Quantifying Contributions of Different Repulsion to Film Drainage Time during the Bubble-Solid Surface Attachment and Implications for the Flotation of Fine Particles.

The flotation recovery of fine particles faces serious challenges due to the lack of kinetic energy required for supporting their radial displacement and attachment with bubbles. Generally, the hydrodynamic resistance and repulsive disjoining pressure successively inhibit the liquid outflow intervening between the bubble and solid surfaces. To quantitatively characterize the influence of the main repulsion on film thinning time, experiments have been designed in three different aqueous systems. Bubble surface mobility closely associated with hydrodynamic resistance was determined by the rising bubble technique, and the DLVO theory was employed to confirm the evolution of electrostatic repulsion. The film drainage process was then measured based on the high-speed microscopic interferometry. Furthermore, the influence of the main repulsion on bubble-solid surface interactions was examined by flotation recovery. Results show that the earlier buildup of hydrodynamic force ran through the whole film thinning process, and under immobile conditions, the central region gradually became dominant in film thinning due to the very limited fluid flow at the thinnest rim position. Therefore, to achieve the identical film thickness (∼100 nm), the large hydrodynamic resistance could prolong the film thinning time by about 1 order of magnitude, compared with that induced by electrostatic repulsion, which accounts for the increased flotation recovery by 10% using mobile bubbles. This study not only enhances the understanding of how typical repulsive forces work in film drainage dynamics but also opens up an avenue for enhancing flotation and avoiding wasting resources by modulating bubble surface mobility and thus micro/nanoscale fluid flow.

Nanoscale Transport during Liquid Film Thinning Inhibits Bubble Coalescing Behavior in Electrolyte Solutions.

The long-standing puzzle of why two colliding bubbles in an electrolyte solution do not coalesce immediately upon contact is resolved. The water film between the bubbles needs to be drained out first before its rupture, i.e., coalescence. Experiments reveal clearly that the film thinning exhibits a rather sudden slowdown (around 30-50 nm), which is orders of magnitude smaller than similar experiments involving surfactants. A critical step in explaining this phenomenon is to realize that the solute concentration is different in bulk and at the surface. During thinning, this will generate an electrolyte concentration difference in film solution along the interacting region, which in turn causes a Marangoni stress to resist film thinning. We develop a film drainage model that explains the experimentally observed phenomena well. The underlying physical mechanism, that confused the scientific community for decades, is now finally revealed.

Water Film Drainage between a Very Viscous Oil Drop and a Mica Surface.

We investigate thin film drainage between a viscous oil drop and a mica surface, clearly illustrating the competing effects of Laplace pressure and viscous normal stress (τ_{v}) in the drop. τ_{v} dominates the initial stage of drainage, leading to dimple formation (h_{d}) at a smaller critical thickness with an increase in the drop viscosity (the dimple is the inversion of curvature of the drop in the film region). Surface forces and interfacial tension control the last stage of film drainage. A scaling analysis shows that h_{d} is a function of the drop size R and the capillary numbers of the film (Ca_{f}) and drop (Ca_{d}), which we estimate by h_{d}=0.5Rsqrt[Ca_{f}/(1+2Ca_{d})]. This equation clearly indicates that the drop viscosity needs to be considered when Ca_{d}>0.1. These results have implications for industrial systems where very viscous liquids are involved, for example, in 3D printing and heavy oil extraction process.

Inward Flow of Intervening Liquid Films Driven by the Marangoni Effect during Bubble-Solid Collisions in Ethyl Alcohol-NaCl Aqueous Solutions.

The drainage dynamics of confined thin liquid films between an air bubble and a freshly cleaved mica surface were investigated in ethyl alcohol aqueous solutions. Focus was given to the holding stage, in which an unexpected increase in the thickness of a few hundred nanometers at the center of the film was captured by interferometry in ethyl alcohol-500 mM NaCl aqueous solutions. Such an increase in film thickness occurred when the ethyl alcohol concentration exceeded the critical value at a bubble approach velocity of 100 µm/s. For a given ethyl alcohol concentration, the increase in thickness at the center of the film did not happen when the bubble approach velocity was decreased to 10 µm/s. Compared to the cases in ethyl alcohol-500 mM NaCl solutions, no increase in thickness at the center of the film was observed in ethyl alcohol-water solutions under the same ethyl alcohol concentration and bubble approach velocity. The phenomenon of the increasing thickness at the center of the film was attributed to the net inward flow in the film, resulting from competition between the inward Marangoni flow and the outward drainage flow that was hindered by the narrow channel at the barrier rim of the film under a high electrolyte concentration. The inward Marangoni flow was achieved by a concentration gradient of ethyl alcohol between the film and the bulk solution resulting from the mobile air-liquid interface in the initial approaching period.

