Effects of Charged Surfactants on Interfacial Water Structure and Macroscopic Properties of the Air-Water Interface.

Surfactants are used to control the macroscopic properties of the air-water interface. However, the link between the surfactant molecular structure and the macroscopic properties remains unclear. Using sum-frequency generation spectroscopy and molecular dynamics simulations, two ionic surfactants (dodecyl trimethylammonium bromide, DTAB, and sodium dodecyl sulphate, SDS) with the same carbon chain lengths and charge magnitude (but different signs) of head groups interact and reorient interfacial water molecules differently. DTAB forms a thicker but sparser interfacial layer than SDS. It is due to the deep penetration into the adsorption zone of Br- counterions compared to smaller Na+ ones, and also due to the flip-flop orientation of water molecules. SDS alters two distinctive interfacial water layers into a layer where H+ points to the air, forming strong hydrogen bonding with the sulphate headgroup. In contrast, only weaker dipole-dipole interactions with the DTAB headgroup are formed as they reorient water molecules with H+ point down to the aqueous phase. Hence, with more molecules adsorbed at the interface, SDS builds up a higher interfacial pressure than DTAB, producing lower surface tension and higher foam stability at a similar bulk concentration. Our findings offer improved knowledge for understanding various processes in the industry and nature.

Enhancing shear strength and handleability of dewatered clay-rich coal tailings for dry-stacking.

Mineral tailings dams pose high pollution risks to the environment and catastrophic failures. Dry stacking has been identified as a promising alternative to mitigate these risks and offers various benefits to the mining industry but lacks systematic research outcomes. To facilitate dry stacking, coal tailings slurries were dewatered using either filtration or centrifugation methods, resulting in a semi-solid form (cake) that can be safely disposed of. The handleability and disposability of these cakes are greatly influenced by the selection of chemical aids (such as polymer flocculants) and the mechanical dewatering technique employed. The effects of polyacrylamide (PAM) flocculants with a range of molecular weight, charge, and charge density are presented. Coal tailings samples with differences in clay mineralogy were dewatered using press filtration, solid bowl centrifugation, and natural air drying. Handleability and disposability of the tailings were assessed by their rheological properties, including yield stress, adhesive and cohesive stresses, and stickiness. Residue moisture, type of polymer flocculants, and clay mineralogy were found to be crucial factors affecting the handleability and disposability of the dewatered cakes. The tailing yield stress (shear strength) increased as the solid concentration increased. In the semi-solid regime (above 60 wt% solids), the tailings displayed stiff exponential growth. Similar trends were observed for stickiness and adhesive/cohesive energy of the tailings with a steel (truck) surface. Adding polymer flocculants increased the shear strength of the dewatered tailings by 10-15%, thus favouring disposability. However, the polymer selection for coal tailing handling and processing is a trade-off between its disposability and handleability, which requires a multi-criteria decision-making process. The current results also suggested that cationic PAM could be most suitable for dewatering by press filtration, while anionic PAM should be selected for dewatering by solid bowl centrifugation.

Lean management for improving hospital waiting times-Case study of a Vietnamese public/general hospital emergency department.

INTRODUCTION: Emergency departments (EDs) at public hospitals in Vietnam typically face problems with overcrowding, as well as being populated by a wide variety of illnesses, resulting in increasing dissatisfaction from patients. To alleviate these problems, we used the increasingly popular value-stream mapping (VSM) and lean strategy approaches to (1) evaluate the current patient flow in EDs; (2) identify and eliminate the non-valued-added components; and (3) modify the existing process in order to improve waiting times. METHODS: Data from a total of 742 patients who presented at the ED of 108 Military Central Hospital in Hanoi, Vietnam, were collected. A VSM was developed where improvement possibilities were identified and attempts to eliminate non-value-added activities were made. A range of issues that were considered as a resource waste were highlighted, which led to a re-design process focusing on prioritizing blood tests and ultrasound procedures. On the administrative side, various measures were considered, including streamlining communication with medical departments, using QR codes for healthcare insurance payments, and efficient management of X-ray and CT scan online results. RESULTS: By implementing a lean approach, the following reductions in delay and waiting time were incurred: (1) pre-operative test results (for patients requiring medical procedures/operations) by 33.3% (from 134.4 to 89.4 min); (2) vascular interventions by 10.4% (from 54.6 to 48.9 min); and (3) admission to other hospital departments by 49.5% (from 118.3 to 59.8 min). Additionally, prior to the implementation of the lean strategy approach, only 22.9% of patients or their proxies (family members or friends), who responded to the survey, expressed satisfaction with the ED services. This percentage increased to 76.5% following the curtailment of non-value-added activities. Through statistical inferential test analyses, it can be confidently concluded that applying lean strategy and tools can improve patient flow in public/general hospital EDs and achieve better staff coordination within the various clinical and administrative hospital departments. To the authors' knowledge, such analysis in a Vietnamese hospital's ED context has not been previously undertaken.

