Negative Pressure within a Liquid-Fluid Interface Determines Its Thickness

The density within the interface between two fluid phases at equilibrium gradually changes from that of one phase to that of the other. The main change in density, according to experimental measurements, practically occurs over a finite distance of O [1 nm]. If we assume that the average stress difference within the interface is on the order of magnitude of ambient pressure, then the Bakker equation implies that for a liquid with surface tensions, say ∼50 mN/m, we get an interface thickness of ∼500 nm. This is certainly too big because it contradicts experimental findings. Alternatively, if the thickness is assumed to be O [10 nm] or less, as is usually believed, the average stress difference must be ∼5 × 10⁶ N/m² or bigger, which is surprisingly high. This paper shows using a few approaches that such a high average stress difference is due to negative stresses in the interface.

Profiling Single Cancer Cells with Volatolomics Approach

Single-cell analysis is a rapidly evolving to characterize molecular information at the individual cell level. Here, we present a new approach with the potential to overcome several key challenges facing the currently available techniques. The approach is based on the identification of volatile organic compounds (VOCs), viz. organic compounds having relatively high vapor pressure, emitted to the cell's headspace. This concept is demonstrated using lung cancer cells with various p53 genetic status and normal lung cells. The VOCs were analyzed by gas chromatography combined with mass spectrometry. Among hundreds of detected compounds, 18 VOCs showed significant changes in their concentration levels in tumor cells versus control. The composition of these VOCs was found to depend, also, on the sub-molecular structure of the p53 genetic status. Analyzing the VOCs offers a complementary way of querying the molecular mechanisms of cancer as well as of developing new generation(s) of biomedical approaches for personalized screening and diagnosis.

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Measurement of VOCs was achieved at the single-cell level

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Genetic changes influence the emitted volatiles of single and bulk cancer cells

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Single-cell VOC analysis measures population heterogeneity in initial stage of tumors

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Volatolomics research can promote non-invasive, simple, and cost-effective diagnostics

Physico-Chemical Explanation of Blood Cell Adhesion in Thrombus Formation

A model is suggested which assumes that the rate of deposition of cells is determined both by hydrodynamic factors and by Brownian motion over the potential barrier caused by London and double-layer forces in the immediate vicinity of the deposition surface. The height of the barrier in the potential energy of interaction between blood cells and various surfaces is analyzed in relation to the physical properties of the cells, surfaces, and solutions. Based on this analysis, the adhesion of platelets to injured blood vessel walls and to non-biologic materials, the lack of adhesion of red blood cells under the same conditions, the mechanism of ADP induced aggregation and the interaction with blood flow are explained. The qualitative predictions of the model are substantiated by available experimental information. Quantitative results are presented in terms of a time constant, which typifies a period of contact with a surface, during which appreciable deposition occurs.

Sedimentation and Adhesion of Platelets onto a Horizontal Glass Surface

An experimental method for measuring platelet adhesion to a glass surface and platelet sedimentation rate is described. Anticoagulated platelet-rich plasma is placed on a horizontal glass slide for various contact periods. The number of platelets adhering to the slide per unit area is recorded as a function of time. The experimental results are used to verify theoretical predictions which account for the effect of the slow sedimentation rate of the platelets and for their escape over the potential barrier between them and the solid surface. By a least-squares fit of the theoretical equation to the experimental data, both the platelet adhesiveness, in terms of P the probability to overcome the potential barrier, and the platelet sedimentation rate V are evaluated. A range of values of P and V for healthy humans is presented.