Role of Surfactants Based on Fatty Acids in the Wetting Behavior of Solid-Oil-Aqueous Solution Systems.

Surfactants based on fatty acids have attracted extensive attention thanks to their eco-friendly and pH-responsive features. Here, we studied two fatty acid-based surfactants that were paired with the same organic counterion but distinguished by their aliphatic chain lengths (monoethanolamine-oleic acid (MEA-OA) and monoethanolamine-lauric acid (MEA-LA)). Both surfactants exhibited the ability to lower the oil-water interfacial tension but lost their interfacial activity in a low-pH environment. We experimentally investigated their influence on the receding and spreading of oil droplets on solid surfaces. It was found that the interfacial tension reduction could decrease the static contact angle of the aqueous phase and hindered displacement dynamics during the oil droplet receding. Meanwhile, the interfacial activity was more likely to suppress the initiation of the oil droplet spreading due to the more stable thin-film forming prior to the spreading process. Nevertheless, the experimental results also exhibited that MEA-OA was more effective than MEA-LA in suppressing the receding dynamics and the spreading initiation even when they were characterized by similar interfacial tension values. Such an interesting observation could be attributed to the more considerable Marangoni flow in the solution of MEA-OA whose molecules have longer aliphatic chains. The insight from this study is expected to improve the knowledge on the molecular design for more efficient applications of fatty acid-based surfactants.

Interaction Between the Cyclopentane Hydrate Particle and Water Droplet in Hydrocarbon Oil.

The presence of immiscible water drops in bulk hydrocarbon is likely to bridge hydrate particles to cause hydrate agglomeration, leading to potential pipeline blockage. This can become a major challenge for flow assurance in offshore petroleum transportation. To avoid hydrate aggregation, the attachment between hydrate and water drops should be avoided. In this study, we used our home-designed integrated thin film drainage apparatus to investigate the interactions between a hydrate particle and a water drop inside model oil (i.e., mixture of cyclopentane and toluene with a volumetric ratio of 1:1). Our experiments showed that asphaltenes, a natural component in crude oil, were an effective inhibitor for the attachment between water drops and hydrate particles. Without asphaltenes in the system, the water drop adhered to the hydrate particle immediately after the two surfaces contacted. By adding 0.03 g/L asphaltenes into the oil phase, the attachment was delayed by 0.7 s when the applied preload force was set to around 0.05 mN. By increasing the asphaltenes addition to 0.05 g/L, the attachment between the hydrate and water drop was prevented even when the contact time lasted up to 25 s. This phenomenon could be explained by the adsorption of an asphaltenes layer along the interface between the aqueous drop and hydrocarbon. Measurements of the dynamic interfacial tension and crumping ratio confirmed the presence of the adsorption layer. The addition of 0.6 mol/L NaCl or 0.3 mol/L CaCl2 in the aqueous drop could further enhance the strength of the adsorption layer. Results of this research provide understanding of the benefits of asphaltenes and salt in preventing hydrate agglomeration.

Coalescence of Bubbles with Mobile Interfaces in Water.

The fluid flow inside a thin liquid film can be dramatically modified by the hydrodynamic boundary condition at the interfaces. Aqueous systems can be easily contaminated by trace amounts of impurities, rendering the air-liquid interface immobile, thereby significantly resisting the fluid flow. Using high speed interferometry, rapid thinning of the liquid film, on the order of the collision speed, was observed between two fast approaching air bubbles in water, indicating negligible resistance and a fully mobile boundary condition at the air-water interface. By adding trace amounts of surfactants that changed the interfacial tension by 10^{-4} N/m, a transition from mobile to immobile was observed. This provides a fundamental explanation why the bubble coalescence time can vary by over 3 orders of magnitude.

Unraveling Interaction Mechanisms between Molybdenite and a Dodecane Oil Droplet Using Atomic Force Microscopy.