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.

From Surface Tension to Molecular Distribution: Modeling Surfactant Adsorption at the Air-Water Interface.

Surfactants are centrally important in many scientific and engineering fields and are used for many purposes such as foaming agents and detergents. However, many challenges remain in providing a comprehensive understanding of their behavior. Here, we provide a brief historical overview of the study of surfactant adsorption at the air-water interface, followed by a discussion of some recent advances in this area from our group. The main focus is on incorporating an accurate description of the adsorption layer thickness of surfactant at the air-water interface. Surfactants have a wide distribution at the air-water interface, which can have a significant effect on important properties such as the surface excess, surface tension, and surface potential. We have developed a modified Poisson-Boltzmann (MPB) model to describe this effect, which we outline here. We also address the remaining challenges and future research directions in this area. We believe that experimental techniques, modeling, and simulation should be combined to form a holistic picture of surfactant adsorption at the air-water interface.

Measuring the effective surface tension of a floating liquid marble using X-ray imaging.

A liquid marble (LM) is a droplet coated with microparticles that isolate the liquid interior from its surroundings, making it perfectly non-wetting. This attractive feature allows the LM to perform useful tasks such as coalescence, targeted delivery, and controlled release. The non-wetting characteristic also allows the LM to float on a carrier liquid. The growing number of applications in digital microfluidics requires further insights into the fundamental properties of a LM such as its effective surface tension. Although the coating provides the LM with various desirable characteristics, its random construction presents a major obstacle to accurate optical analysis. This paper presents a novel method to measure the effective surface tension of a floating LM using X-ray imaging and curve fitting procedures. X-ray imaging reveals the true LM liquid-air interface hidden by the coating particles. Analysis of this interface showed that the effective surface tension of a LM is not significantly different from that of its liquid content. This indicates that the particle coating might not have significantly altered the behaviour of the liquid interface. We also found that our method is sensitive enough to detect the variations across individual LMs.

The Effect of Dissolved Gases on the Short-Range Attractive Force between Hydrophobic Surfaces in the Absence of Nanobubble Bridging.

The short-range attractive forces between hydrophobic surfaces are key factors in a wide range of areas such as protein folding, lipid self-assembly, and particle-bubble interaction such as in industrial flotation. Little is certain about the effect of dissolved (well-controlled) gases on the interaction forces, in particular in those systems where the formation of surface nanobubble bridges is suppressed. Here, we probe the short-range attractive force between hydrophobized silica surfaces in aqueous solutions with varying but well-controlled isotherms of gas solubility. The first contact approach force measurement method using AFM shows that decreasing gas solubility results in a decrease of the force magnitude as well as shortening of its range. The behavior was found to be consistent across all four aqueous systems and gas solubilities tested. Using numerical computations, we corroborate that attractive force can be adequately explained by a multilayer dispersion force model, which accounts for an interfacial gas enrichment (IGE), that results in the formation of a dense gas layer (DGL) adjacent to the hydrophobic surface. We found that the DGL on the hydrophobic surface is affected only by the concentration of dissolved gases and is independent of the salt type, used to control the gas solubility, which excludes the effect of electrical double-layer interactions on the hydrophobic force.

Quantifying the Counterion-Specific Effect on Surfactant Adsorption Using Modeling, Simulation, and Experiments.