A biophysical vascular bubble model for devising decompression procedures

Vascular bubble models, which present a realistic biophysical approach, hold great promise for devising suitable diver decompression procedures. Nanobubbles were found to nucleate on a flat hydrophobic surface, expanding to form bubbles after decompression. Such active hydrophobic spots (AHS) were formed from lung surfactants on the luminal aspect of ovine blood vessels. Many of the phenomena observed in these bubbling vessels correlated with those known to occur in diving. On the basis of our previous studies, which proposed a new model for the formation of arterial bubbles, we now suggest the biophysical model presented herein. There are two phases of bubble expansion after decompression. The first is an extended initiation phase, during which nanobubbles are transformed into gas micronuclei and begin to expand. The second, shorter phase is one of simple diffusion‐driven growth, the inert gas tension in the blood remaining almost constant during bubble expansion. Detachment of the bubble occurs when its buoyancy exceeds the intermembrane force. Three mechanisms underlying the appearance of arterial bubbles should be considered: patent foramen ovale, intrapulmonary arteriovenous anastomoses, and the evolution of bubbles in the distal arteries with preference for the spinal cord. Other parameters that may be quantified include age, acclimation, distribution of bubble volume, AHS, individual sensitivity, and frequency of bubble formation. We believe that the vascular bubble model we propose adheres more closely to proven physiological processes. Its predictability may therefore be higher than other models, with appropriate adjustments for decompression illness (DCI) data.

Capillary Condensation with a Grain of Salt

Capillary condensation (CC), namely, the formation from the vapor of a stable phase of drops below the saturation pressure, is a prevalent phenomenon. It may occur inside porous structures or between surfaces of particles. CC between surfaces, a liquid "bridge", is of particular practical interest because of its resulting adhesive force. To date, studies have focused on pure water condensation. However, nonvolatile materials, such as salts and surfactants, are prevalent in many environments. In the current study, the effect of these contaminants on CC is investigated from a thermodynamic point of view. This is done by computing the Gibbs energy of such systems and developing the modified Kelvin equation, based on the Kohler theory. The results demonstrate that nonvolatile solutes may have a number of major effects, including an increase in the critical radius and the stabilization of the newly formed phase.

Interfaces at equilibrium: A guide to fundamentals

The fundamentals of the thermodynamics of interfaces are reviewed and concisely presented. The discussion starts with a short review of the elements of bulk thermodynamics that are also relevant to interfaces. It continues with the interfacial thermodynamics of two-phase systems, including the definition of interfacial tension and adsorption. Finally, the interfacial thermodynamics of three-phase (wetting) systems is discussed, including the topic of non-wettable surfaces. A clear distinction is made between equilibrium conditions, in terms of minimizing energies (internal, Gibbs or Helmholtz), and equilibrium indicators, in terms of measurable, intrinsic properties (temperature, chemical potential, pressure). It is emphasized that the equilibrium indicators are the same whatever energy is minimized, if the boundary conditions are properly chosen. Also, to avoid a common confusion, a distinction is made between systems of constant volume and systems with drops of constant volume.

Expansion of bubbles under a pulsatile flow regime in decompressed ovine blood vessels

After decompression of ovine large blood vessels, bubbles nucleate and expand at active hydrophobic spots on their luminal aspect. These bubbles will be in the path of the blood flow within the vessel, which might replenish the supply of gas-supersaturated plasma in their vicinity and thus, in contrast with our previous estimations, enhance their growth. We used the data from our previous study on the effect of pulsatile flow in ovine blood vessels stretched on microscope slides and photographed after decompression from hyperbaric exposure. We measured the diameter of 46 bubbles in 4 samples taken from 3 blood vessels (pulmonary artery, pulmonary vein, and aorta) in which both a "multi-bubble active spot" (MBAS)--which produces several bubbles at a time, and at least one "single-bubble active spot" (SBAS)--which produces a single bubble at a time, were seen together. The linear expansion rate for diameter in SBAS ranged from 0.077 to 0.498 mm/min and in MBAS from 0.001 to 0.332 mm/min. There was a trend toward a reduced expansion rate for bubbles in MBAS compared with SBAS. The expansion rate for bubbles in an MBAS when it was surrounded by others was very low. Bubble growth is related to gas tension, and under a flow regime, bubbles expand from a diameter of 0.1 to 1mm in 2-24 min at a gas supersaturation of 620 kPa and lower. There are two phases of bubble development. The slow and disperse initiation of active spots (from nanobubbles to gas micronuclei) continues for more than 1h, whereas the fast increase in size (2-24 min) is governed by diffusion. Bubble-based decompression models should not artificially reduce diffusion constants, but rather take both phases of bubble development into consideration.

