Flexible solar cells based on foldable silicon wafers with blunted edges.

Flexible solar cells have a lot of market potential for application in photovoltaics integrated into buildings and wearable electronics because they are lightweight, shockproof and self-powered. Silicon solar cells have been successfully used in large power plants. However, despite the efforts made for more than 50 years, there has been no notable progress in the development of flexible silicon solar cells because of their rigidity1-4. Here we provide a strategy for fabricating large-scale, foldable silicon wafers and manufacturing flexible solar cells. A textured crystalline silicon wafer always starts to crack at the sharp channels between surface pyramids in the marginal region of the wafer. This fact enabled us to improve the flexibility of silicon wafers by blunting the pyramidal structure in the marginal regions. This edge-blunting technique enables commercial production of large-scale (>240 cm2), high-efficiency (>24%) silicon solar cells that can be rolled similarly to a sheet of paper. The cells retain 100% of their power conversion efficiency after 1,000 side-to-side bending cycles. After being assembled into large (>10,000 cm2) flexible modules, these cells retain 99.62% of their power after thermal cycling between -70 °C and 85 °C for 120 h. Furthermore, they retain 96.03% of their power after 20 min of exposure to air flow when attached to a soft gasbag, which models wind blowing during a violent storm.

Why Bubbles Coalesce Faster than Droplets: The Effects of Interface Mobility and Surface Charge.

Air bubbles in pure water appear to coalesce much faster compared to oil emulsion droplets at the same water solution conditions. The main factors explaining this difference in coalescence times could be interface mobility and/or pH-dependent surface charge at the water interface. To quantify the relative importance of these effects, we use high-speed imaging to monitor the coalescence of free-rising air bubbles with the water-air interface as well as free-falling fluorocarbon-oil emulsion droplets with a water-oil interface. We measure the coalescence times of such bubbles and droplets over a range of different water pH values (3.0, 5.6, 11.0). In the case of bubbles, a very fast coalescence (milliseconds) is observed for the entire pH range in pure water, consistent with the hydrodynamics of fully mobile interfaces. However, when the water-air interface is immobilized by the deposition of a monolayer of arachidic acid, the coalescence is significantly delayed. Furthermore, the coalescence times increase with increasing pH. In the case of fluorocarbon-oil droplets, the coalescence is always much slower (seconds) and consistent with immobile interface coalescence. The fluorocarbon droplet's coalescence time is also pH-dependent, with a complete stabilization (no coalescence) observed at pH 11. In the high electrolyte concentration, a 0.6 M NaCl water solution, bubbles, and droplets have similar coalescence times, which could be related to the bubble interface immobilization at the late stage of the coalescence process. Numerical simulations are used to evaluate the time scale of mobile and immobile interface film drainage.

Interferometry and Simulation of the Thin Liquid Film between a Free-Rising Bubble and a Glass Substrate.

Because of their practical importance and complex underlying physics, the thin liquid films formed between colliding bubbles or droplets have long been the subject of experimental investigations and theoretical modeling. Here, we examine the possibility of accurately predicting the dynamics of the thin liquid film drainage using numerical simulations when compared to an experimental investigation of millimetric bubbles free-rising in pure water and colliding with a flat glass interface. A high-speed camera is used to track the bubble bounce trajectory, and a second high-speed camera together with a pulsed laser is used for interferometric determination of the shape and evolution of the thin liquid film profile during the bounce. The numerical simulations are conducted with the open source Gerris flow solver. The simulation reliability was first confirmed by comparison with the experimental bubble bounce trajectory and bubble shape evolution during the bounce. We further demonstrate that the simulation predicted time evolution for the shape of the thin liquid film profiles is in excellent agreement with the high-speed interferometry measured profiles for the entire experimentally accessible film size range. Finally, we discuss the implications of using numerical simulation together with theoretical modeling for resolving the complex processes of high velocity bubble and droplet collisions.

Direct imaging of polymer filaments pulled from rebounding drops.

