Threshold current density for diffusion-controlled stability of electrolytic surface nanobubbles.

Understanding the stability mechanism of surface micro/nanobubbles adhered to gas-evolving electrodes is essential for improving the efficiency of water electrolysis, which is known to be hindered by the bubble coverage on electrodes. Using molecular simulations, the diffusion-controlled evolution of single electrolytic nanobubbles on wettability-patterned nanoelectrodes is investigated. These nanoelectrodes feature hydrophobic islands as preferential nucleation sites and allow the growth of nanobubbles in the pinning mode. In these simulations, a threshold current density distinguishing stable nanobubbles from unstable nanobubbles is found. When the current density remains below the threshold value, nucleated nanobubbles grow to their equilibrium states, maintaining their nanoscopic size. However, for the current density above the threshold value, nanobubbles undergo unlimited growth and can eventually detach due to buoyancy. Increasing the pinning length of nanobubbles increases the degree of nanobubble instability. By connecting the current density with the local gas oversaturation, an extension of the stability theory for surface nanobubbles [Lohse and Zhang, Phys. Rev. E 91, 031003(R) (2015)] accurately predicts the nanobubble behavior found in molecular simulations, including equilibrium contact angles and the threshold current density. For larger systems that are not accessible to molecular simulations, continuum numerical simulations with the finite difference method combined with the immersed boundary method are performed, again demonstrating good agreement between numerics and theories.

Performance Enhancement of Electrocatalytic Hydrogen Evolution through Coalescence-Induced Bubble Dynamics.

The evolution of electrogenerated gas bubbles during water electrolysis can significantly hamper the overall process efficiency. Promoting the departure of electrochemically generated bubbles during (water) electrolysis is therefore beneficial. For a single bubble, a departure from the electrode surface occurs when buoyancy wins over the downward-acting forces (e.g., contact, Marangoni, and electric forces). In this work, the dynamics of a pair of H2 bubbles produced during the hydrogen evolution reaction in 0.5 M H2SO4 using a dual platinum microelectrode system is systematically studied by varying the electrode distance and the cathodic potential. By combining high-speed imaging and electrochemical analysis, we demonstrate the importance of bubble-bubble interactions in the departure process. We show that bubble coalescence may lead to substantially earlier bubble departure as compared to buoyancy effects alone, resulting in considerably higher reaction rates at a constant potential. However, due to continued mass input and conservation of momentum, repeated coalescence events with bubbles close to the electrode may drive departed bubbles back to the surface beyond a critical current, which increases with the electrode spacing. The latter leads to the resumption of bubble growth near the electrode surface, followed by buoyancy-driven departure. While less favorable at small electrode spacing, this configuration proves to be very beneficial at larger separations, increasing the mean current up to 2.4 times compared to a single electrode under the conditions explored in this study.

Launching a Drop via Interplay of Buoyancy and Stick-Jump Dissolution.

According to Archimedes' principle, a submerged object with a density lower than that of aqueous acid solution is more buoyant than a smaller one. In this work, a remarkable phenomenon is reported wherein a dissolving drop on a substrate rises in the water only after it has diminished to a much smaller size, though the buoyancy is smaller. The drop consisting of a polymer solution reacts with the acid in the surrounding, yielding a water-soluble product. During drop dissolution, water-rich microdroplets form within the drop, merging with the external aqueous phase along the drop-substrate boundary. Two key elements determine the drop rise dynamics. The first is the stick-jump behavior during drop dissolution. The second is that buoyancy exerts a strong enough force on the drop at an Archimedean number greater than 1, while the stick-jump behavior is ongoing. The time of the drop rise is controlled by the initial size and the reaction rate of the drop. This novel mechanism for programmable drop rise may be beneficial for many future applications, such as microfluidics, microrobotics, and device engineering where the spontaneous drop detachment may be utilized to trigger a cascade of events in a dense medium.

Freezing-induced topological transition of double-emulsion.

