Theory of non-equilibrium force measurements involving deformable drops and bubbles

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.

Stratification and film ripping induced by structural forces in granular micellar thin films

HYPOTHESIS

Interactions across incredibly thin layers of fluids, known as thin films, underpin many important processes involving colloids, such as wetting-dewetting phenomena. Often in these systems, thin films are composed of complex fluids that contain dispersed components, such as spherical micelles, giving rise to oscillatory structural forces due to preferential layering under confinement. Modelling of thin film dynamics involving Derjaguin-Landau-Verwey-Overbeek (DLVO) type forces has been widely reported using the Stokes-Reynolds-Young-Laplace (SRYL) model, and we hypothesize that this theory can be extended to a concentrated micellar system by including an oscillatory structural force term in the disjoining pressure.

EXPERIMENTS

We study the drainage behaviour of thin films comprising sodium dodecyl sulfate (SDS) micelles across a range of concentrations and interaction conditions between an air bubble and a mica disk using a custom-built dual-wave interferometry apparatus.

FINDINGS

Early-stage film behaviour is dominated by hydrodynamics, which can be well reproduced by the SRYL model. However, experimental profiles drain significantly faster than predicted, transitioning into a structural force dominated phase characterised by four types of film ripping instabilities that we term 'waving', 'ridging', 'webbing', and 'hole-sheeting'. These instabilities were mapped according to SDS concentration and approach velocity, providing insight into the interplay between structural forces and hydrodynamic conditions.

Ion-Specific Bubble Coalescence Dynamics in Electrolyte Solutions

Bubble coalescence time scale is important in applications such as froth flotation, food and pharmaceutical industries, and two-phase thermal management. The time scale of coalescence is sensitive to the dissolved ions. In this study, we investigate the evolution of a thin electrolyte film between a bubble and a hydrophilic substrate during coalescence. We present a thin-film equation-based numerical model that accounts for the dependence of the surface tension gradient and electric double layer (EDL) on the concentration of ions at the air-liquid interface. The influence of Marangoni stresses and the EDL on the hydrodynamics of drainage determines the coalescence time scale. We show that the electrolytes, such as NaCl, Na2SO4, and NaI retard coalescence, in contrast to HCl and HNO3 that have little effect on the coalescence time scale. We also show that the drainage of the electrolyte films with higher concentrations is retarded due to increased Marangoni stresses at the air-water interface. The slow drainage triggers an early formation of the dimple in the thin film, thus trapping more fluid within, which further decreases the drainage rate. For a hydrophilic substrate, EDL along with van der Waals for a given concentration governs the final dynamics of thin films, eventually resulting in a stable thin layer of the electrolyte between the bubble and the substrate. The stabilizing thickness reduces by an order of magnitude as the NaCl concentration increases from 0.01 to 10 mM. For Na2SO4 solution, the film is stabilized at a smaller thickness due to higher valency cations resulting in higher screening of the EDL repulsion.

Particle-Bubble Interactions: an Investigation of the Three-Phase Contact Line by Atomic Force Microscopy

The dynamics of the three-phase contact line during particle-bubble interactions determine the stability of particle-bubble aggregates in flotation. The interaction of particles and sessile gas bubbles can be studied by colloidal probe atomic force microscopy (CP-AFM). This paper demonstrates a method to obtain the contact angle, the position of the three-phase contact line on the particle, and the bubble profile by utilizing the full information contained in AFM force-distance curves, i.e., force and CP-position information as well as the work done to move the three-phase contact line on the CP-particle. The proposed method does not require any assumption of a constant contact angle or a constant opening angle. This is achieved by the combined solution of the particle force balance and an expression for the work required to move the three-phase contact line over the colloid probe. The applicability to AFM force-distance measurements was demonstrated for the interaction of a hydrophobic SiO2 or a hydrophobic Al2O3 colloidal probe particle with sessile gas bubbles having radii between 45 and 80 μm.

Surface interaction mechanisms of air bubbles, asphaltenes and oil drops in aqueous solutions with implications for interfacial engineering processes

HYPOTHESIS

Surface interactions of bubbles and oil with interface-active species like asphaltenes influence many interfacial phenomena in various engineering processes. It holds both fundamental and practical significance to quantitatively characterize these interactions.

EXPERIMENTS

The surface forces of air bubbles, asphaltenes and asphaltenes-toluene droplets in various aqueous solutions have been quantified using an integrated thin film drainage apparatus and an atomic force microscope coupled with bubble probe. The effects of asphaltenes concentration, pH, salinity, Ca²⁺ ions and surfactants have been examined.

FINDINGS

Hydrophobic interaction drives attachment of bubbles and asphaltenes surfaces or oil droplets under high salinity condition. Increasing asphaltenes concentration in oil droplets enhances their hydrophobic attraction with bubbles due to strengthened asphaltenes adsorption and aggregation at oil-water interface. Increasing pH weakens the hydrophobic interaction as oil surfaces become more negatively charged and less hydrophobic. Under low salinity condition, strong electrical double layer and van der Waals repulsion inhibits the bubble-oil droplet contact. Introducing Ca²⁺ ions and surfactants leads to strong steric repulsion, preventing bubble-oil contact. This research has advanced our mechanistic understanding of how bubbles and oil droplets interact in aqueous systems and offers useful insights to modulate such interactions in oil production, water treatment and other interfacial processes.

