the cavity that is created during the impact. We contrast the model predictions against experiments, in which we vary the liquid properties of the pendant droplet and find good agreement. In addition, we assess how surfactants and viscoelastic effects influence the critical impact velocity. Our results increase the knowledge of the jet interaction with materials of well-known physical properties.

Impact cratering in sand: comparing solid and liquid intruders.

How does the impact of a deformable droplet on a granular bed differ from that caused by a solid impactor of similar size and density? Here, we experimentally study this question and focus on the effect of intruder deformability on the crater shape. For comparable impact energies, we show that the crater diameter is larger for droplets than for solid intruders but that the impact of the latter results in deeper craters. Interestingly, for initially dense beds of packing fractions larger than 0.58, we find that the resultant excavated crater volume is independent of the intruder deformability, suggesting an impactor-independent dissipation mechanism within the sand for these dense beds.

Growth of a bubble cloud in CO2-saturated water under microgravity.

The diffusion-driven growth of a dense cloud of bubbles immersed in a gas-supersaturated liquid is a problem that finds applications in several modern technologies such as solvent-exchange micro-reactors, nanotechnology or the manufacturing of foamy materials. However, under Earth's gravity conditions, these dynamics can only be observed for a very limited time if the cloud is not attached to a surface, due to the action of buoyancy, i.e. of gravity effects. Here, we present experimental observations of the time evolution of dense bubble clouds growing in CO2-supersaturated water under microgravity conditions. We report the existence of three regimes where the bubble cloud exhibits different growth rates. At short times, each bubble grows independently following the Epstein-Plesset equation. Later on, bubbles start to interact with each other and their growth rate diminishes as they compete for the available CO2. When this happens, the growth rate slows down. This occurs earlier the deeper the bubble is in the cloud. Finally, at long times, only those bubbles on the husk continue growing. These regimes may be qualitatively described by a mathematical model where each individual bubble grows in the presence of a constellation of point mass sinks. Despite the model being only valid for dilute bubble clouds, its predictions are consistent with the experimental observations, even though the bubble clouds we observe are rather dense.

Inverse leidenfrost drop manipulation using menisci.

Drops deposited on an evaporating liquid bath can be maintained in an inverse Leidenfrost state by the vapor emanating from the bath, making them levitate and hover without effective friction. These perfectly non-wetting droplets create a depression in the liquid interface that sustains their weight, which generates repellent forces when they approach a meniscus rising against a wall. Here, we study this reflection in detail, and show that frictionless Leidenfrost drops are a simple and efficient tool to probe the shape of an unknown interface. We then use the menisci to control the motion of the otherwise elusive drops. We create waveguides to direct and accelerate them and use parabolic walls to reflect and focus them. This could be particularly beneficial in the scale up of droplet cryopreservation processes: capillary interactions can be used to transport, gather and collect vitrified biological samples in absence of contact and contamination.

Capillary orbits.

Millimeter-sized objects trapped at a liquid surface distort the interface by their weight, which in turn attracts them towards each other. This ubiquitous phenomenon, colloquially called the "Cheerios effect" is seen in the clumping of cereals in a breakfast bowl, and turns out to be a highly promising route towards controlled self-assembly of colloidal particles at the water surface. Here, we study capillary attraction between levitating droplets, maintained in an inverse Leidenfrost state above liquid nitrogen. We reveal that the drops spontaneously orbit around each other - mirroring a miniature celestial system. In this unique situation of negligible friction, the trajectories are solely shaped by the Cheerios-interaction potential, which we obtain directly from the droplet's dynamics. Our findings offer an original perspective on contactless and contamination-free droplet cryopreservation processing, where the Leidenfrost effect and capillarity would be used in synergy to vitrify and transport biological samples.

Deep pool water-impacts of viscous oil droplets.