Solidification of complex liquids is pertinent to numerous natural and industrial processes. Here, we examine the freezing of a W/O/W double-emulsion, i.e., water-in-oil compound droplets dispersed in water. We show that the solidification of such hierarchical emulsions can trigger a topological transition; for example, in our case, we observe the transition from the stable W/O/W state to a (frozen) O/W single-emulsion configuration. Strikingly, this transition is characterised by sudden expulsion of the inner water drop from the encapsulating oil droplet. We propose that this topological transition is triggered by the freezing of the encapsulating oil droplet from the outside in, putting tension on the inner water drop thus, destabilizing the W/O/W configuration. Using high-speed imaging we characterize the destabilization process. Interestingly, we find that below a critical size of the inner drop, Rin,crit ≈ 19 µm, the topological transition does not occur any more and the double-emulsion remains stable, in line with our interpretation.

On explosive boiling of a multicomponent Leidenfrost drop.

The gasification of multicomponent fuel drops is relevant in various energy-related technologies. An interesting phenomenon associated with this process is the self-induced explosion of the drop, producing a multitude of smaller secondary droplets, which promotes overall fuel atomization and, consequently, improves the combustion efficiency and reduces emissions of liquid-fueled engines. Here, we study a unique explosive gasification process of a tricomponent droplet consisting of water, ethanol, and oil ("ouzo"), by high-speed monitoring of the entire gasification event taking place in the well-controlled, levitated Leidenfrost state over a superheated plate. It is observed that the preferential evaporation of the most volatile component, ethanol, triggers nucleation of the oil microdroplets/nanodroplets in the remaining drop, which, consequently, becomes an opaque oil-in-water microemulsion. The tiny oil droplets subsequently coalesce into a large one, which, in turn, wraps around the remnant water. Because of the encapsulating oil layer, the droplet can no longer produce enough vapor for its levitation, and, thus, falls and contacts the superheated surface. The direct thermal contact leads to vapor bubble formation inside the drop and consequently drop explosion in the final stage.

Periodic bouncing of a plasmonic bubble in a binary liquid by competing solutal and thermal Marangoni forces.

The physicochemical hydrodynamics of bubbles and droplets out of equilibrium, in particular with phase transitions, display surprisingly rich and often counterintuitive phenomena. Here we experimentally and theoretically study the nucleation and early evolution of plasmonic bubbles in a binary liquid consisting of water and ethanol. Remarkably, the submillimeter plasmonic bubble is found to be periodically attracted to and repelled from the nanoparticle-decorated substrate, with frequencies of around a few kilohertz. We identify the competition between solutal and thermal Marangoni forces as the origin of the periodic bouncing. The former arises due to the selective vaporization of ethanol at the substrate's side of the bubble, leading to a solutal Marangoni flow toward the hot substrate, which pushes the bubble away. The latter arises due to the temperature gradient across the bubble, leading to a thermal Marangoni flow away from the substrate, which sucks the bubble toward it. We study the dependence of the frequency of the bouncing phenomenon from the control parameters of the system, namely the ethanol fraction and the laser power for the plasmonic heating. Our findings can be generalized to boiling and electrolytically or catalytically generated bubbles in multicomponent liquids.

Thin-Film-Mediated Deformation of Droplet during Cryopreservation.

Freezing of dispersions is omnipresent in science and technology. While the passing of a freezing front over a solid particle is reasonably understood, this is not so for soft particles. Here, using an oil-in-water emulsion as a model system, we show that when engulfed into a growing ice front, a soft particle severely deforms. This deformation strongly depends on the engulfment velocity V, even forming pointy-tip shapes for low values of V. We find such singular deformations are mediated by interfacial flows in nanometric thin liquid films separating the nonsolidifying dispersed droplets and the solidifying bulk. We model the fluid flow in these intervening thin films using a lubrication approximation and then relate it to the deformation sustained by the dispersed droplet.

Bistability in Radiatively Heated Melt Ponds.

Melting and solidification processes, intertwined with convective flows, play a fundamental role in geophysical contexts. One of these processes is the formation of melt ponds on glaciers, ice shelves, and sea ice. It is driven by solar radiation and is of great significance for Earth's heat balance, as it significantly lowers the albedo. Through direct numerical simulations and theoretical analysis, we unveil a bistability phenomenon in the melt pond dynamics. As solar radiation intensity and the melt pond's initial depth vary, an abrupt transition occurs: this tipping point transforms the system from a stable fully frozen state to another stable equilibrium state, characterized by a distinct melt pond depth. The physics of this transition can be understood within a heat flux balance model, which exhibits excellent agreement with our numerical results. Together with the Grossmann-Lohse theory for internally heated convection, the model correctly predicts the bulk temperature and the flow strength within the melt ponds, offering insight into the coupling of phase transitions with adjacent turbulent flows and the interplay between convective melting and radiation-driven processes.