Molybdenite (MoS2) is a mineral that has drawn great interest because of its potential application in various fields. To facilitate the flotation of molybdenite, the mineral pulp is commonly treated with nonpolar oil additives to promote hydrophobicity and to form an oil bridge between ultrafine molybdenite particles for agglomeration. In this study, dodecane was chosen as a model oil to investigate the flotation mechanisms of molybdenite with nonpolar oil. The interaction forces between a micrometer-sized dodecane droplet and the molybdenite basal plane in various electrolyte solutions were directly measured by the atomic force microscope droplet probe technique. The effects of added salts, ionic strength, and solution pH on interaction forces were evaluated by considering van der Waals, electrical double-layer (EDL), and hydrophobic forces. The experimentally measured force curves were found to agree well with the Reynolds lubrication model and the augmented Young-Laplace equation. The results show that the competition between repulsive EDL forces and attractive hydrophobic forces was directly responsible for oil-molybdenite attachment behavior. High pH and low salinity (<24 mM NaCl) led to strong repulsive EDL forces, which stabilized the interaction and prevented the attachment of oil to molybdenite. Both low pH and high salinity facilitated the attachment of oil to molybdenite through the depression of EDL force, allowing attractive hydrophobic force to dominate. The hydrophobic attraction was quantified with an exponential decay length of 1.0 ± 0.1 nm. Furthermore, calcium ions decreased the magnitude of the surface potentials of both oil and molybdenite more than that seen with the same ionic strength of sodium ions, suggesting the suppressed EDL repulsion. This study provides quantitative information about the surface forces between oil and the molybdenite basal plane and an improved understanding of the fundamental interaction mechanisms governing molybdenite recovery by mineral flotation.

Spontaneous Displacement of High Viscosity Micrometer Size Oil Droplets from a Curved Solid in Aqueous Solutions.

Spontaneous displacement of high viscosity (∼103 Pa·s) micrometer size oil droplets from a curved solid in aqueous solutions was investigated. For high viscosity oils, the dynamic droplet shape was found to deviate significantly from a spherical cap shape due to the considerable viscous force in the oil phase. The displacement dynamics of high viscosity droplets were analyzed using molecular kinetic and hydrodynamic models. The molecular kinetic model was found to describe the dynamic displacement well for the droplets of small departure from the spherical cap shape, while the hydrodynamic model is more applicable to the droplets of higher three-phase contact line displacement velocities and hence larger deviation of the droplets from the spherical cap shape.

Probing Boundary Conditions at Hydrophobic Solid-Water Interfaces by Dynamic Film Drainage Measurement.

A newly developed dynamic force apparatus was used to determine hydrodynamic boundary conditions of a liquid on a hydrophobic silica surface. For a given approach velocity of bubble to solid surfaces in an electrolyte solution, a reduced dimple formation and faster film drainage were observed by increasing the hydrophobicity of silica surfaces, indicating a significant change in hydrodynamic boundary conditions of water molecules from an immobile to a mobile water-hydrophobic silica interface. By comparing the measured film profiles with the predictions from the Stokes-Reynolds-Young-Laplace model, the slippage boundary condition of water on the hydrophobic silica surface of surface nanoroughness was quantified. Increasing the surface hydrophobicity was found to increase the mobility of water in the thin liquid film, promoting faster drainage of the liquid. For a given hydrophobicity of solids, the mobility of water occurred only above a critical bubble approach velocity and increased with increasing bubble approach velocity. In contrast, similar experiments with hydrophobized mica surfaces showed no-slip boundary condition of water at the molecularly smooth hydrophobic surface. The results collectively suggest that the observed mobility of water with more than 100 nm in thickness on the studied hydrophobic silica surfaces was due to the nanoroughness of hydrophobic surfaces. Such finding sheds light on one possible way of reducing the friction of water on hydrophobic solid surfaces by creating nanostructured surface of nanoroughness.

Dynamic Interaction between a Millimeter-Sized Bubble and Surface Microbubbles in Water.