We experimentally study the impacts of viscous, immiscible oil drops into a deep pool of water. Within the target liquid pool, the impacting drop creates a crater, whose dynamics are studied. It is found that the inertia of pool liquid and drop viscosity are the main factors that determine the crater's maximum depth, while the additional factor of mutual immiscibility between the drop and pool liquids leads to interesting interfacial dynamics along the oil-water interface. We discuss how this can change the crater dynamics in its retraction phase, making possible a type of double-entrainment, whereby a tiny air bubble is entrapped inside a water-entrained oil drop. Further, we report the observation of a type of 'fingering' that occurs along the oil-drop rim, which we discuss, arises as a remnant of the well-known crown-splash instability.

Self-propulsion of inverse Leidenfrost drops on a cryogenic bath.

When deposited on a hot bath, volatile drops are observed to stay in levitation: the so-called Leidenfrost effect. Here, we discuss drop dynamics in an inverse Leidenfrost situation where room-temperature drops are deposited on a liquid-nitrogen pool and levitate on a vapor film generated by evaporation of the bath. In the seconds following deposition, we observe that the droplets start to glide on the bath along a straight path, only disrupted by elastic bouncing close to the edges of the container. Initially at rest, these self-propelled drops accelerate within a few seconds and reach velocities on the order of a few centimeters per second before slowing down on a longer time scale. They remain self-propelled as long as they are sitting on the bath, even after freezing and cooling down to liquid-nitrogen temperature. We experimentally investigate the parameters that affect liquid motion and propose a model, based on the experimentally and numerically observed (stable) symmetry breaking within the vapor film that supports the drop. When the film thickness and the cooling dynamics of the drops are also modeled, the variations of the drop velocities can be accurately reproduced.

The Nucleation Rate of Single O2 Nanobubbles at Pt Nanoelectrodes.

Nanobubble nucleation is a problem that affects efficiency in electrocatalytic reactions since those bubbles can block the surface of the catalytic sites. In this article, we focus on the nucleation rate of O2 nanobubbles resulting from the electrooxidation of H2O2 at Pt disk nanoelectrodes. Bubbles form almost instantaneously when a critical peak current, inbp, is applied, but for lower currents, bubble nucleation is a stochastic process in which the nucleation (induction) time, tind, dramatically decreases as the applied current approaches inbp, a consequence of the local supersaturation level, ζ, increasing at high currents. Here, by applying different currents below inbp, nanobubbles take some time to nucleate and block the surface of the Pt electrode at which the reaction occurs, providing a means to measure the stochastic tind. We study in detail the different conditions in which nanobubbles appear, concluding that the electrode surface needs to be preconditioned to achieve reproducible results. We also measure the activation energy for bubble nucleation, Ea, which varies in the range from (6 to 30) kT, and assuming a spherically cap-shaped nanobubble nucleus, we determine the footprint diameter L = 8-15 nm, the contact angle to the electrode surface θ = 135-155°, and the number of O2 molecules contained in the nucleus (50 to 900 molecules).

Experiments and characterization of low-frequency oscillations in a granular column.

The behavior of a vertically vibrated granular bed is reminiscent of a liquid in that it exhibits many phenomena such as convection and Faraday-like surface waves. However, when the lateral dimensions of the bed are confined such that a quasi-one-dimensional geometry is formed, the only phenomena that remain are bouncing bed and the granular Leidenfrost effect. This permits the observation of the granular Leidenfrost state for a wide range of energy injection parameters and more specifically allows for a thorough characterization of the low-frequency oscillation (LFO) that is present in this state. In both experiments and particle simulations we determine the LFO frequency from the power spectral density of the center-of-mass signal of the grains, varying the amplitude and frequency of the driving, the particle diameter, and the number of layers in the system. We thus find that the LFO frequency (i) is inversely proportional to the fast inertial timescale and (ii) decorrelates with a typical decay time proportional to the slow dissipative timescale in the system. The latter is consistent with the view that the LFO is driven by the inherent noise that is present in the granular Leidenfrost state with a low number of particles.