Surface Tension and Adsorption without a Dividing Surface

The ingenious concept of a dividing surface of zero thickness that was introduced by Gibbs is the basis of the theory of surface tension and adsorption. However, some fundamental questions, mainly those related to the location of the dividing surface and the proper definition of relative adsorption, have remained open over the years. To avoid these questions, the present paper proposes to analyze an interfacial phase by defining a thermodynamic system of constant, but nonzero thickness. The interfacial phase is analyzed as it really is, namely a nonuniform three-dimensional entity. The current analysis redevelops the equation for calculating surface tension, though with different assumptions. However, the main point in the proposed model is that the thermodynamic interfacial system, due to its fixed thickness, conforms to the requirement of first-order homogeneity of the internal energy. This property is the key that allows using the Gibbs adsorption isotherm. It is also characteristic of the Gibbs dividing surface model, but has not always been discussed with regard to subsequent models. The resulting equation leads to a simple, "natural" expression for the relative adsorption. This expression may be compared with simulations and sophisticated surface concentration measurements, and from which the dependence of interfacial tension on the solution composition can be derived. Finally, it is important to point out that in order to calculate the interfacial tension as well as the relative adsorption from data on the properties of the interfacial phase, there is no need to know its exact thickness, as long as it is bigger than the actual thickness but sufficiently small.

Vapor-liquid nucleation: the solid touch

Vapor-liquid nucleation is a ubiquitous process that has been widely researched in many disciplines. Yet, case studies are quite scattered in the literature, and the implications of some of its basic concepts are not always clearly stated. This is especially noticeable for heterogeneous nucleation, which involves a solid surface in touch with the liquid and vapor. The current review attempts to offer a comprehensive, though concise, thermodynamic discussion of homogeneous and heterogeneous nucleation in vapor-liquid systems. The fundamental concepts of nucleation are detailed, with emphasis on the role of the chemical potential, and on intuitive explanations whenever possible. We review various types of nucleating systems and discuss the effect of the solid geometry on the characteristics of the new phase formation. In addition, we consider the effect of mixing on the vapor-liquid equilibrium. An interesting sub-case is that of a non-volatile solute that modifies the chemical potential of the liquid, but not of the vapor. Finally, we point out topics that need either further research or more exact, accurate presentation.

Stabilization of Boiling Nuclei by Insoluble Gas: Can a Nanobubble Cloud Exist?

Liquid boiling that starts off with an insoluble gas bubble is thermodynamically analyzed. This case is an idealization of very low gas solubility and very slow diffusion of this gas in the boiling liquid. The analysis is made for a spherical, freely suspended bubble as well as for a bubble attached to a solid surface. The results predict the spontaneous formation of a stable, critical bubble at pressures higher than the saturation pressure. Stable critical radii are also predicted for pressures lower than the saturation pressure but in addition to unstable, larger critical bubbles. These bubbles are affected by the presence and nature of a solid surface. The present analysis provides a basis for a feasible explanation of the long-debated, long-time stability of nanobubbles.