Unraveling the hydrophobic interaction mechanisms of hydrocarbon and fluorinated surfaces

HYPOTHESIS

Numerous hydrocarbon and fluorine-based hydrophobic surfaces have been widely applied in various engineering and bioengineering fields. It is hypothesized that the hydrophobic interactions of hydrocarbon and fluorinated surfaces in aqueous media would show some differences.

EXPERIMENTS

The hydrophobic interactions of hydrocarbon and fluorinated surfaces with air bubbles in aqueous solutions have been systematically and quantitatively measured using a bubble probe atomic force microscopy (AFM) technique. Ethanol was introduced to water for modulating the solution polarity. The experimental force profiles were analyzed using a theoretical model combining the Reynolds lubrication theory and augmented Young-Laplace equation by including disjoining pressure arisen from the Derjarguin-Landau-Verwey-Overbeek (DLVO) and non-DLVO interactions (i.e., hydrophobic interactions).

FINDINGS

The experiment results show that the hydrophobic interactions were firstly weakened and then strengthened by increasing ethanol content in the aqueous media, mainly due to the variation in interfacial hydrogen bonding network. The fluorinated surface exhibited less sensitivity to ethanol than hydrocarbon surface, which is attributed to the presence of ordered interfacial water layer. Our work reveals the different hydrophobic effects of hydrocarbon and fluorinated surfaces, with useful implications on modulating the interfacial interactions of relevant materials in various engineering and bioengineering applications.

Effect of Oil-Soluble/Water-Soluble Surfactants on the Stability of Water-in-Oil Systems, an Atomic Force Microscopy Study

The stabilization mechanism of water-in-oil (W/O) emulsions has been studied by measuring the interactions between two water droplets in n-tetradecane using atomic force microscopy. The effects of water-soluble surfactants (SDS/CTAB/Tween 80), an oil-soluble surfactant (Span 20), and the coexistence of the water and oil-soluble surfactants on the stability of water droplets in oil were investigated separately. It is found that the addition of oil-soluble surfactants (Span 20) prevents the coalescence of water droplets in oil. To discuss the role of an oil-soluble surfactant, we analyzed the force curve by applying the theoretical model. The results demonstrate that the oil-soluble surfactant (Span 20) stabilizes dispersed droplets by adsorbing onto the interface and forming a relatively tighter layer with the increase in surfactant concentration, which hinders film rupture. This behavior of the surfactant could also be properly characterized by steric hindrance. A further step was taken by introducing another water-soluble surfactant. It is found that the addition of either SDS or CTAB into the water phase is futile in inducing droplet coalescence in the presence of Span 20. In contrast, Tween 80 was found to be effective in destabilizing water droplets, which could be due to the competitive adsorption between Tween 80 and Span 20 at the interface. By characterizing the interfacial adsorption of Tween 80 and Span 20 with a theoretical adsorption isotherm model, the result indicates that interface replacement would result in a loose adsorption layer that is insufficient to hinder droplet coalescence. Our study provides an intriguing understanding of the role of surfactants in the stabilization and destabilization of water-in-oil emulsions.

Anti-Oil-Adhesion Property of Superhydrophilic/Underwater Superoleophobic Phytic Acid-FeIII Complex Coatings

Crude oil adhesion issues are widespread in the petroleum industry, leading to inefficient production and high maintenance costs. Developing efficient antifouling materials and investigating the microscopic adhesion mechanism are of substantial significance. In the present work, a superhydrophilic/underwater superoleophobic PAFC coating with excellent antifouling properties was constructed by the coordination-driven self-assembly of phytic acid (PA) and FeCl₃ (FC). The atomic force microscope (AFM) droplet probe technique was employed to elucidate the underlying mechanism of the anti-oil-adhesion property of the PAFC coating. Results showed that the PAFC modification achieved the optimum effect at a molar ratio of 1:3 between PA and Fe^III. Applying a (3-aminopropyl)triethoxysilane (APTES) interlayer can effectively improve the performance of the PAFC coating on silica substrates. AFM droplet probe experiments indicated that the adhesion force between submerged micrometer-sized oil droplets and PAFC-modified substrates was significantly weaker than that with the untreated substrate. Meanwhile, the adhesion forces between oil droplets and surfaces were inversely proportional to the contact angle of the oil in water and were enhanced by higher salinity, lower collision velocity, and stronger loading force. The oil injection and wall sticking tests also confirmed the effectiveness of the PAFC modification in resisting the adhesion of crude oil.