Ionic surfactants behave differently in the presence of various counterions, which plays an important role in many scientific and engineering processes. Previous work has shown that the counterion-specific surface tension can be reproduced with classical adsorption models, but the underlying origin of this effect has not been explained. In this paper, we extend our previously developed adsorption model to account for the specific counterion adsorption. This model can accurately predict the surface tension of surfactant solutions like sodium dodecyl sulfate (SDS) in the presence of the monovalent salts LiCl, NaCl, KCl, and CsCl. The predicted surface excess and surface potential are validated by corresponding sum-frequency generation (SFG) spectroscopy experiments. We also used molecular dynamic (MD) simulation to explain the origin of the counterion-specific effect for surfactant behavior. Our study shows that for SDS, binding of the counterion to both the headgroup and a few CH2 fragments close to the surfactant head contributes to the counterion-specific effect. In general, SDS behaves like a large ion, and it prefers to bind with large counterions such as Cs+, which is consistent with Collins's law of matching water affinity. Therefore, large counterions enhance the surface adsorption and lower the surface tension the most.

The Contact Angle Variation of Floating Particles Makes It Difficult to Use the Neumann Condition To Quantify the Air-Water Interface Deformation in Three-Dimensional Space.

Capillary force is critical to the floatability of particles at the air-water interface. Quantification of the capillary force requires solving the Young-Laplace equation using suitable boundary conditions (BCs) at the triple contact line. For axisymmetric (two-dimensional, 2D) systems, such as single spheres floating at an initially flat air-water surface, both the Dirichlet (constant contact depth) and Neumann (constant contact angle) BCs can be applied. For three-dimensional (3D) systems, Neumann BCs (NBCs) have been successfully used. In this paper, we have challenged the use of NBCs for the 3D deformation of the air-water surface induced by floating particles, which always exhibit intrinsic contact angle (CA) hysteresis that is significantly amplified in 3D systems. Specifically, we designed and conducted the experiments using single prismatic particles, which allowed for the determination of two characteristic CAs at the two diagonal axes with a high degree of certainty. We calibrated the numerical solution to the 3D Young-Laplace equation using the deformed air-water interface profiles at the two diagonal axes and then validated the numerical solution for the capillary force on the floating particles with the measured force. We obtained reliable data for the CA along the three-phase contact line (TPCL), which displayed a significant distribution. We also discussed the findings that were significant to floating spheres in asymmetric systems, such as pairs of floating spheres. This paper provides experimental and theoretical evidence that the CA is not constant along the contact line in a 3D geometry, which invalidates the use of NBCs for 3D systems of floating particles. This study highlights the significance of the CA variation known as CA hysteresis, which should be considered when predicting the floatability of particles at the air-water interface.

New Evidence of Head-to-Tail Complex Formation of SDS-DOH Mixtures Adsorbed at the Air-Water Interface as Revealed by Vibrational Sum Frequency Generation Spectroscopy and Isotope Labelling.

Details about the molecular structures of surfactant mixtures adsorbed at the air-water interface have been controversial. Using sum frequency generation vibrational spectroscopy (SFG) and isotope labeling, we show here for the first time that mixtures of dodecanol (DOH) and sodium dodecyl sulfate (SDS) adsorb at the air-water interface with the formation of a head-to-tail complex. We observed this complex formation to occur first in the aqueous subphase, followed by complex adsorption onto the interface. This new piece of evidence for the head-to-tail complex conformation contradicts the conjectured tail-to-tail adsorption of the surfactant mixtures. The SFG data also show the dominating adsorption of the SDS-DOH complex over the single molecules of SDS and DOH at the air-water interface. The interfacial DOH-to-SDS molecular ratio of approximately 2.2:1 at a DOH-to-SDS bulk concentration ratio of 10 µM/2 mM was determined by isotope labeling of the surfactants. In addition to a smaller number of gauche defects, the DOH-SDS complex was found to adopt a higher level of orderliness than the adsorbed single surfactants. These findings provide important insights into the descriptions and interpretation of DOH-SDS adsorption at the air-water interface and its properties.

Influence of Interfacial Gas Enrichment on Controlled Coalescence of Oil Droplets in Water in Microfluidics.