Bubble size on detachment from the luminal aspect of ovine large blood vessels after decompression: The effect of mechanical disturbance

Bubbles nucleate and develop after decompression at active spots on the luminal aspect of ovine large blood vessels. Series of bubbles were shown to detach from the active spot with a mean diameter of 0.7-1.0mm in calm conditions. The effect of mechanical disturbance (striking the bowl containing the vessel or tangential flow) was studied on ovine blood vessels stretched on microscope slides and photographed after hyperbaric exposure. Diameter on detachment after a heavy blow to the bowl was 0.87 ± 0.43 mm (mean ± SD), no different from bubbles which detached without striking the bowl (0.86 ± 0.28 mm). Bubble diameter on detachment during pulsatile tangential flow at 234 cm/min, 0.99 ± 0.36 mm, was not smaller than that seen in the same blood vessels in calm conditions (0.81 ± 0.34 mm). The active spots were stained for lipids, proving their hydrophobicity. The most abundant active spots, which produced only a few bubbles, did not stain for lipids thereafter. The possibility that phospholipids were removed along with detached bubbles may correlate with acclimation to diving. The finding of bubble production at the active spots matches observed phenomena in divers: variable sensitivity to decompression, acclimation to diving, the effect of elevated gas load on increased bubble formation, a higher bubble score in the second dive on the same day, and unexplained neurological symptoms after decompression. Large bubbles released from the arterial circulation give serious cause for concern.

Rate of bubble coalescence following dynamic approach: collectivity-induced specificity of ionic effect

A simple, quantitative model is suggested to explain the specificity of ions with respect to inhibition of bubble coalescence following a dynamic approach. For the first time, the mode of thinning of the film in between the bubbles, as determined by the density of the bubble dispersion, is recognized as a determining factor. The specificity of the ionic effect is explained by a major difference in adsorption properties of ions, which is enhanced by the film thinning. This leads to charge separation that forms an electrical double layer at each interface of the thin, liquid film, and consequently to electrostatic repulsion. This effect is described by a simple theoretical model that consists of two fundamental equations: mass conservation of each ion in the film, and the Gibbs adsorption equation. In addition, we explain the rapid coalescence of bubbles in purified water under dynamic conditions, which is in contrast with the very slow coalescence under quasi-static conditions.

Ex vivo bubble production from ovine large blood vessels: size on detachment and evidence of "active spots"

Nanobubbles formed on the hydrophobic silicon wafer were shown to be the source of gas micronuclei from which bubbles evolved during decompression. Bubbles were also formed after decompression on the luminal surface of ovine blood vessels. Four ovine blood vessels: aorta, pulmonary vein, pulmonary artery, and superior vena cava, were compressed to 1013 kPa for 21 h. They were then decompressed, photographed at 1-s intervals, and bubble size was measured on detachment. There were certain spots at which bubbles appeared, either singly or in a cluster. Mean detachment diameter was between 0.7 and 1.0 mm. The finding of active spots at which bubbles nucleate is a new, hitherto unreported observation. It is possible that these are the hydrophobic spots at which bubbles nucleate, stabilise, and later transform into the gas micronuclei that grow into bubbles. The possible neurological effects of these large arterial bubbles should be further explored.

Rate of bubble coalescence following quasi-static approach: screening and neutralization of the electric double layer

Air-bubble coalescence in aqueous electrolytic solutions, following quasi-static approach, was studied in order to understand its slow rate in purified water and high rate in electrolytic solutions. The former is found to be due to surface charges, originating from the speciation of dissolved CO₂, which sustain the electric double layer repulsion. Rapid coalescence in electrolytic solutions is shown to occur via two different mechanisms: (1) neutralization of the carbonaceous, charged species by acids; or (2) screening of the repulsive charge effects by salts and bases. The results do not indicate any ion specificity. They can be explained within the DLVO theory for the van der Waals and electric double layer interactions between particles, in contrast to observations of coalescence following dynamic approach. The present conclusions should serve as a reference point to understanding the dynamic behavior.