Thermodynamic nonequilibrium effects in bubble coalescence: A discrete Boltzmann study

The thermodynamic nonequilibrium (TNE) effects in a coalescence process of two initially static bubbles under thermal conditions are investigated by a discrete Boltzmann model. The spatial distributions of the typical nonequilibrium quantity, i.e., nonorganized momentum fluxes (NOMFs), during evolutions are investigated in detail. The density-weighted statistical method is used to highlight the relationship between the TNE effects and the morphological and kinetics characteristics of bubble coalescence. The results show that the xx component and yy component of NOMFs are antisymmetrical; the xy component changes from an antisymmetric internal and external double quadrupole structure to an outer octupole structure during the coalescence process. Moreover, the evolution of the averaged xx component of NOMFs provides two characteristic instants, which divide the nonequilibrium process into three stages. The first instant, when the averaged xx component of the NOMFs reaches its first local minimum, corresponds to the moment when the mean coalescence speed gets the maximum, and at this time the ratio of minor and major axes is about 1/2. The second instant, when the averaged xx component of the NOMFs gets its second local maximum, corresponds to the moment when the ratio of minor and major axes becomes 1 for the first time. It is interesting to find that the three quantities, TNE intensity, acceleration of coalescence, and the slope of boundary length, show a high degree of correlation and attain their maxima simultaneously. The surface tension and the heat conduction accelerate the process of bubble coalescence, while the viscosity delays it. Both the surface tension and the viscosity enhance the global nonequilibrium intensity, whereas the heat conduction restrains it. These TNE features and findings present some insights into the kinetics of bubble coalescence.

Probing Hydrophobic Interactions between Polymer Surfaces and Air Bubbles or Oil Droplets: Effects of Molecular Weight and Surfactants

Hydrophobic interaction plays an important role in numerous interfacial phenomena and biophysical and industrial processes. In this work, polystyrene (PS) was used as a model hydrophobic polymer for investigating its hydrophobic interaction with highly deformable objects (i.e., air bubbles and oil droplets) in aqueous solutions. The effects of polymer molecular weight, solvent (i.e., addition of ethanol to water), the presence of surface-active species, and hydrodynamic conditions were investigated, via direct surface force measurements using the bubble/drop probe atomic force microscopy (AFM) technique and theoretical calculations based on the Reynolds lubrication theory and augmented Young-Laplace equation by including the effect of disjoining pressure. It was found that the PS of low molecular weight (i.e., PS590 and PS810) showed slightly weaker hydrophobic interactions with air bubbles or oil droplets, as compared to glassy PS of higher molecular weight (i.e., PS1110, PS2330, PS46300, and PS1M). The hydrophobic interaction between PS and air bubbles in a 1 M NaCl aqueous solution with 10 vol % ethanol was weaker than that in the bare aqueous solution. Such effects on the hydrophobic interactions are possibly achieved by influencing the structuring/ordering of water molecules close to the hydrophobic polymer surfaces by tuning the surface chain mobility and surface roughness of polymers. It was found that the addition of three surface-active species, i.e., cetyltrimethylammonium chloride (CTAC), Pluronic F-127, and sodium dodecyl sulfate (SDS), to the aqueous media could suppress the attachment of the hydrophobic polymer and air bubbles or oil droplets, most likely caused by the additional steric repulsion due to the adsorbed surface-active species at the bubble/polymer/oil interfaces. Our results have improved the fundamental understanding of the interaction mechanisms between hydrophobic polymers and gas bubbles or oil droplets, with useful implications on developing effective methods for modulating the related interfacial interactions in many engineering applications.

Interferometric Probing of Physical and Chemical Properties of Solutions: Noncontact Investigation of Liquids

Interferometry is a highly versatile tool for probing physical and chemical phenomena. In addition to the benefit of noncontact investigations, even spatially resolved information can be obtained by choosing a suitable setup. This review presents the evolution of the various setups that have evolved since the first interferometers were developed in the mid-nineteenth century and highlights the benefits, limitations, and typical areas of application. This review focuses on interferometry based on electromagnetic waves in the near-infrared and visible range applied to liquid samples, categorizes the chemical/physical properties (e.g., pressure, temperature, composition) and phenomena (e.g., evaporation, crystal growth, diffusion, thermophoresis) that can be assessed, and presents a comprehensive literature review of specific existing applications. Finally, it discusses some fundamental open questions with respect to geometric considerations and overlapping effects. Expected final online publication date for the Annual Review of Chemical and Biomolecular Engineering, Volume 13 is October 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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.

Probing the Interactions between Pickering Emulsion Droplets Stabilized with pH-Responsive Nanoparticles

The presence and adsorption of particles at the oil/water interface play a critical role in stabilizing Pickering emulsions and affecting their bulk behavior. For water-in-oil (W/O) and oil-in-water (O/W) Pickering emulsions with pH-responsive nanoparticles, their interaction forces and stabilization mechanisms at the nanoscale have not been reported. Herein, the Pickering emulsions formed by oil/water mixtures under different pH values with bilayer oleic acid-coated Fe₃O₄ nanoparticles (Fe₃O₄@2OA NPs) were characterized using microscopy imaging and zeta potential and interfacial tension (IFT) measurements. The interaction forces between formed emulsion droplets were quantified using an atomic force microscope (AFM) drop probe technique. A W/O emulsion formed at pH 2 and 4 is mainly stabilized by the steric barrier formation of confined particle layers (with Fe₃O₄@2OA NPs and aggregates). At pH 9 and 11, an O/W emulsion is formed, and its stabilization mechanism is mainly due to relatively low IFT, strong electrostatic repulsion due to carboxyl groups, and steric repulsion from confined nanoparticles and aggregates, leading to a stable confined thin water film. Increasing the maximum loading force and dwelling time enhances the confinement of Fe₃O₄@2OA particles and aggregates at the oil/water interface. This work provides useful insights into the interaction and stabilization mechanisms of Pickering emulsions with stimuli-responsive interface-active particles.