Sodium chloride inhibits effective bubbly drag reduction in turbulent bubbly Taylor-Couette flows.

Using the Taylor-Couette geometry we experimentally investigate the effect of salt on drag reduction caused by bubbles present in the flow. We combine torque measurements with optical high-speed imaging to relate the bubble size to the drag experienced by the flow. Previous studies have shown that a small percentage of air (4%) can lead to dramatic drag reduction (40%). In contrast to previous laboratory experiments, which mainly used fresh water, we will vary the salinity from that of fresh water to the average salinity of ocean water. We find that the drag reduction is increasingly more inhibited for increasing salt concentrations, going from 40% for fresh water to just 15% for sea water. Salts present in the working fluid inhibit coalescence events, resulting in smaller bubbles in the flow and, with that, a decrease in the drag reduction. Above a critical salinity, increasing the salinity has no further effect on the size of bubbles in the flow and thus the drag experienced by the flow. Our new findings demonstrate the importance of sodium chloride on the bubbly drag reduction mechanism, and will further challenge naval architects to implement promising air lubrication systems on marine vessels. This article is part of the theme issue 'Taylor-Couette and related flows on the centennial of Taylor's seminal Philosophical Transactions paper (part 1)'.

Multiple states and transport properties of double-diffusive convection turbulence.

When fluid stratification is induced by the vertical gradients of two scalars with different diffusivities, double-diffusive convection (DDC) may occur and play a crucial role in mixing. Such a process exists in many natural and engineering environments. Especially in the ocean, DDC is omnipresent since the seawater density is affected by temperature and salinity. The most intriguing phenomenon caused by DDC is the thermohaline staircase, i.e., a stack of alternating well-mixed convection layers and sharp interfaces with very large gradients in both temperature and salinity. Here we investigate DDC and thermohaline staircases in the salt finger regime, which happens when warm saltier water lies above cold fresher water and is commonly observed in the (sub)tropic regions. By conducting direct numerical simulations over a large range of parameters, we reveal that multiple equilibrium states exist in fingering DDC and staircases even for the same control parameters. Different states can be established from different initial scalar distributions or different evolution histories of the flow parameters. Hysteresis appears during the transition from a staircase to a single salt finger interface. For the same local density ratio, salt finger interfaces in the single-layer state generate very different fluxes compared to those within staircases. However, the salinity flux for all salt finger interfaces follows the same dependence on the salinity Rayleigh number of the layer and can be described by an effective power law scaling. Our findings have direct applications to oceanic thermohaline staircases.

Evaporating droplets on oil-wetted surfaces: Suppression of the coffee-stain effect.

The evaporation of suspension droplets is the underlying mechanism in many surface-coating and surface-patterning applications. However, the uniformity of the final deposit suffers from the coffee-stain effect caused by contact line pinning. Here, we show that control over particle deposition can be achieved through droplet evaporation on oil-wetted hydrophilic surfaces. We demonstrate by flow visualization, theory, and numerics that the final deposit of the particles is governed by the coupling of the flow field in the evaporating droplet, the movement of its contact line, and the wetting state of the thin film surrounding the droplet. We show that the dynamics of the contact line can be tuned through the addition of a surfactant, thereby controlling the surface energies, which then leads to control over the final particle deposit. We also obtain an analytical expression for the radial velocity profile which reflects the hindering of the evaporation at the rim of the droplet by the nonvolatile oil meniscus, preventing flow toward the contact line, thus suppressing the coffee-stain effect. Finally, we confirm our physical interpretation by numerical simulations that are in qualitative agreement with the experiment.

Fast-freezing kinetics inside a droplet impacting on a cold surface.