Evolution of bubbles from gas micronuclei formed on the luminal aspect of ovine large blood vessels

It has been shown that tiny gas nanobubbles form spontaneously on a smooth hydrophobic surface submerged in water. These nanobubbles were shown to be the source of gas micronuclei from which bubbles evolved during decompression of silicon wafers. We suggest that the hydrophobic inner surface of blood vessels may be a site of nanobubble production. Sections from the right and left atria, pulmonary artery and vein, aorta, and superior vena cava of sheep (n=6) were gently stretched on microscope slides and exposed to 1013 kPa for 18 h. Hydrophobicity was checked in the six blood vessels by advancing contact angle with a drop of saline of 71±19°, with a maximum of about 110±7° (mean±SD). Tiny bubbles ~30 μm in diameter rose vertically from the blood vessels and grew on the surface of the saline, where they were photographed. All of the blood vessels produced bubbles over a period of 80 min. The number of bubbles produced from a square cm was: in the aorta, 20.5; left atrium, 27.3; pulmonary artery, 17.9; pulmonary vein, 24.3; right atrium, 29.5; superior vena cava, 36.4. More than half of the bubbles were present for less than 2 min, but some remained on the saline-air interface for as long as 18 min. Nucleation was evident in both the venous (superior vena cava, pulmonary artery, right atrium) and arterial (aorta, pulmonary vein, left atrium) blood vessels. This newly suggested mechanism of nucleation may be the main mechanism underlying bubble formation on decompression.

Detection of Alzheimer’s and Parkinson’s disease from exhaled breath using nanomaterial-based sensors

Aim: To study the feasibility of a novel method in nanomedicine that is based on breath testing for identifying Alzheimer’s disease (AD) and Parkinson’s disease (PD), as representative examples of neurodegenerative conditions. Patients & methods: Alveolar breath was collected from 57 volunteers (AD patients, PD patients and healthy controls) and analyzed using combinations of nanomaterial-based sensors (organically functionalized carbon nanotubes and gold nanoparticles). Discriminant factor analysis was applied to detect statistically significant differences between study groups and classification success was estimated using cross-validation. The pattern identification was supported by chemical analysis of the breath samples using gas chromatography combined with mass spectrometry. Results: The combinations of sensors could clearly distinguish AD from healthy states, PD from healthy states, and AD from PD states, with a classification accuracy of 85, 78 and 84%, respectively. Gas chromatography combined with mass spectrometry analysis showed statistically significant differences in the average abundance of several volatile organic compounds in the breath of AD, PD and healthy subjects, thus supporting the breath prints observed with the sensors. Conclusion: The breath prints that were identified with combinations of nanomaterial-based sensors have future potential as cost-effective, fast and reliable biomarkers for AD and PD.

Original submitted 29 January 2012; Revised submitted 8 May 2012; Published online 15 October 2012

Dynamics of gas micronuclei formed on a flat hydrophobic surface, the predecessors of decompression bubbles

It is a long-standing hypothesis that the bubbles which evolve as a result of decompression have their origin in stable gas micronuclei. In a previous study (Arieli and Marmur, 2011), we used hydrophilic and monolayer-covered hydrophobic smooth silicon wafers to show that nanobubbles formed on a flat hydrophobic surface may be the gas micronuclei responsible for the bubbles that evolve to cause decompression sickness. On decompression, bubbles appeared only on the hydrophobic wafers. The purpose of the present study was to examine the dynamics of bubble evolution. The numbers of bubbles after decompression were greater with increasing hydrophobicity. Bubbles appeared after decompression from 150 kPa, and their density increased with elevation of the exposure pressure (and supersaturation), up to 400 kPa. The normal force of attraction between the hydrophobic surface and the bubble, as determined from the volume of bubbles leaving the surface of the wafer, was 38×10(-5) N and the tangential force was 20×10(-5) N. We discuss the correlation of these results with previous reports of experimental decompression and bubble formation, and suggest to consider appropriate modification of decompression models.

The role of multiscale roughness in the Lotus effect: is it essential for super-hydrophobicity?