Atomic Force Microscopy Study of Non-DLVO Interactions between Drops and Bubbles

The heterointeraction between liquid drops and air bubbles dispersed in another immiscible liquid is studied with the application of the atomic force microscopy (AFM) probe techniques. The tetradecane drops and air bubbles readily coalescence to form a lens-like structure in 100 mM sodium chloride aqueous solution, demonstrating strong hydrophobic (HB) attraction. The interaction range and strength of this hydrophobic attraction between oil drops and air bubbles is investigated by fine control of electrical double layer thicknesses related to specific electrolyte concentrations, and a midrange term in combination with a short-range term is found to present a proper characterization of this hydrophobic attraction. A further step is taken by introducing a triblock copolymer (Pluronic F68) into the aqueous solution, with results indicating that a relatively long-range steric hindrance (SH) furnished by a polymer "brush" surmounts the hydrophobic attraction. Finally, the interaction between a water drop and an air bubble in tetradecane is also measured as a comparison. The repelling action between a hydrophobic body (air bubble) and water drop indicates a strong repulsion. The present results show an interesting understanding of hydrophobic interactions between drops and bubbles, which is of potential application in controlling dispersion stability.

The Role of Electric Pressure/Stress Suppressing Pinhole Defect on Coalescence Dynamics of Electrified Droplet

The dimple occurs by sudden pressure inversion at the droplet’s bottom interface when a droplet collides with the same liquid-phase or different solid-phase. The air film entrapped inside the dimple is a critical factor affecting the sequential dynamics after coalescence and causing defects like the pinhole. Meanwhile, in the coalescence dynamics of an electrified droplet, the droplet’s bottom interfaces change to a conical shape, and droplet contact the substrate directly without dimple formation. In this work, the mechanism for the dimple’s suppression (interfacial change to conical shape) was studied investigating the effect of electric pressure. The electric stress acting on a droplet interface shows the nonlinear electric pressure adding to the uniform droplet pressure. This electric stress locally deforms the droplet’s bottom interface to a conical shape and consequentially enables it to overcome the air pressure beneath the droplet. The electric pressure, calculated from numerical tracking for interface and electrostatic simulation, was at least 108 times bigger than the air pressure at the center of the coalescence. This work helps toward understanding the effect of electric stress on droplet coalescence and in the optimization of conditions in solution-based techniques like printing and coating.

Quantitative Analysis of Attachment Time of Air Bubbles to Solid Surfaces in Water

The attachment of air bubbles to solid surfaces in water is encountered in many natural processes and industrial applications. It has been established that the attachment can occur between hydrophobic surfaces and air bubbles. In this paper, we present novel experimental results to quantify the attachment in terms of the attachment time. We show that the attachment time can be determined from either the transient force curve or the transient film thickness. These techniques for determining the attachment time are based on the fact that the rupture of a thin liquid film produces a large attachment force and a rapid expansion of the three-phase contact radius in comparison with the expansion of the film radius. The experimental results are quantitatively analyzed using thin-film drainage theory and intermolecular forces, which include the advanced multilayer van der Waals force and the electrical double-layer force. The advanced van der Waals force theory allows us to incorporate the effect of interfacial gas enrichment (IGE) of dissolved gas in water at hydrophobic surfaces on the bubble-surface attachment. Critically, if the presence of IGE is ignored, the experimental results do not agree with the theory. Finally, IGE is shown to be a significant factor in controlling hydrophobic attraction between an air bubble and a hydrophobic surface and their attachment.

Interfacial ion specificity modulates hydrophobic interaction

HYPOTHESIS

Ion specificity is crucial in assembly and aggregation of polymers in water driven by hydrophobic interaction. An increasing number of studies have suggested that specific ion adsorption and consequent impact on interfacial water molecules should play an important role in modulating hydrophobic interaction.

EXPERIMENTS

Here, bubble probe atomic force microscopy (AFM) combined with theoretical modeling analysis was applied to quantify hydrophobic interactions involving three model polymers in solutions containing different ions.

FINDINGS

For polystyrene, the hydrophobic interaction's decay length D₀ was reduced from 0.75 nm to 0.60 nm by introducing weakly hydrated cations (e.g., K⁺ and NH₄⁺), while varying anion type had little effect. For poly(methyl methacrylate) and polydimethylsiloxane, anion specificity was demonstrated more evident in shortening the hydrophobic interaction range, with D₀ decreasing from 0.63 nm to 0.50 nm and from 0.72 nm to 0.58 nm respectively when strongly hydrated F^- or Cl^- was replaced by weakly hydrated I^-. Such results could arise from specific ion adsorption at water/polymer interface which disrupts the water structuring effect. From the nanomechanical perspective, this work has revealed the importance of interfacial ion specificity in modulating hydrophobic interaction, which offers novel implications for tuning assembly behavior of macromolecules in relevant engineering applications such as micelle formation and foam stabilization.