Polymer filaments form the foundation of biology from cell scaffolding to DNA. Their study and fabrication play an important role in a wide range of processes from tissue engineering to molecular machines. We present a simple method to deposit stretched polymer fibers between micro-pillars. This occurs when a polymeric drop impacts on and rebounds from an inclined superhydrophobic substrate. It wets the top of the pillars and pulls out liquid filaments which are stretched and can attach to adjacent pillars leaving minuscule threads, with the solvent evaporating to leave the exposed polymers. We use high-speed video at the microscale to characterize the most robust filament-forming configurations, by varying the impact velocity, substrate structure and inclination angle, as well as the PEO-polymer concentration. Impacts onto plant leaves or a randomized nano-structured surface leads to the formation of a branched structure, through filament mergers at the free surface of the drop. SEM shows the deposition of filament bundles which are thinner than those formed by evaporation or rolling drops. Raman spectroscopy identifies the native mode B stretched DNA filaments from aqueous-solution droplets.

To Split or Not to Split: Dynamics of an Air Disk Formed under a Drop Impacting on a Pool.

When a drop falls and impacts on a liquid pool, it entraps an air disk below the drop, which then contracts into a central bubble. Here, we use high-speed imaging and high-resolution numerical simulations to characterize the air-disk contraction dynamics for different liquid properties. We show that the air disk can contract into a single central bubble, form a toroidal bubble, or split vertically into two smaller bubbles. We demonstrate that the transitions between the different regimes can be separated by an Ohnesorge number, Oh_{e}, based on the air-disk thickness. For the lowest Oh_{e}, we find a new regime, where vortex shedding from the rim of the contracting air disk breaks the vertical symmetry and prevents the bubble from splitting in two.

Free-Rising Bubbles Bounce More Strongly from Mobile than from Immobile Water-Air Interfaces.

Recently it was reported that the interface mobility of bubbles and emulsion droplets can have a dramatic effect not only on the characteristic coalescence times but also on the way that bubbles and droplets bounce back after collision (Vakarelski, I. U.; Yang, F.; Tian, Y. S.; Li, E. Q.; Chan D. Y. C.; Thoroddsen, S. T. Sci. Adv. 2019, 5, eaaw4292). Experiments with free-rising bubbles in a pure perfluorocarbon liquid showed that collisions involving mobile interfaces result in a stronger series of rebounds before the eventual rapid coalescence. Here we examine this effect for the case of pure water. We compare the bounce of millimeter-sized free-rising bubbles from a pure water-air interface with the bounce from a water-air interface on which a Langmuir monolayer of arachidic acid molecules has been deposited. The Langmuir monolayer surface concentration is kept low enough not to affect the water surface tension but high enough to fully immobilize the interface due to Marangoni stress effects. Bubbles were found to bounce much stronger (up to a factor of 1.8 increase in the rebounding distance) from the clean water interface compared to the water interface with the Langmuir monolayer. These experiments confirm that mobile surfaces enhance bouncing and at the same time demonstrate that the pure water-air interfaces behave as mobile fluid interfaces in our system. A complementary finding in our study is that the ethanol-air interface behaves as a robust mobile liquid interface. The experimental findings are supported by numerical simulations of the bubble bouncing from both mobile and immobile fluid interfaces.

Droplet impacts onto soft solids entrap more air.

We investigate the effects of surface stiffness on the air cushioning at the bottom of a liquid drop impacting onto a soft solid and the resulting entrapment of a central bubble. This was achieved using ultra-high-speed interferometry at 5 million frames per second and spatial resolution of 1.05 µm per pixel. The soft solid delays the effects of gas compressibility resulting in much larger air discs than corresponding impacts onto rigid surfaces. Using an effective impact velocity equal to half of the actual impact velocity brings the soft solid scaling behavior better in line with rigid substrate scaling. We also observe extended gliding of the drop as it initially avoids contact with the surface spreading over a thin layer of air and investigate the threshold velocity for the transition from gliding to ring contact. Such extended gliding layers have previously been seen for high-viscosity drop impacts, but not for low-viscosity liquids at the impact velocities used herein.

Stable-streamlined cavities following the impact of non-superhydrophobic spheres on water.