The coalescence between microbubbles and millimeter-sized bubbles is an elementary process in various industrial applications such as froth flotation and wastewater treatment. Fundamental understanding of the coalescence behavior between two colliding bubbles requires knowledge of water drainage from the thin liquid film between the deformable air-water surfaces, a simple phenomenon with high complexity in physics because of the interplay of surface forces, hydrodynamic drainage, and surface rheology. In this work, we performed simultaneous measurements of the interaction force and spatial thin-film thickness during the collision between a millimeter-sized bubble (radius 1.2 mm) and surface microbubbles (radii between 30 and 700 µm) using our recently developed dynamic force apparatus. The interaction force during the collision agrees well with the prediction from the Stokes-Reynolds-Young-Laplace model with the tangentially immobile boundary condition at the air-liquid interface. However, the measured coalescence times for different bubble sizes are shorter than the model predictions, possibly caused by a rapid drainage behavior along with the loss of symmetry of the thin liquid film. In dozens of experimental runs, the bubbles coalesced at a critical film thickness of 25 ± 15 nm, which agrees reasonably well with the predicted rupture thickness using attractive van der Waals interaction force. These results suggest that the nonsymmetric drainage process, rather than the rupture thickness, contributes to the scattering of the experimental coalescence time between two fast-colliding air bubbles. Furthermore, our results suggest that smaller surface bubbles (30-100 µm) are more effective for the attachment onto a large bubble as the coalescence time decreases considerably when the microbubbles are smaller than 100 µm.

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.

The impact and bounce of air bubbles at a flat fluid interface.

The rise and impact of bubbles at an initially flat but deformable liquid-air interface in ultraclean liquid systems are modelled by taking into account the buoyancy force, hydrodynamic drag, inertial added mass effect and drainage of the thin film between the bubble and the interface. The bubble-surface interaction is analyzed using lubrication theory that allows for both bubble and surface deformation under a balance of normal stresses and surface tension as well as the long-range nature of deformation along the interface. The quantitative result for collision and bounce is sensitive to the impact velocity of the rising bubble. This velocity is controlled by the combined effects of interfacial tension via the Young-Laplace equation and hydrodynamic stress on the surface, which determine the deformation of the bubble. The drag force that arises from the hydrodynamic stress in turn depends on the hydrodynamic boundary conditions on the bubble surface and its shape. These interrelated factors are accounted for in a consistent manner. The model can predict the rise velocity and shape of millimeter-size bubbles in ultra-clean water, in two silicone oils of different densities and viscosities and in ethanol without any adjustable parameters. The collision and bounce of such bubbles with a flat water/air, silicone oil/air and ethanol/air interface can then be predicted with excellent agreement when compared to experimental observations.

Simultaneous measurement of dynamic force and spatial thin film thickness between deformable and solid surfaces by integrated thin liquid film force apparatus.

Interactions involving deformable surfaces reveal a number of distinguishing physicochemical characteristics that do not exist in interactions between rigid solid surfaces. A unique fully custom-designed instrument, referred to as integrated thin liquid film force apparatus (ITLFFA), was developed to study the interactions between one deformable and one solid surface in liquid. Incorporating a bimorph force sensor with interferometry, this device allows for the simultaneous measurement of the time-dependent interaction force and the corresponding spatiotemporal film thickness of the intervening liquid film. The ITLFFA possesses the specific feature of conducting measurement under a wide range of hydrodynamic conditions, with a displacement velocity of deformable surfaces ranging from 2 µm s-1 to 50 mm s-1. Equipped with a high speed camera, the results of a bubble interacting with hydrophilic and partially hydrophobic surfaces in aqueous solutions indicated that ITLFFA can provide information on interaction forces and thin liquid film drainage dynamics not only in a stable film but also in films of the quick rupture process. The weak interaction force was extracted from a measured film profile. Because of its well-characterized experimental conditions, ITLFFA permits the accurate and quantitative comparison/validation between measured and calculated interaction forces and temporal film profiles.

Force Balance Model for Bubble Rise, Impact, and Bounce from Solid Surfaces.

A force balance model for the rise and impact of air bubbles in a liquid against rigid horizontal surfaces that takes into account effects of buoyancy and hydrodynamic drag forces, bubble deformation, inertia of the fluid via an added mass force, and a film force between the bubble and the rigid surface is proposed. Numerical solution of the governing equations for the position and velocity of the center of mass of the bubbles is compared against experimental data taken with ultraclean water. The boundary condition at the air-water interface is taken to be stress free, which is consistent for bubbles in clean water systems. Features that are compared include bubble terminal velocity, bubbles accelerating from rest to terminal speed, and bubbles impacting and bouncing off different solid surfaces for bubbles that have already or are yet to attain terminal speed. Excellent agreement between theory and experiments indicates that the forces included in the model constitute the main physical ingredients to describe the bouncing phenomenon.