Freezing or solidification of impacting droplets is omnipresent in nature and technology, be it a rain droplet falling on a supercooled surface; in inkjet printing, where often molten wax is used; in additive manufacturing or metal-production processes; or in extreme ultraviolet lithography (EUV) for the chip production, where molten tin is used to generate the EUV radiation. For many of these industrial applications, a detailed understanding of the solidification process is essential. Here, by adopting an optical technique in the context of freezing-namely, total-internal reflection (TIR)-we elucidate the freezing kinetics during the solidification of a droplet while it impacts on an undercooled surface. We show that at sufficiently high undercooling, a peculiar freezing morphology exists that involves sequential advection of frozen fronts from the center of the droplet to its boundaries. This phenomenon is examined by combining elements of classical nucleation theory to the large-scale hydrodynamics on the droplet scale, bringing together two subfields which traditionally have been quite separated. Furthermore, we report a self-peeling phenomenon of a frozen splat that is driven by the existence of a transient crystalline state during solidification.

Impact Forces of Water Drops Falling on Superhydrophobic Surfaces.

A falling liquid drop, after impact on a rigid substrate, deforms and spreads, owing to the normal reaction force. Subsequently, if the substrate is nonwetting, the drop retracts and then jumps off. As we show here, not only is the impact itself associated with a distinct peak in the temporal evolution of the normal force, but also the jump-off, which was hitherto unknown. We characterize both peaks and elucidate how they relate to the different stages of the drop impact process. The time at which the second peak appears coincides with the formation of a Worthington jet, emerging through flow focusing. Even low-velocity impacts can lead to a surprisingly high second peak in the normal force, even larger than the first one, namely when the Worthington jet becomes singular due to the collapse of an air cavity in the drop.

Aspect Ratio Dependence of Heat Transfer in a Cylindrical Rayleigh-Bénard Cell.

While the heat transfer and the flow dynamics in a cylindrical Rayleigh-Bénard (RB) cell are rather independent of the aspect ratio Γ (diameter/height) for large Γ, a small-Γ cell considerably stabilizes the flow and thus affects the heat transfer. Here, we first theoretically and numerically show that the critical Rayleigh number for the onset of convection at given Γ follows Ra_{c,Γ}∼Ra_{c,∞}(1+CΓ^{-2})^{2}, with C≲1.49 for Oberbeck-Boussinesq (OB) conditions. We then show that, in a broad aspect ratio range (1/32)≤Γ≤32, the rescaling Ra→Ra_{ℓ}≡Ra[Γ^{2}/(C+Γ^{2})]^{3/2} collapses various OB numerical and almost-OB experimental heat transport data Nu(Ra,Γ). Our findings predict the Γ dependence of the onset of the ultimate regime Ra_{u,Γ}∼[Γ^{2}/(C+Γ^{2})]^{-3/2} in the OB case. This prediction is consistent with almost-OB experimental results (which only exist for Γ=1, 1/2, and 1/3) for the transition in OB RB convection and explains why, in small-Γ cells, much larger Ra (namely, by a factor Γ^{-3}) must be achieved to observe the ultimate regime.

Surface Nanodroplet-Based Extraction Combined with Offline Analytic Techniques for Chemical Detection and Quantification.

Liquid-liquid extraction based on surface nanodroplets can be a green and sustainable technique to extract and concentrate analytes from a sample flow. However, because of the extremely small volume of each droplet (<10 fL, tens of micrometers in base radius and a few or less than 1 µm in height), only a few in situ analytical techniques, such as surface-enhanced Raman spectroscopy, were applicable for the online detection and analysis based on nanodroplet extraction. To demonstrate the versatility of surface nanodroplet-based extraction, in this work, the formation of octanol surface nanodroplets and extraction were performed inside a 3 m Teflon capillary tube. After extraction, surface nanodroplets were collected by injecting air into the tube, by which the contact line of surface droplets was collected by the capillary force. As the capillary allows for the formation of ∼1012 surface nanodroplets on the capillary wall, ≥2 mL of octanol can be collected after extraction. The volume of the collected octanol was enough for the analysis of offline analytical techniques such as UV-vis, GC-MS, and others. Coupled with UV-vis, reliable extraction and detection of two common water pollutants, triclosan and chlorpyrifos, was shown by a linear relationship between the analyte concentration in the sample solution and UV-vis absorbance. Moreover, the limit of detection (LOD) as low as 2 × 10-9 M for triclosan (∼0.58 µg/L) and 3 × 10-9 M for chlorpyrifos (∼1.05 µg/L) could be achieved. The collected surface droplets were also analyzed via gas chromatography (GC) and fluorescence microscopy. Our work shows that surface nanodroplet extraction may potentially streamline the process in sample pretreatment for sensitive chemical detection and quantification by using common analytic tools.