Electrolysis-Driven and Pressure-Controlled Diffusive Growth of Successive Bubbles on Microstructured Surfaces.

Control over the bubble growth rates forming on the electrodes of water-splitting cells or chemical reactors is critical with respect to the attainment of higher energy efficiencies within these devices. This study focuses on the diffusion-driven growth dynamics of a succession of H2 bubbles generated at a flat silicon electrode substrate. Controlled nucleation is achieved by means of a single nucleation site consisting of a hydrophobic micropit etched within a micrometer-sized pillar. In our experimental configuration of constant-current electrolysis, we identify gas depletion from (i) previous bubbles in the succession, (ii) unwanted bubbles forming on the sidewalls, and (iii) the mere presence of the circular cavity where the electrode is being held. The impact of these effects on bubble growth is discussed with support from numerical simulations. The time evolution of the dimensionless bubble growth coefficient, which is a measure of the overall growth rate of a particular bubble, of electrolysis-generated bubbles is compared to that of CO2 bubbles growing on a similar surface in the presence of a supersaturated solution of carbonated water. For electrolytic bubbles and under the range of current densities considered here (5-15 A/m2), it is observed that H2 bubble successions at large gas-evolving substrates first experience a stagnation regime, followed by a fast increase in the growth coefficient before a steady state is reached. This clearly contradicts the common assumption that constant current densities must yield time-invariant growth rates. Conversely, for the case of CO2 bubbles, the growth coefficient successively decreases for every subsequent bubble as a result of the persistent depletion of dissolved CO2.

Crater formation during raindrop impact on sand.

After a raindrop impacts on a granular bed, a crater is formed as both drop and target deform. After an initial, transient, phase in which the maximum crater depth is reached, the crater broadens outwards until a final steady shape is attained. By varying the impact velocity of the drop and the packing density of the bed, we find that avalanches of grains are important in the second phase and hence affect the final crater shape. In a previous paper, we introduced an estimate of the impact energy going solely into sand deformation and here we show that both the transient and final crater diameter collapse with this quantity for various packing densities. The aspect ratio of the transient crater is however altered by changes in the packing fraction.

Dramatic effect of fluid chemistry on cornstarch suspensions: Linking particle interactions to macroscopic rheology.

Suspensions of cornstarch in water exhibit strong dynamic shear thickening. We show that partly replacing water with ethanol strongly alters the suspension rheology. We perform steady and nonsteady rheology measurements combined with atomic force microscopy to investigate the role of fluid chemistry on the macroscopic rheology of the suspensions and its link with the interactions between cornstarch grains. Upon increasing the ethanol content, the suspension goes through a yield-stress fluid state and ultimately becomes a shear-thinning fluid. On the cornstarch grain scale, atomic force microscopy measurements reveal the presence of polymers on the cornstarch surface, which exhibit a cosolvency effect. At intermediate ethanol content, a maximum of polymer solubility induces high microscopic adhesion which we relate to the macroscopic yield stress.

Liquid-Grain Mixing Suppresses Droplet Spreading and Splashing during Impact.

Would a raindrop impacting on a coarse beach behave differently from that impacting on a desert of fine sand? We study this question by a series of model experiments, where the packing density of the granular target, the wettability of individual grains, the grain size, the impacting liquid, and the impact speed are varied. We find that by increasing the grain size and/or the wettability of individual grains the maximum droplet spreading undergoes a transition from a capillary regime towards a viscous regime, and splashing is suppressed. The liquid-grain mixing is discovered to be the underlying mechanism. An effective viscosity is defined accordingly to quantitatively explain the observations.

Scaling behavior of coarsening Faraday heaps.