Universal behavior of the initial stage of drop impact.

During the early stages of the impact of a drop on a solid surface, pressure builds up in the intervening thin lubricating air layer and deforms the drop. The extent of the characteristic deformation is determined by the competition between capillary, gravitational, and inertial forces that has been encapsulated in a simple analytic scaling law. For millimetric drops, variations of the observed deformation with impact velocity V exhibit a maximum defined by the Weber and Eötvös numbers: We=1+Eo. The deformation scales as V(1/2) at the low-velocity capillary regime and as V(-1/2) at the high-velocity inertia regime, in excellent agreement with a variety of experimental systems.

Dynamic interactions between microbubbles in water.

The interaction between moving bubbles, vapor voids in liquid, can arguably represent the simplest dynamical system in continuum mechanics as only a liquid and its vapor phase are involved. Surprisingly, and perhaps because of the ephemeral nature of bubbles, there has been no direct measurement of the time-dependent force between colliding bubbles which probes the effects of surface deformations and hydrodynamic flow on length scales down to nanometers. Using ultrasonically generated microbubbles (approximately 100 microm size) that have been accurately positioned in an atomic force microscope, we have made direct measurements of the force between two bubbles in water under controlled collision conditions that are similar to Brownian particles in solution. The experimental results together with detailed modeling reveal the nature of hydrodynamic boundary conditions at the air/water interface, the importance of the coupling of hydrodynamic flow, attractive van der Waals-Lifshitz forces, and bubble deformation in determining the conditions and mechanisms that lead to bubble coalescence. The observed behavior differs from intuitions gained from previous studies conducted using rigid particles. These direct force measurements reveal no specific ion effects at high ionic strengths or any special role of thermal fluctuations in film thickness in triggering the onset of bubble coalescence.

Cellulose-based slippery covalently attached liquid surfaces for synergistic rain and solar energy harvesting.

For solar cell-triboelectric nanogenerator (TENG) integration, the design of the solid substrate for the TENG device becomes one of the challenges. The TENG needs to have superior contact electrification properties and be transparent so as to ensure light transmittance. Here, by spontaneous polymerization of dichlorodimethylsilane in the absence of any toxic solvent, we have fabricated a controllable liquid-like polydimethylsiloxane brush, featuring hydrophobicity, long-term stability, robustness, and UV resistance. A drop of liquid slides off at tilt angles below 5° and there is dynamic contact angle hysteresis of no more than 10° that can provide strong self-cleaning ability to the solid substrate. This recipe is also applicable to surfaces composed of hydroxyl group-rich cellulose-based surfaces, such as flexible cellulose acetate film (CAF). Importantly, PDMS@CAF, a flexible, transparent, and self-cleaning TENG device with a light transmission rate of 99% or more, was prepared using a conductive polymer film of PH 1000. The hybrid energy harvesting system formed by the combination of this transparent TENG equipped with solar cells is promising for harvesting energy from the environment in different weather conditions.

Spatiotemporal evolution of thin liquid films during impact of water bubbles on glass on a micrometer to nanometer scale.

Collisions between millimeter-size bubbles in water against a glass plate are studied using high-speed video. Bubble trajectory and shape are tracked simultaneously with laser interferometry between the glass and bubble surfaces that monitors spatial-temporal evolution of the trapped water film. Initial bubble bounces and the final attachment of the bubble to the surface have been quantified. While the global Reynolds number is large (∼10(2)), the film Reynolds number remains small and permits analysis with lubrication theory with tangentially immobile boundary condition at the air-water interface. Accurate predictions of dimple formation and subsequent film drainage are obtained.

Anomalous pull-off forces between surfactant-free emulsion drops in different aqueous electrolytes.

A systematic study of collisions between surfactant-free organic drops in aqueous electrolyte solutions reveals the threshold at which continuum models provide a complete description of thin-film interactions. For collision velocities above ~1 µm/s, continuum models of hydrodynamics and surface forces provide a complete description of the interaction, despite the absence of surfactant. This includes accurate prediction of coalescence at high salt concentration (500 mM). In electrolyte solutions at intermediate salt concentration (50 mM), drop-drop collisions at lower velocity (<1 µm) or extended time of forced drop-drop interaction exhibit a strong pull-off force of systematically varying magnitude. The observations have implications on the effects of ion-specificity and time-dependence in drop-drop interactions where kinetic stability is marginal.