Interfacial gas enrichment (IGE) of dissolved gases in water is shown to govern the strong attraction between solid hydrophobic surfaces of an atomic force microscopy (AFM) colloidal probe and solid substrate. However, the role of IGE in controlling the attraction between fluid-fluid interfaces of foam films and emulsion films is difficult to establish by AFM techniques because of the extremely fast coalescence. Here, we applied droplet-based microfluidics to capture the fast coalescence event under the creeping flow condition and quantify the effect of IGE on the drainage and stability of water films between coalescing oil droplets. The amount of dissolved gases is controlled by partially degassing the oil phase. When the amount of dissolved gases (oxygen) in oil decreases (from 7.89 to 4.59 mg/L), the average drainage time of coalescence significantly increases (from 19 to 50 ms). Our theoretical quantification of the coalescence by incorporating IGE into the multilayer van der Waals attraction theory confirms the acceleration of film drainage dynamics by the van der Waals attractive force generated by IGE. The thickness of the IGE layer decreases from 5.5 to 4.9 nm when the amount of dissolved gas decreases from 7.89 to 4.59 mg/L. All these results establish the universal role of dissolved gases in governing the strong attraction between particulate hydrophobic interfaces.

Analytical Model for Diffusive Evaporation of Sessile Droplets Coupled with Interfacial Cooling Effect.

Current analytical models for sessile droplet evaporation do not consider the nonuniform temperature field within the droplet and can overpredict the evaporation by 20%. This deviation can be attributed to a significant temperature drop due to the release of the latent heat of evaporation along the air-liquid interface. We report, for the first time, an analytical solution of the sessile droplet evaporation coupled with this interfacial cooling effect. The two-way coupling model of the quasi-steady thermal diffusion within the droplet and the quasi-steady diffusion-controlled droplet evaporation is conveniently solved in the toroidal coordinate system by applying the method of separation of variables. Our new analytical model for the coupled vapor concentration and temperature fields is in the closed form and is applicable for a full range of spherical-cap shape droplets of different contact angles and types of fluids. Our analytical results are uniquely quantified by a dimensionless evaporative cooling number Eo whose magnitude is determined only by the thermophysical properties of the liquid and the atmosphere. Accordingly, the larger the magnitude of Eo, the more significant the effect of the evaporative cooling, which results in stronger suppression on the evaporation rate. The classical isothermal model is recovered if the temperature gradient along the air-liquid interface is negligible ( Eo = 0). For substrates with very high thermal conductivities (isothermal substrates), our analytical model predicts a reversal of temperature gradient along the droplet-free surface at a contact angle of 119°. Our findings pose interesting challenges but also guidance for experimental investigations.

Combined Sum Frequency Generation and Thin Liquid Film Study of the Specific Effect of Monovalent Cations on the Interfacial Water Structure.

Some salts have been recently shown to decrease the sum frequency generation (SFG) intensity of the hydrogen-bonded water molecules, but a quantitative explanation is still awaited. Here, we report a similar trend for the chloride salts of monovalent cations, that is, LiCl, NaCl, and CsCl, at low concentrations. Specifically, we revealed not only the specific adsorption of cations at the water surface but also the concentration-dependent effect of ions on the SFG response of the interfacial water molecules. Our thin-film pressure balance (TFPB) measurements (stabilized by 10 mM of methyl isobutyl carbinol) enabled the determination of the surface potential that governs the surface electric field affecting interfacial water dipoles. The use of the special alcohol also enabled us to identify a remarkable specific screening effect of cations on the surface potential. We explained the concentration dependency by considering the direct ion-water interactions and water reorientation under the influence of surface electric field as the two main contributors to the overall SFG signal of the hydrogen-bonded water molecules. Although the former was dominant only at the low-concentration range, the effect of the latter intensified with increasing salt concentration, leading to the recovery of the band intensity at medium concentrations. We discussed the likelihood of a correlation between the effect of ions on reorientation dynamics of water molecules and the broad-band intensity drop in the SFG spectra of salt solutions. We proposed a mechanism for the cation-specific effect through the formation of an ionic capacitance at the solution surface. It explains how cations could impart the ion specificity while they are traditionally believed to be repelled from the interfacial region. The electrical potential of this capacitance varies with the charge separation and ion density at the interface. The charge separation being controlled by the polarizability difference between anions and cations was identified using the SFG response of the interfacial water molecules as an indirect probe. The ion density being affected by the absolute polarizability of ions was tracked through the measurement of the surface potentials and Debye-Hückel lengths using the TFPB technique.