The formation of a stable-streamlined gas cavity following the impact of a heated Leidenfrost sphere on a liquid surface or a superhydrophobic sphere on water is a recently demonstrated phenomenon. A sphere encapsulated in a teardrop-shaped gas cavity was found to have near-zero hydrodynamic drag due to the self-adjusting streamlined shape and the free-slip boundary condition on the cavity interface. Here we show that such cavities can as well be formed following water impact from a sufficient height of non-superhydrophobic spheres with water contact angles between >30° and 120°. In this case the streamlined cavity is attached just above the sphere's equator, instead of entirely wrapping the sphere. Nevertheless, this sphere with attached cavity formation has near-zero drag and a predetermined free fall velocity in compliance with the Bernoulli law of potential flow. The effect of surfactant addition to the water solution is investigated. The shape and fall velocity of a sphere with streamlined cavity formation were unaffected by the addition of low surface modulus synthetic surfactants, but were destabilised when solutions containing high surface modulus surfactants, such as soaps, were used.

Coalescence Dynamics of Mobile and Immobile Fluid Interfaces.

Coalescence dynamics between deformable bubbles and droplets can be dramatically affected by the mobility of the interfaces with fully tangentially mobile bubble-liquid or droplet-liquid interfaces expected to accelerate the coalescence by orders of magnitude. However, there is a lack of systematic experimental investigations that quantify this effect. By using high speed camera imaging we examine the free rise and coalescence of small air-bubbles (100 to 1300 µm in diameter) with a liquid interface. A perfluorocarbon liquid, PP11, is used as a model liquid to investigate coalescence dynamics between fully mobile and immobile deformable interfaces. The mobility of the bubble surface was determined by measuring the terminal rise velocity of small bubbles rising at Reynolds numbers, Re, less than 0.1 and the mobility of free PP11 surface by measuring the deceleration kinetics of the small bubble toward the interface. Induction or film drainage times of a bubble at the mobile PP11-air surface were found to be more than 2 orders of magnitude shorter compared to the case of bubble and an immobile PP11-water interface. A theoretical model is used to illustrate the effect of hydrodynamics and interfacial mobility on the induction time or film drainage time. The results of this study are expected to stimulate the development of a comprehensive theoretical model for coalescence dynamics between two fully or partially mobile fluid interfaces.

Drag crisis moderation by thin air layers sustained on superhydrophobic spheres falling in water.

We investigate the effect of thin air layers naturally sustained on superhydrophobic surfaces on the terminal velocity and drag force of metallic spheres free falling in water. The surface of 20 mm to 60 mm steel or tungsten-carbide spheres is rendered superhydrophobic by a simple coating process that uses a commercially available hydrophobic agent. By comparing the free fall of unmodified spheres and superhydrophobic spheres in a 2.5 meter tall water tank, it is demonstrated that even a very thin air layer (∼1-2 µm) that covers the freshly dipped superhydrophobic sphere can reduce the drag force on the spheres by up to 80%, at Reynolds numbers from 105 to 3 × 105, owing to an early drag crisis transition. This study complements prior investigations on the drag reduction efficiency of model gas layers sustained on heated metal spheres falling in liquid by the Leidenfrost effect. The drag reduction effects are expected to have significant implications for the development of sustainable air-layer-based energy saving technologies.

The air entrapment under a drop impacting on a nano-rough surface.

We study the impact of drops onto a flat surface with a nano-particle-based superhydrophobic coating, focusing on the earliest contact using 200 ns time-resolution. A central air-disc is entrapped when the drop impacts the surface, and when the roughness is appropriately accounted for, the height and radial extent of the air-disc follow the scaling laws established for impacts onto smooth surfaces. The roughness also modifies the first contact of the drop around the central air-disc, producing a thick band of micro-bubbles. The initial bubbles within this band coalesce and grow in size. We also infer the presence of an air-film residing inside the microstructure, at radial distances outside the central air-disc. This is manifest by the sudden appearance of microbubbles within a few microseconds after impact. The central air-disc remains pinned on the roughness, unless it is chemically altered to make it superhydrophilic.

Stabilization of Leidenfrost vapour layer by textured superhydrophobic surfaces.