Hydrodynamic-Colloidal Interactions of an Oil Droplet and a Membrane Surface

Membranes have been shown to be exceptionally successful in the challenging separation of stable oil/water emulsions but suffer from severe fouling that limits their performance. Understanding the mechanisms leading to oil deposition on the membrane surface, as influenced by hydrodynamics and colloidal surface interactions, is imperative for informing better engineered membrane surfaces and process conditions. Here, we study the interactions between an oil droplet and a membrane surface. Hydrodynamics within the water film, confined between the droplet and the membrane, are captured within the framework of the lubrication approximation, coupled with the van der Waals (vdW) and electrostatic interactions through the droplet shape, which is governed by an augmented Young-Laplace equation. The model is used to calculate possible equilibrium positions, where the droplet is held at a finite distance from the membrane by a balance of the forces present. An equilibrium phase diagram is constructed as a function of various process parameters and is shown in terms of the scaled permeation rate through the membrane. The phase diagram identifies the range of conditions leading to deposition, characterized by a "critical" permeation rate, beyond which no equilibrium exists. When equilibrium positions are permitted, we find that these may be classified as stable/unstable, in the kinetic sense. Further, our results demonstrate the link between the deformation of the droplet and the stability of equilibria. An upward deflection of the droplet surface, owing to a dominant, long-range repulsion, has a stabilizing effect, as it maintains the separation between the droplet and membrane. Conversely, a downward deflection is destabilizing because of the self-amplifying effect of strongly increasing attractive forces with separation distance-as the surfaces are pulled together because of deformation, the attractive force increases, causing further deformation. This is also manifested by a dependence of the bistable region on the deformability of the droplet, which is represented by a capillary number, modified so as to account for the effect of the permeable boundary. As the droplet becomes more easy to deform, the transition from an unconditionally stable region of the phase diagram to a point beyond which there is no equilibrium (interpreted as deposition) becomes abrupt. These results provide valuable physical insights into the mechanisms that govern oil fouling of membrane surfaces.

Foamability of aqueous solutions: Role of surfactant type and concentration

In this paper we study the main surface characteristics which control the foamability of solutions of various surfactants. Systematic series of experiments with anionic, cationic and nonionic surfactants with different head groups and chain lengths are performed in a wide concentration range, from 0.001 mM to 100 mM. The electrolyte (NaCl) concentration is also varied from 0 up to 100 mM. For all surfactants studied, three regions in the dependence of the foamability, V_A, on the logarithm of surfactant concentration, lgC_S, are observed. In Region 1, V_A is very low and depends weakly on C_S. In Region 2, V_A increases steeply with C_S. In Region 3, V_A reaches a plateau. To analyse these results, the dynamic and equilibrium surface tensions of the foamed solutions are measured. A key new element in our interpretation of the foaming data is that we use the surface tension measurements to determine the dependence of the main surface properties (surfactant adsorption, surface coverage and surface elasticity) on the surface age of the bubbles. In this way we interpret the results from the foaming tests by considering the properties of the dynamic adsorption layers, formed during foaming. The performed analysis reveals a large qualitative difference between the nonionic and ionic surfactants with respect to their foaming profiles. The data for the nonionic and ionic surfactants merge around two master curves when plotted as a function of the surface coverage, the surface mobility factor, or the Gibbs elasticity of the dynamic adsorption layers. This difference between the ionic and nonionic surfactants is explained with the important contribution of the electrostatic repulsion between the foam film surfaces for the ionic surfactants which stabilizes the dynamic foam films even at moderate surface coverage and at relatively high ionic strength (up to 100 mM). In contrast, the films formed from solutions of nonionic surfactants are stabilized via steric repulsion which becomes sufficiently high to prevent bubble coalescence only at rather high surface coverage (> 90%) which corresponds to related high Gibbs elasticity (> 150 mN/m) and low surface mobility of the dynamic adsorption layers. Mechanistic explanations of all observed trends are provided and some important similarities and differences with the process of emulsification are outlined.

Mobile Surface Charge Can Immobilize the Air/Water Interface

Recent Surface Force Apparatus measurements on thin film drainage as a bubble approaches a surface are reinterpreted in terms of a new model for the air/water interface. In this model, surface charge at the interface can be convected and can diffuse along the surface as the film drains. This creates surface tension gradients, since surface tension includes a charge-dependent contribution from the double-layer free energy. Although this electrocapillary effect is relatively small, we show here that the gradients are large enough to create Marangoni effects that influence the hydrodynamic flow in real systems. The new model can account for observed changes in hydrodynamic boundary condition from mobile initially to immobile during early stages of film drainage, and back to partially mobile as drainage progresses. Experimental film profiles for a millimeter-size bubble in 1 mM KCl solution driven toward a mica surface at 27 μm/s are reasonably well described with this mobile surface charge model. At longer times, there are still features of the experimental data that remain to be explained, which suggests further modeling is warranted.

Interaction Forces between Water Droplets and Solid Surfaces across Air Films

Wetting of solid surfaces occurs when the intervening air film between a water droplet and a solid surface ruptures. Although this rupturing phenomenon is well known, the underlying mechanism has not yet been well understood. In this work, the rupture of intervening air films is systematically studied by measuring the spatiotemporal thickness profiles of the air films between droplets of deionized water and flat solid surfaces using a synchronized triwavelength reflection interferometry microscope. It has been shown that the critical rupture thickness of the air film (h _c) depends on the surface hydrophobicity of solid surfaces. The h _c value was increased from 50 nm on a hydrophobic surface having an equilibrium water contact angle (θ_w) of 96° to 1.42 μm on a hydrophilic surface having a θ_w of 25°. In addition, an increase in the critical rupture thickness with decreasing surface hydrophobicity was found to be applicable not only to chemically treated quartz surfaces but also to a variety of natural mineral surfaces. By determining the pressure within the air films, we have shown that a strong attractive force is present between water droplets and hydrophilic surfaces, thereby accelerating the draining of air films. The measured forces might be of electrostatic origin, and the forces become less attractive with increasing hydrophobicity of solid surfaces. The present result provides a fundamental insight into the rupture of air films from the perspective of surface forces.