The role of multiscale (hierarchical) roughness in optimizing the structure of nonwettable (superhydrophobic) solid surfaces was theoretically studied for 2D systems of a drop on three different types of surface topographies with up to four roughness scales. The surface models considered here were sinusoidal, flat-top pillars, and triadic Koch curves. Three criteria were used to compare between the various topographies and roughness scales. The first is the transition contact angle (CA) between the Wenzel (W) and Cassie-Baxter (CB) wetting states, above which the CB state is the thermodynamically stable one. The second is the solid-liquid (wetted) interfacial area, as an indicator for the ease of roll-off of a drop from the superhydrophobic surfaces. The third is the protrusion height that reflects the mechanical stability of the surface against breakage. The results indicate that multiscale roughness per se is not essential for superhydrophobicity; however, it mainly decreases the necessary protrusion height. Thus, multiscale roughness is beneficial for the Lotus effect mostly with regard to mechanical stability. The sinusoidal topography with three levels of roughness scales is best for nonwettability out of the topographies studied here. This observation may partially explain why Nature chose rounded-top protrusions, such as those on the Lotus leaf. The least useful topography is the flat-top pillars with three roughness scales. In the case of the triadic Koch topography, four roughness scales are required to have nonwettable surface.

Comparison of sessile drop and captive bubble methods on rough homogeneous surfaces: a numerical study

Quasi-static experiments using sessile drops and captive bubbles are the most employed methods for measuring advancing and receding contact angles on real surfaces. These observable contact angles are the most easily accessible and reproducible. However, some properties of practical surfaces induce certain phenomena that cause a built-in uncertainty in the estimation of advancing and receding contact angles. These phenomena are well known in surface thermodynamics as stick-slip phenomena. Following the work of Marmur (Marmur, A. Colloids Surf., A 1998, 136, 209-215), where the stick-slip effects were studied with regard to sessile drops and captive bubbles on heterogeneous surfaces, we developed a novel extension of this study by adding the effects of roughness to both methods for contact angle measurement. We found that the symmetry between the surface roughness problem and the chemical heterogeneity problem breaks down for drops and bubbles subjected to stick-slip effects.

Superhydrophobic and superoleophobic nanocellulose aerogel membranes as bioinspired cargo carriers on water and oil

We demonstrate that superhydrophobic and superoleophobic nanocellulose aerogels, consisting of fibrillar networks and aggregates with structures at different length scales, support considerable load on a water surface and also on oils as inspired by floatation of insects on water due to their superhydrophobic legs. The aerogel is capable of supporting a weight nearly 3 orders of magnitude larger than the weight of the aerogel itself. The load support is achieved by surface tension acting at different length scales: at the macroscopic scale along the perimeter of the carrier, and at the microscopic scale along the cellulose nanofibers by preventing soaking of the aerogel thus ensuring buoyancy. Furthermore, we demonstrate high-adhesive pinning of water and oil droplets, gas permeability, light reflection at the plastron in water and oil, and viscous drag reduction of the fluorinated aerogel in contact with oil. We foresee applications including buoyant, gas permeable, dirt-repellent coatings for miniature sensors and other devices floating on generic liquid surfaces.

Chemical nano-heterogeneities detection by contact angle hysteresis: theoretical feasibility

The theoretical feasibility of detecting chemical nanoheterogeneities on solid surfaces by measurement of contact angle hysteresis (CAH) was studied, using simplified models of cylindrical (2D) and axisymmetric (3D) drops on corresponding models of chemically heterogeneous, smooth solid surfaces. This feasibility depends on the ratio between the external energy input to the drop and the energies needed to deform its liquid-gas interface and move the contact line across energy barriers. A ubiquitous source of external energy is building vibrations, since most contact-angle measurements are done in buildings. The energy barriers that oppose the motion of the contact line were numerically calculated for various parameters of the two systems. The variations of the liquid-gas interfacial energy are discussed in terms of orders of magnitude. By comparing these energies, it is concluded that under regular ("barely perceptible") building vibrations CAH measurements may detect chemical heterogeneities at the few nanometers scale.