Detecting the undetectable: The role of trace surfactant in the Jones-Ray effect.

The surface tension of dilute salt water is a fundamental property that is crucial to understanding the complexity of many aqueous phase processes. Small ions are known to be repelled from the air-water surface leading to an increase in the surface tension in accordance with the Gibbs adsorption isotherm. The Jones-Ray effect refers to the observation that at extremely low salt concentration, the surface tension decreases. Determining the mechanism that is responsible for this Jones-Ray effect is important for theoretically predicting the distribution of ions near surfaces. Here we use both experimental surface tension measurements and numerical solution of the Poisson-Boltzmann equation to demonstrate that very low concentrations of surfactant in water create a Jones-Ray effect. We also demonstrate that the low concentrations of the surfactant necessary to create the Jones-Ray effect are too small to be detectable by surface sensitive spectroscopic measurements. The effect of surface curvature on this behavior is also examined, and the implications for unexplained bubble phenomena are discussed. This work suggests that the purity standards for water may be inadequate and that the interactions between ions with background impurities are important to incorporate into our understanding of the driving forces that give rise to the speciation of ions at interfaces.

The Floatability of Single Spheres versus Their Pairs on the Water Surface.

Particle floatability at the water surface encountered in nature and industrial systems often occurs in the presence of many particles, but the available theoretical developments are based on the flotation of single particles. Here experiments were conducted to compare the floatabilities of single and multiple spheres on the air-water interfaces. Specifically, the forces on floating single spheres and their pairs versus the depth of deformed interface were measured using a force sensor combined with high-speed video microscopy and modeled based on the 3D Young-Laplace equation which was numerically solved. The experimental and theoretical results for the vertical forces supporting the floatability of the pairs of spheres agree well. The maximum measured forces on the pairs were equal to the sum of the maximum forces measured on two single spheres individually, but the forces measured on the single spheres and their pairs at different depths of interface deformation were different. The vertical forces supporting the floatability of the sphere pairs can better tolerate the interface deformation than the same force on two single particles. This evidence is also supported by the experiments with multiple particles floating at the surface of water-ethanol mixtures. Adding ethanol into water reduced the surface tension of water and the floatability of particles at the water surface, but the floatability of multiple particles was sustainable at much lower critical surface tensions than that for single particles, invalidating the classical theories. Lateral interparticle interactions influence the floatability of particles and should be considered in its modeling.

How Does the Gibbs Inequality Condition Affect the Stability and Detachment of Floating Spheres from the Free Surface of Water?

Floating objects on the air-water interfaces are central to a number of everyday activities, from walking on water by insects to flotation separation of valuable minerals using air bubbles. The available theories show that a fine sphere can float if the force of surface tension and buoyancies can support the sphere at the interface with an apical angle subtended by the circle of contact being larger than the contact angle. Here we show that the pinning of the contact line at the sharp edge, known as the Gibbs inequality condition, also plays a significant role in controlling the stability and detachment of floating spheres. Specifically, we truncated the spheres with different angles and used a force sensor device to measure the force of pushing the truncated spheres from the interface into water. We also developed a theoretical modeling to calculate the pushing force that in combination with experimental results shows different effects of the Gibbs inequality condition on the stability and detachment of the spheres from the water surface. For small angles of truncation, the Gibbs inequality condition does not affect the sphere detachment, and hence the classical theories on the floatability of spheres are valid. For large truncated angles, the Gibbs inequality condition determines the tenacity of the particle-meniscus contact and the stability and detachment of floating spheres. In this case, the classical theories on the floatability of spheres are no longer valid. A critical truncated angle for the transition from the classical to the Gibbs inequality regimes of detachment was also established. The outcomes of this research advance our understanding of the behavior of floating objects, in particular, the flotation separation of valuable minerals, which often contain various sharp edges of their crystal faces.