Coalescence or Bounce? How Surfactant Adsorption in Milliseconds Affects Bubble Collision

The coalescence between two colliding bubbles in ultraclean water can be 3 or 4 orders of magnitude faster than coalescence in contaminated solutions. This surprising result can be mostly explained by the mobile or immobile boundary conditions at the air-water interface. In this work, we employ a rising bubble technique to study bubble collisions in aqueous solutions with up to 2 mM surfactant. The experimental results clearly show that freshly generated bubbles can coalesce within milliseconds if they collide right after generation. However, once the bubbles reside in the bulk for tens of milliseconds, the coalescence is heavily hindered. Considering these results, we conclude that a clean air-water interface, rather than clean water, is required to achieve the mobile boundary condition that allows quick coalescence. These findings provide fundamental understanding for further improvements in bubble generation that will benefit industrial processes such as mineral flotation, oil extraction, and wastewater treatment.

Modeling Bubble Collisions at Liquid?Liquid and Compound Interfaces

The collision of a bubble at liquid?liquid, solid?liquid?liquid, and gas?liquid?liquid interfaces, the latter two of which are referred to as compound interfaces, is modeled to predict the bubble?s velocity profile and the pressure buildup and drainage rate of the film(s) formed at impact. A force balance approach, previously outlined for bubble collisions at solid and free surfaces, is employed, which takes into account four forces acting on the bubble: buoyancy, drag, inertia of the surrounding liquid through an added mass force, and a film force resulting from the pressure buildup in the liquid film formed between the bubble and the interface upon impact. The augmented Young?Laplace equation is applied to define the pressure buildup in the film(s), while lubrication theory is employed to define the film drainage rate(s) through the use of the Stokes?Reynolds equation. This is the first time this modeling technique has been implemented for bubble collisions with these interface types as all previous models have relied only on grid-based simulations. The models were validated through experiments conducted here with water and silicone oils of various viscosities and from data found in literature. A reasonable agreement is observed between the theoretical and experimental velocity profiles found for these liquid combinations under varying conditions of impact velocity and top film thickness. The spatiotemporal film thickness and pressure profile evolution, features not yet able to be captured through experiment, are also presented and discussed.

Juggling bubbles in square capillaries: an experimental proof of non-pairwise bubble interactions

The physical properties of an ensemble of tightly packed particles like bubbles, drops or solid grains are controlled by their interactions. For the case of bubbles and drops it has recently been shown theoretically and computationally that their interactions cannot generally be represented by pair-wise additive potentials, as is commonly done for simulations of soft grain packings. This has important consequences for the mechanical properties of foams and emulsions, especially for strongly deformed bubbles or droplets well above the jamming point. Here we provide the first experimental confirmation of this prediction by quantifying the interactions between bubbles in simple model foams consisting of trains of equal-volume bubbles confined in square capillaries. The obtained interaction laws agree quantitatively with Surface Evolver simulations and are well described by an analytically derived expression based on the recently developed non-pairwise interaction model of Höhler et al. [Soft Matter, 2017, 13(7), 1371], based on Morse-Witten theory. While all experiments are done at Bond numbers sufficiently low for the hydrostatic pressure variation across one bubble to be negligible, we provide the full analysis taking into account gravity in the appendix for the interested reader. Even though the article focuses on foams, all results directly apply to the case of emulsions.

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.

Quantifying the force between mercury and mica across an ionic liquid using white light interferometry

HYPOTHESIS

Under axisymmetric conditions, changes in the thickness of the thin film between a fluid drop and a solid revealed by white light interferometry can provide information about the interaction of the bodies. Thus, in principle one can quantify the force between the surfaces using interferometric information of film thickness profile. This is needed to quantify and analyze drop-solid interactions across complex fluids such as an ionic liquid to independently characterize new surface forces.

EXPERIMENTS

Interferometric fringes were obtained in experiments on the interaction between a mercury drop and mica across a film of room temperature ionic liquid. The data is analyzed using a novel formula giving the total force acting on the drop. The calculations are compared with two other approaches to estimating forces. Qualitative and quantitative differences are discussed.

FINDINGS

This is the first report of forces measured between mercury and mica across an ionic liquid. The system is subjected to different applied electric potentials. In each case a long ranged, exponentially decaying repulsive force is found. At small separations, the system becomes unstable and the surfaces jump into contact. The comparison of force calculation methods demonstrates the superiority of the force approach proposed here.

Can liquid foams and emulsions be modeled as packings of soft elastic particles?