In 1756, Leidenfrost observed that water drops skittered on a sufficiently hot skillet, owing to levitation by an evaporative vapour film. Such films are stable only when the hot surface is above a critical temperature, and are a central phenomenon in boiling. In this so-called Leidenfrost regime, the low thermal conductivity of the vapour layer inhibits heat transfer between the hot surface and the liquid. When the temperature of the cooling surface drops below the critical temperature, the vapour film collapses and the system enters a nucleate-boiling regime, which can result in vapour explosions that are particularly detrimental in certain contexts, such as in nuclear power plants. The presence of these vapour films can also reduce liquid-solid drag. Here we show how vapour film collapse can be completely suppressed at textured superhydrophobic surfaces. At a smooth hydrophobic surface, the vapour film still collapses on cooling, albeit at a reduced critical temperature, and the system switches explosively to nucleate boiling. In contrast, at textured, superhydrophobic surfaces, the vapour layer gradually relaxes until the surface is completely cooled, without exhibiting a nucleate-boiling phase. This result demonstrates that topological texture on superhydrophobic materials is critical in stabilizing the vapour layer and thus in controlling--by heat transfer--the liquid-gas phase transition at hot surfaces. This concept can potentially be applied to control other phase transitions, such as ice or frost formation, and to the design of low-drag surfaces at which the vapour phase is stabilized in the grooves of textures without heating.

Double Contact During Drop Impact on a Solid Under Reduced Air Pressure.

Drops impacting on solid surfaces entrap small bubbles under their centers, owing to the lubrication pressure which builds up in the thin intervening air layer. We use ultrahigh-speed interference imaging, at 5 Mfps, to investigate how this air layer changes when the ambient air pressure is reduced below atmospheric. Both the radius and the thickness of the air disc become smaller with reduced air pressure. Furthermore, we find the radial extent of the air disc bifurcates, when the compressibility parameter exceeds ∼25. This bifurcation is also imprinted onto some of the impacts, as a double contact. In addition to the central air disc inside the first ring contact, this is immediately followed by a second ring contact, which entraps an outer toroidal strip of air, which contracts into a ring of bubbles. We find this occurs in a regime where Navier slip, due to rarefied gas effects, enhances the rate gas can escape from the path of the droplet.

Evaporative Lithography in Open Microfluidic Channel Networks.

We demonstrate a direct capillary-driven method based on wetting and evaporation of various suspensions to fabricate regular two-dimensional wires in an open microfluidic channel through continuous deposition of micro- or nanoparticles under evaporative lithography, akin to the coffee-ring effect. The suspension is gently placed in a loading reservoir connected to the main open microchannel groove on a PDMS substrate. Hydrophilic conditions ensure rapid spreading of the suspension from the loading reservoir to fill the entire channel length. Evaporation during the spreading and after the channel is full increases the particle concentration toward the end of the channel. This evaporation-induced convective transport brings particles from the loading reservoir toward the channel end where this flow deposits a continuous multilayered particle structure. The particle deposition front propagates backward over the entire channel length. The final dry deposit of the particles is thereby much thicker than the initial volume fraction of the suspension. The deposition depth is characterized using a 3D imaging profiler, whereas the deposition topography is revealed using a scanning electron microscope. The patterning technology described here is robust and passive and hence operates without an external field. This work may well become a launching pad to construct low-cost and large-scale thin optoelectronic films with variable thicknesses and interspacing distances.

Leidenfrost Vapor Layers Reduce Drag without the Crisis in High Viscosity Liquids.

The drag coefficient C_{D} of a solid smooth sphere moving in a fluid is known to be only a function of the Reynolds number Re and diminishes rapidly at the drag crisis around Re∼3×10^{5}. A Leidenfrost vapor layer on a hot sphere surface can trigger the onset of the drag crisis at a lower Re. By using a range of high viscosity perfluorocarbon liquids, we show that the drag reduction effect can occur over a wide range of Re, from as low as ∼600 to 10^{5}. The Navier slip model with a viscosity dependent slip length can fit the observed drag reduction and wake shape.

Drag Moderation by the Melting of an Ice Surface in Contact with Water.