Comparing contact angle measurements and surface tension assessments of solid surfaces

Four types of contact angles (receding, most stable, advancing, and "static") were measured by two independent laboratories for a large number of solid surfaces, spanning a large range of surface tensions. It is shown that the most stable contact angle, which is theoretically required for calculating the Young contact angle, is a practical, useful tool for wettability characterization of solid surfaces. In addition, it is shown that the experimentally measured most stable contact angle may not always be approximated by an average angle calculated from the advancing and receding contact angles. The "static" CA is shown in many cases to be very different from the most stable one. The measured contact angles were used for calculating the surface tensions of the solid samples by five methods. Meaningful differences exist among the surface tensions calculated using four previously known methods (Owens-Wendt, Wu, acid-base, and equation of state). A recently developed, Gibbsian-based correlation between interfacial tensions and individual surface tensions was used to calculate the surface tensions of the solid surfaces from the most stable contact angle of water. This calculation yielded in most cases higher values than calculated with the other four methods. On the basis of some low surface energy samples, the higher values appear to be justified.

Correlating interfacial tensions with surface tensions: a gibbsian approach

The Gibbs approach to the definition of interfacial and surface tensions is used for developing a general form for a correlation between interfacial tensions and their corresponding surface tensions. This general equation can serve as a starting point for either further fundamental development or an empirical search for a correlation that fits experimental data. In this Article, the latter approach is followed. The general equation is transformed by a few reasonable assumptions into a relatively simple framework for empirically correlating interfacial tensions with their corresponding surface tensions. The agreement of results of the present empirical correlation with a large body of experimental data for interfacial tensions in saturated liquid-liquid systems is better than that of previously suggested correlations. It is hoped that this correlation will be useful also for solid-liquid interfacial tensions, for which direct measurements are not yet available.

Optical control of thermocapillary effects in complex nanofluids

We study the strong coupling of light and nanoparticle suspensions and their surface tension effect in capillaries. We show experimentally and theoretically that increasing the intensity of a narrow laser beam passing through a capillary far away from the surface results in a significant decrease in the fluid level. The underlying mechanism relies on light-induced redistribution of nanoparticles in the bulk and the surface of the fluid, facilitating continuous optical control over the surface position. The experiments manifest optical control from afar over properties of fluid surfaces.

Filled nanoporous surfaces: controlled formation and wettability

The controlled filling of hydrophobic nanoporous surfaces with hydrophilic molecules and their wetting properties are described and demonstrated by using thiocholesterol (TC) self-assembled monolayers (SAMs) on gold and mercaptoundecanoic acid (MUA) as the filling agent. A novel procedure was developed for filling the nanopores in the TC SAMs by immersing them into a "cocktail" solution of TC and MUA, with TC in huge excess. This procedure results in an increasing coverage of MUA with increasing immersion time up to an area fraction of approximately 23%, while the amount of TC remains almost constant. Our findings strongly support earlier observations where linear omega-substituted alkanethiols selectively fill defects (nanopores) in the TC SAM (Yang et al. Langmuir 1997, 12, 1704-1707). They also support the formation of a homogeneously mixed SAM, given by the distribution of TC on the gold surface, rather than of a phase-segregated overlayer structure with domains of varying size, shape, and composition. The wetting properties of the filled SAMs were investigated by measuring the most stable contact angle as well as contact angle hysteresis. It is shown that the most stable contact angle is very well described by the Cassie equation, since the drops are much larger than the scale of chemical heterogeneity of the SAM surfaces. In addition, it is demonstrated that contact angle hysteresis is sensitive to the chemical heterogeneity of the surface, even at the nanometric scale.