When two immersed bubbles are pushed against each other, a facet is formed at their contact, leading to an increase of interfacial energy and hence a repulsive interaction force. Foams (and concentrated emulsions) in mechanical equilibrium may thus be modeled as an assembly of soft elastic interacting particles. Such a model has been used in many studies of their structure and mechanical properties, in particular near the jamming transition (or wet limit) where the contact forces are so small that bubbles remain roughly spherical. We review analytical ab initio models and simulations, based on the equilibration of pressure and surface tension forces or, equivalently, minimization of interfacial energy. Two-body interaction behavior dominates asymptotically at packing fractions approaching the jamming transition, but the interaction is intrinsically anharmonic and cannot be captured by a power law. This phenomenon was first identified by D. Morse and T. Witten: we offer a detailed analysis and transparent derivation of their classic result. For packing fractions well above the jamming transition point, the coupling among contacts mediated by bubble volume conservation has a significant impact on the macroscopic elastic response of foam. This effect is captured by a many-body interaction law, derived from first principles. Applications are explored in two and three dimensions, as are future directions for this kind of theory.

Measurement of Instability of Thin Liquid Films by Synchronized Tri-wavelength Reflection Interferometry Microscope

Film thickness measurement of unstable thin liquid films (TLFs) remains a challenge due to the difficulty in determining the order of fringes prior to the film rupture. In the present work, a synchronized tri-wavelength reflection interferometry microscope (STRIM) was developed and employed to determine the spatiotemporal thickness profiles of the TLFs between air bubbles and various hydrophobic surfaces in 10^-2 M NaCl solutions. Both accuracy and precision of film thickness measurements were found to be better than 3 nm over the range of 0-1 μm. It was found that when the radii of air bubbles were in the range 0.71-0.88 mm, the critical rupture thicknesses of the wetting films formed on hydrophobic quartz surfaces having water contact angles of 95° scattered over a range of 57-335 nm with a medium rupture thickness of 122 nm. For smaller air bubbles with radii of 0.13-0.26 mm, the critical rupture thicknesses were much more narrowly distributed with a medium rupture thickness of 27 nm. The result obtained with the TLFs between two air bubbles, i.e., foam film, showed that the critical rupture thickness was increased from 25 to 40 nm, when the sizes of air bubbles were increased from 220 to 960 μm. Compared to rupture thickness of the foam film, the critical rupture thickness of the TLF between an air bubble and a dodecane droplet was smaller, indicating that the film rupture might be related to the hydrophobicity of interacting surfaces. In addition to attractive surface forces, both wave motions and gas molecules in TLF might be associated with the film rupture.

Intermolecular and surface forces at solid/oil/water/gas interfaces in petroleum production

Many challenging issues are encountered along the petroleum production such as the wettability alteration of reservoir solids due to deposition of petroleum materials, stabilization/destabilization of water-in-oil and oil-in-water emulsions and treatment of tailings water. All these problems are essentially driven by the fundamental intermolecular and surface forces among the different components (i.e., water, oil, solid and gas) in the surrounding complex fluid media, and comprehensive understanding of the interactions among these components will pave the way to the development of advanced materials and technologies for improved petroleum production processes. In this work, we have reviewed the quantitative force measurement methods in different petroleum systems by using nanomechanical techniques including surface forces apparatus (SFA) and atomic force microscope (AFM). Interaction forces between petroleum components (e.g., asphaltenes) and mineral solids in both organic solvents and aqueous solutions are reviewed and correlated to the wettability change of the reservoir solids. The recent key progress in quantifying the surface forces of water-in-oil and oil-in-water emulsion drops using AFM drop probe techniques are discussed. The interaction forces of polymer flocculants and colloidal particles are correlated to the performance of tailings water treatment. The current knowledge gap and future perspectives are also presented.

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.

Anisotropic Polymer Adsorption on Molybdenite Basal and Edge Surfaces and Interaction Mechanism With Air Bubbles

The anisotropic surface characteristics and interaction mechanisms of molybdenite (MoS₂) basal and edge planes have attracted much research interest in many interfacial processes such as froth flotation. In this work, the adsorption of a polymer depressant [i.e., carboxymethyl cellulose (CMC)] on both MoS₂ basal and edge surfaces as well as their interaction mechanisms with air bubbles have been characterized by atomic force microscope (AFM) imaging and quantitative force measurements. AFM imaging showed that the polymer coverage on the basal plane increased with elevating polymer concentration, with the formation of a compact polymer layer at 100 ppm CMC; however, the polymer adsorption was much weaker on the edge plane. The anisotropy in polymer adsorption on MoS₂ basal and edge surfaces coincided with water contact angle results. Direct force measurements using CMC functionalized AFM tips revealed that the adhesion on the basal plane was about an order of magnitude higher than that on the edge plane, supporting the anisotropic CMC adsorption behaviors. Such adhesion difference could be attributed to their difference in surface hydrophobicity and surface charge, with weakened hydrophobic attraction and strengthened electrostatic repulsion between the polymers and edge plane. Force measurements using a bubble probe AFM showed that air bubble could attach to the basal plane during approach, which could be effectively inhibited after polymer adsorption. The edge surface, due to the negligible polymer adsorption, showed similar interaction behaviors with air bubbles before and after polymer treatment. This work provides useful information on the adsorption of polymers on MoS₂ basal/edge surfaces as well as their interaction mechanism with air bubbles at the nanoscale, with implications for the design and development of effective polymer additives to mediate the bubble attachment on solid particles with anisotropic surface properties in mineral flotation and other engineering processes.