We report measurements of the effects of a melting ice surface on the hydrodynamic drag of ice-shell-metal-core spheres free falling in water at a Reynolds of number Re~2×10^{4}-3×10^{5} and demonstrate that the melting surface induces the early onset of the drag crisis, thus reducing the hydrodynamic drag by more than 50%. Direct visualization of the flow pattern demonstrates the key role of surface melting. Our observations support the hypothesis that the drag reduction is due to the disturbance of the viscous boundary layer by the mass transfer from the melting ice surface.

Stabilization of thin liquid films by repulsive van der Waals force.

Using high-speed video recording of bubble rise experiments, we study the stability of thin liquid films trapped between a rising bubble and a surfactant-free liquid-liquid meniscus interface. Using different combinations of nonpolar oils and water that are all immiscible, we investigate the extent to which film stability can be predicted by attractive and repulsive van der Waals (vdW) interactions that are indicated by the relative magnitude of the refractive indices of the liquid combinations, for example, water (refractive index, n = 1.33), perfluorohexane (n = 1.23), and tetradecane (n = 1.43). We show that, when the film-forming phase was oil (perfluorohexane or tetradecane), the stability of the film could always be predicted from the sign of the vdW interaction, with a repulsive vdW force resulting in a stable film and an attractive vdW force resulting in film rupture. However, if aqueous electrolyte is the film-forming bulk phase between the rising air bubble and the upper oil phase, the film always ruptured, even when a repulsive vdW interaction was predicted. We interpret these results as supporting the hypothesis that a short-ranged hydrophobic attraction determines the stability of the thin water film formed between an air phase and a nonpolar oil phase.

Leidenfrost vapour layer moderation of the drag crisis and trajectories of superhydrophobic and hydrophilic spheres falling in water.

We investigate the dynamic effects of a Leidenfrost vapour layer sustained on the surface of heated steel spheres during free fall in water. We find that a stable vapour layer sustained on the textured superhydrophobic surface of spheres falling through 95 °C water can reduce the hydrodynamic drag by up to 75% and stabilize the sphere trajectory for the Reynolds number between 10(4) and 10(6), spanning the drag crisis in the absence of the vapour layer. For hydrophilic spheres under the same conditions, the transition to drag reduction and trajectory stability occurs abruptly at a temperature different from the static Leidenfrost point. The observed drag reduction effects are attributed to the disruption of the viscous boundary layer by the vapour layer whose thickness depends on the water temperature. Both the drag reduction and the trajectory stabilization effects are expected to have significant implications for development of sustainable vapour layer based technologies.

Foam-film-stabilized liquid bridge networks in evaporative lithography and wet granular matter.

Evaporative lithography using latex particle templates is a novel approach for the self-assembly of suspension-dispersed nanoparticles into ordered microwire networks. The phenomenon that drives the self-assembly process is the propagation of a network of interconnected liquid bridges between the template particles and the underlying substrate. With the aid of video microscopy, we demonstrate that these liquid bridges are in fact the border zone between the underlying substrate and foam films vertical to the substrate, which are formed during the evaporation of the liquid from the suspension. The stability of the foam films and thus the liquid bridge network stability are due to the presence of a small amount of surfactant in the evaporating solution. We show that the same type of foam-film-stabilized liquid bridge network can also propagate in 3D clusters of spherical particles, which has important implications for the understanding of wet granular matter.

Dynamic air layer on textured superhydrophobic surfaces.

We provide an experimental demonstration that a novel macroscopic, dynamic continuous air layer or plastron can be sustained indefinitely on textured superhydrophobic surfaces in air-supersaturated water by a natural gas influx mechanism. This type of plastron is an intermediate state between Leidenfrost vapor layers on superheated surfaces and the equilibrium Cassie-Baxter wetting state on textured superhydrophobic surfaces. We show that such a plastron can be sustained on the surface of a centimeter-sized superhydrophobic sphere immersed in heated water and variations of its dynamic behavior with air saturation of the water can be regulated by rapid changes of the water temperature. The simple experimental setup allows for quantification of the air flux into the plastron and identification of the air transport model of the plastron growth. Both the observed growth dynamics of such plastrons and millimeter-sized air bubbles seeded on the hydrophilic surface under identical air-supersaturated solution conditions are consistent with the predictions of a well-mixed gas transport model.