Evaporation of a Sessile Colloidal Water-Glycerol Droplet: Marangoni Ring Formation.

The transport and aggregation of particles in suspensions is an important process in many physicochemical and industrial processes. In this work, we study the transport of particles in an evaporating binary droplet. Surprisingly, the accumulation of particles occurs not only at the contact line (due to the coffee-stain effect) or at the solid substrate (due to sedimentation) but also at a particular radial position near the liquid-air interface, forming a "ring", which we term as the Marangoni ring. The formation of this ring is primarily attributed to the solutal Marangoni flow triggered by the evaporation dynamics of the water-glycerol droplet. Experiments and simulations show fair agreement in the volume evolution and the general structure of the solutal Marangoni flow, that is, the Marangoni vortex. Experiments show that the location of the Marangoni ring is strongly correlated with the Marangoni vortex. However, finite element numerical simulations fail to describe the particle distribution seen in the experiments. Interestingly, the particles not only accumulate to form the Marangoni ring but also assemble as colloidal crystals close to the liquid-air interface, yielding iridescence. The formation of the colloidal crystals in the experiments is strong evidence that non-hydrodynamic interactions, which are not represented in the simulations, also play a significant role in our system.

Transition in the growth mode of plasmonic bubbles in binary liquids.

Multi-component fluids with phase transitions show a plethora of fascinating phenomena with rich physics. Here we report on a transition in the growth mode of plasmonic bubbles in binary liquids. By employing high-speed imaging we reveal that the transition is from slow evaporative to fast convective growth and accompanied by a sudden increase in radius. The transition occurs as the three-phase contact line reaches the spinodal temperature of the more volatile component leading to massive, selective evaporation. This creates a strong solutal Marangoni flow along the bubble which marks the beginning of convective growth. We support this interpretation by simulations. After the transition the bubble starts to oscillate in position and in shape. Though different in magnitude the frequencies of both oscillations follow the same power law , which is characteristic of bubble shape oscillations, with the surface tension σ as the restoring force and the bubble's added mass as inertia. The transitions and the oscillations both induce a strong motion in the surrounding liquid, opening doors for various applications where local mixing is beneficial.

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.

Resonance behavior of a compliant piezo-driven inkjet channel with an entrained microbubble.

Microbubbles entrained in a piezo-driven drop-on-demand printhead disturb the acoustics of the microfluidic ink channel and, thereby, the jetting behavior. Here, the resonance behavior of an ink channel as a function of the microbubble size and number of bubbles is studied through theoretical modeling and experiments. The system is modeled as a set of two coupled harmonic oscillators: one corresponds to the compliant ink channel and the other corresponds to the microbubble. The predicted and measured eigenfrequencies are in excellent agreement. It was found that the resonance frequency is independent of the bubble size as long as the compliance of the bubble dominates over that of the piezo actuator. An accurate description of the eigenfrequency of the coupled system requires the inclusion of the increased inertance of the entrained microbubble due to confinement. It is shown that the inertance of a confined bubble can be accurately obtained by using a simple potential flow approach. The model is further validated by the excellent agreement between the modeled and measured microbubble resonance curves. The present work, therefore, provides physical insight into the coupled dynamics of a compliant ink channel with an entrained microbubble.

Leidenfrost Effect as a Directed Percolation Phase Transition.

Volatile drops deposited on a hot solid can levitate on a cushion of their own vapor, without contacting the surface. We propose to understand the onset of this so-called Leidenfrost effect through an analogy to nonequilibrium systems exhibiting a directed percolation phase transition. When performing impacts on superheated solids, we observe a regime of spatiotemporal intermittency in which localized wet patches coexist with dry regions on the substrate. We report a critical surface temperature, which marks the upper bound of a large range of temperatures in which levitation and contact coexist. In this range, with decreasing temperature, the equilibrium wet fraction increases continuously from zero to one. Also, the statistical properties of the spatiotemporally intermittent regime are in agreement with that of the directed percolation universality class. This analogy allows us to redefine the Leidenfrost temperature and shed light on the physical mechanisms governing the transition to the Leidenfrost state.