The application of atomic force microscopy in mineral flotation

During the past years, atomic force microscopy (AFM) has matured to an indispensable tool to characterize nanomaterials in colloid and interface science. For imaging, a sharp probe mounted near to the end of a cantilever scans over the sample surface providing a high resolution three-dimensional topographic image. In addition, the AFM tip can be used as a force sensor to detect local properties like adhesion, stiffness, charge etc. After the invention of the colloidal probe technique it has also become a major method to measure surface forces. In this review, we highlight the advances in the application of AFM in the field of mineral flotation, such as mineral morphology imaging, water at mineral surface, reagent adsorption, inter-particle force, and bubble-particle interaction. In the coming years, the complementary characterization of chemical composition such as using infrared spectroscopy and Raman spectroscopy for AFM topography imaging and the synchronous measurement of the force and distance involving deformable bubble as a force sensor will further assist the fundamental understanding of flotation mechanism.

Emulsions in porous media: From single droplet behavior to applications for oil recovery

Emulsions are suspensions of droplets ubiquitous in oil recovery from underground reservoirs. Oil is typically trapped in geological porous media where emulsions are either formed in situ or injected to elicit oil mobilization and thus enhance the amount of oil recovered. Here, we briefly review basic concepts on geometrical and wetting features of porous media, including thin film stability and fluids penetration modes, which are more relevant for oil recovery and oil-contaminated aquifers. Then, we focus on the description of emulsion flow in porous media spanning from the behaviour of single droplets to the collective flow of a suspension of droplets, including the effect of bulk and interfacial rheology, hydrodynamic and physico-chemical interactions. Finally, we describe the particular case of emulsions used in underground porous media for enhanced oil recovery, thereby discussing some perspectives of future work. Although focused on oil recovery related topics, most of the insights we provide are useful towards remediation of oil-contaminated aquifers and for a basic understanding of emulsion flow in any kind of porous media, such as biological tissues.

Dynamic forces between emulsified water drops coated with Poly-Glycerol-Poly-Ricinoleate (PGPR) in canola oil

The dynamic collision of emulsified water drops in the presence of non-ionic surfactants plays a crucial role in many practical applications. Interaction force between water drops coated with non-ionic food grade surfactants is expected to exhibit rich dynamic behavior that is not yet explored. The collision forces between immobilized water drops in canola oil in the presence of a well-known food grade surfactant polyglycerol polyricinoleate (PGPR) are measured at concentrations well below typically used to form stable emulsions. An extension or kink, attributed to a short-range attractive interaction due to PGPR bridging between the drops, was observed in the retract portion of the force curves at higher applied forces or slower collision velocities. The Stokes-Reynolds-Young-Laplace (SRYL) model was used to calculate theoretical force curves. For higher collisions velocities, the agreement between the calculated and experiment data was acceptable, but the SRYL model failed to describe the extension or kink feature observed at slower velocities below. Both the AFM data and the comparison to the model calculation indicated the presence of a short-range attractive force, not of a hydrodynamic origin, attributed to the bridging and extension of PGPR molecules on the surface of water drops below saturation of the interface.

Effects of Salt-Controlled Self-Assembly of Triblock Copolymers F68 on Interaction Forces between Oil Drops in Aqueous Solution

Nonionic triblock copolymers, surfactant Pluronic F68 (PEO76-PPO29-PEO76), are widely used in industrial processes, such as foaming, emulsification, and stabilization. The behaviors of triblock copolymers such as the salt-dependent self-assembly in bulk solution and the irreversible adsorption at the oil/water interface are mainly focused to explore their effects on the interaction forces between nano-spacing interfaces of oil droplets. In this study, the atomic force microscopy (AFM) technique was employed to measure the drop interaction forces with different F68 bulk concentrations. All selected bulk concentrations (≥100 μM) of copolymers can ensure the formation of a stable layer structure of stretched polymer chains ("brush") at the oil/water interface, which behaved as a mechanical barrier at the interface. This study quantified the forces caused by the space hindrance of F68 copolymers both in the bulk phase and at the interface of oil/F68 aqueous solution during drop interaction. The effects of monovalent electrolyte (NaCl)-induced self-assembly behavior of triblock copolymers F68 in bulk solution on drop interaction forces were measured through the AFM technique.

Superwettability of Gas Bubbles and Its Application: From Bioinspiration to Advanced Materials

Gas bubbles in aqueous media are common and inevitable in, for example, agriculture and industrial processes. The behaviors of gas bubbles on solid interfaces, including generation, growth, coalescence, release, transport, and collection, are crucial to gas-bubble-related applications, which are always determined by gas-bubble wettability on solid interfaces. Here, the recent progress regarding the study of interfaces with gas-bubble superwettability in aqueous media, i.e., superaerophilicity and superaerophobicity, is summarized. Some examples illustrate how to design microstructures and chemical compositions to achieve reliable and effective manipulation of gas-bubble wettability on artificial interfaces. These designed interfaces exhibit excellent performance in gas-evolution reactions, gas-adsorption reactions, and directional gas-bubble transportation. Moreover, progress in the theoretical investigation of gas-bubble superwettability is reported. Lastly, some challenges are presented, such as the reliable manipulation of gas-bubble wettability and the establishment of mature theory for exactly and systematically explaining gas-bubble wetting phenomena.