Evaporation of Ethanol-Water Binary Mixture Sessile Liquid Marbles.

Liquid marble is a liquid droplet coated with particles. Recently, the evaporation process of a sessile liquid marble using geometric measurements has attracted great attention from the research community. However, the lack of gravimetric measurement limits further insights into the physical changes of a liquid marble during the evaporation process. Moreover, the evaporation process of a marble containing a liquid binary mixture has not been reported before. The present paper investigates the effective density and the effective surface tension of an evaporating liquid marble that contains aqueous ethanol at relatively low concentrations. The effective density of an evaporating liquid marble is determined from the concurrent measurement of instantaneous mass and volume. Density measurements combined with surface profile fitting provide the effective surface tension of the marble. We found that the density and surface tension of an evaporating marble are significantly affected by the particle coating.

A Microfluidic Method for Investigating Ion-Specific Bubble Coalescence in Salt Solutions.

This paper reports the direct and precise measurement of bubble coalescence in salt solutions using microfluidics. We directly visualized the bubble coalescence process in a microchannel using high-speed imaging and evaluated the shortest coalescence time to determine the transition concentration of sodium halide solutions. We found the transition concentration is ion-specific, and the capacity of sodium halide salts to inhibit bubble coalescence follows the order of NaF > NaCl > NaBr > NaI. The microfluidic method overcomes the inherent uncertainties in conventional large-scale devices and methods.

A sum-frequency generation spectroscopic study of the Gibbs analysis paradox: monolayer or sub-monolayer adsorption?

The Gibbs adsorption isotherm (GAI) has been considered as the foundation of surfactant adsorption studies for over a century; however, its application in determining the limiting surface excess has recently been intensively discussed, with contradictory experimental evidence either supporting or refuting the theory. The available arguments are based on monolayer adsorption models. In this paper, we experimentally and intellectually propose and validate the contribution of sub-monolayer adsorption to the GAI paradox. We utilize a powerful intrinsically surface-sensitive technique, vibrational sum-frequency generation spectroscopy (SFG), complementing with conventional tensiometric measurements to address these controversies both quantitatively and qualitatively. Our SFG results revealed that the precipitous decrease in surface tension directly corresponds to surface occupancy by adsorbates. In addition, the Gibbs analysis was successfully applied to the soluble monolayer of a surface-active alcohol to full saturation. However, the full saturation of the topmost monolayer does not necessarily mean that the surface adsorption was completed because the adsorption was observed to continuously occur in the sub-monolayer region soon after the topmost monolayer became saturated. Nonetheless, the Gibbs isotherm failed to account for the excess of alcohol adsorbed in this sub-monolayer region. This new concept of surface excess must therefore be treated thermodynamically.

Attractive forces between hydrophobic solid surfaces measured by AFM on the first approach in salt solutions and in the presence of dissolved gases.

Interfacial gas enrichment of dissolved gases (IGE) has been shown to cover hydrophobic solid surfaces in water. The atomic force microscopy (AFM) data has recently been supported by molecular dynamics simulation. It was demonstrated that IGE is responsible for the unexpected stability and large contact angle of gaseous nanobubbles at the hydrophobic solid-water interface. Here we provide further evidence of the significant effect of IGE on an attractive force between hydrophobic solid surfaces in water. The force in the presence of dissolved gas, i.e., in aerated and nonaerated NaCl solutions (up to 4 M), was measured by the AFM colloidal probe technique. The effect of nanobubble bridging on the attractive force was minimized or eliminated by measuring forces on the first approach of the AFM probe toward the flat hydrophobic surface and by using high salt concentrations to reduce gas solubility. Our results confirm the presence of three types of forces, two of which are long-range attractive forces of capillary bridging origin as caused by either surface nanobubbles or gap-induced cavitation. The third type is a short-range attractive force observed in the absence of interfacial nanobubbles that is attributed to the IGE in the form of a dense gas layer (DGL) at hydrophobic surfaces. Such a force was found to increase with increasing gas saturation and to decrease with decreasing gas solubility.