When a layer of sand is vertically shaken, the surface spontaneously breaks up in a landscape of small conical "Faraday heaps," which merge into larger ones on an ever increasing time scale. We propose a model for the heap dynamics and show analytically that the mean lifetime of the transient state with N heaps scales as N(-2). When there is an abundance of sand, such that the vibrating plate always remains completely covered, this means that the average diameter of the heaps grows as t(1/2). Otherwise, when the sand is less plentiful and parts of the plate get depleted during the coarsening process, the average diameter of the heaps grows more slowly, namely as t(1/3). This result compares well with experimental observations.

Emergence of traveling density waves in cyclic multiparticle transport.

Multiparticle flow through a cyclic array of K connected compartments with a preferential direction is found to be able to organize itself in traveling waves. This behavior is connected with the transition between uniform flow and cluster formation. When the bias in the system is large, the particles flow freely in the preferred direction, with all compartments being equally filled at all times. Conversely, when the bias is small the particles cluster together in one compartment. The transition between these two regimes is found to involve an intermediate state in which the flow exhibits a density peak traveling periodically around the system. We relate the emergence of this traveling wave to a Hopf bifurcation and analytically derive the critical value of the "symmetry parameter" at which this bifurcation occurs. This critical value proves to be independent of the number of compartments, but the width of the intermediate regime (and thus the chance of observing traveling wave solutions) decreases sharply with growing K. The reverse transition follows a different course and takes place at a significantly lower value of the symmetry parameter; it is an abrupt transition from a clustered state to a uniform flow without an intermediate regime of stable traveling waves.

Raindrop impact on sand: a dynamic explanation of crater morphologies.

As a droplet impacts upon a granular substrate, both the intruder and the target undergo deformation, during which the liquid may penetrate into the substrate. These three aspects together distinguish it from other impact phenomena in the literature. We perform high-speed, double-laser profilometry measurements and disentangle the dynamics into three aspects: the deformation of the substrate during the impact, the maximum spreading diameter of the droplet, and the penetration of the liquid into the substrate. By systematically varying the impact speed and the packing fraction of the substrate, (i) the substrate deformation indicates a critical packing fraction ϕ* ≈ 0.585; (ii) the maximum droplet spreading diameter is found to scale with a Weber number corrected by the substrate deformation; and (iii) a model of the liquid penetration is established and is used to explain the observed crater morphology transition.

From the granular Leidenfrost state to buoyancy-driven convection.

Grains inside a vertically vibrated box undergo a transition from a density-inverted and horizontally homogeneous state, referred to as the granular Leidenfrost state, to a buoyancy-driven convective state. We perform a simulational study of the precursors of such a transition and quantify their dynamics as the bed of grains is progressively fluidized. The transition is preceded by transient convective states, which increase their correlation time as the transition point is approached. Increasingly correlated convective flows lead to density fluctuations, as quantified by the structure factor, that also shows critical behavior near the transition point. The amplitude of the modulations in the vertical velocity field are seen to be best described by a quintic supercritical amplitude equation with an additive noise term. The validity of such an amplitude equation, and previously observed collective semiperiodic oscillations of the bed of grains, suggests a new interpretation of the transition analogous to a coupled chain of vertically vibrated damped oscillators. Increasing the size of the container shows metastability of convective states, as well as an overall invariant critical behavior close to the transition.

Collapsing granular beds: the role of interstitial air.

A prefluidized sand bed consisting of fine particles compactifies when it is subjected to a shock. We observe that the response depends on both the shock strength and the ambient pressure, where, counterintuitively, at high ambient pressure the compaction is larger, which we connect to a decrease of the static friction inside the bed. We find that the interstitial air is trapped inside the bed during and long after compaction. We deduce this from measuring the pressure changes above and below the bed: The top pressure decreases abruptly, on the time scale of the compaction, whereas that below the bed slowly rises to a maximum. Subsequently, both gently relax to ambient values. We formulate a one-dimensional diffusion model that uses only the change in bed height and the ambient pressure as an input, and we show that it leads to a fully quantitative understanding of the measured pressure variations.