When Wenzel and Cassie are right: reconciling local and global considerations

The condition under which the Wenzel or Cassie equation correctly estimates the most stable contact angle is reiterated and demonstrated: these equations do hold when the drop size is sufficiently large compared with the wavelength of roughness or chemical heterogeneity. The numerical demonstrations somewhat mimic recent experiments that seemingly refuted the Wenzel and Cassie equations and show that these experiments were performed only for drops of sizes similar in order of magnitude to the wavelength of roughness or chemical heterogeneity. Under such conditions, the Wenzel and Cassie equations are a priori not expected to be valid. It is also explained that both the local equilibrium condition at the contact line and the global equilibrium condition involving the wetted area within the contact line are necessary and complementary.

From hygrophilic to superhygrophobic: theoretical conditions for making high-contact-angle surfaces from low-contact-angle materials

The possibility of making high-contact-angle, rough surfaces from low-contact-angle materials has recently been suggested and demonstrated. A thermodynamic analysis of this possibility in terms of feasibility and stability is presented. It turns out that only roughness topographies that conform to a feasibility condition which is developed in the present paper can support this phenomenon. Even under conditions that support the phenomenon, the high-contact-angle state may not be stable, and transition from the heterogeneous (Cassie-Baxter) wetting regime to the homogeneous (Wenzel) regime with a lower contact angle may occur. In addition, it is suggested to use the general terms hygrophilic and hygrophobic (based on the Greek prefix hygro- that means liquid) to describe low- and high-contact-angle surfaces, respectively.

Porous media characterization by the two-liquid method: effect of dynamic contact angle and inertia

The validity of using the Lucas-Washburn (LW) equation for porous media characterization by the two-liquid capillary penetration method was tested numerically and experimentally. A cylindrical capillary of known radius and contact angle was used as a model system for the tests. It was found that using the LW equation (i.e., ignoring inertia and dynamic contact angle effects) may lead to very erroneous assessment of the capillary radius and the equilibrium contact angle, for a relatively wide range of capillary radii and equilibrium contact angles. A correct assessment requires the application of a penetration kinetics equation that considers inertia and the dynamic contact angle.

Groovy drops: effect of groove curvature on spontaneous capillary flow

Spontaneous capillary flow (SCF) of a drop in a groove with an ideally sharp corner is possible when the Concus-Fin (CF) condition is fulfilled. However, since ideally sharp corners do not exist in reality, it is important to understand the effect of finite corner curvature on SCF. This effect is analytically studied for long drops in a V-shaped groove with a curved corner, leading to a generalization of the CF condition for such drops. The generalized condition implies that SCF depends on the geometry of the corner as well as on the dimensionless length of the drop, in addition to its dependence on the opening angle and contact angle that is covered by the CF condition. Specific calculations are presented for rounded corners. In addition, this effect is numerically calculated for short drops in V-shaped grooves with rounded corners, using the Surface Evolver software. The results of both types of calculations show that even a relatively small corner radius strongly affects the possibility of SCF: when the corner is not ideally sharp, SCF requires conditions that are more difficult to achieve than predicted by the CF condition; also, the spreading of the drop stops at a finite length and does not proceed indefinitely.

Soft contact: measurement and interpretation of contact angles

The measurement and interpretation of contact angles deceptively appear to be simple. This paper attempts to summarize the pitfalls in the field, and how to avoid them. First, the fundamental underlying theory that is necessary in order to properly measure and interpret contact angles is discussed, emphasizing recent developments. Then, the practical implications of these theoretical aspects are presented. In addition, the discussion highlights the missing pieces of the picture that need to be completed through future research.

Underwater superhydrophobicity: theoretical feasibility

The possibility of underwater superhydrophobicity is theoretically analyzed. Thermodynamic equilibrium and stability conditions are formulated, and the design goal is defined as minimizing the solid-liquid contact area. It is shown that for sufficiently high roughness ratios, underwater superhydrophobicity may be feasible and thermodynamically stable. In addition, some generic design optimization considerations are demonstrated.

Validity and accuracy in evaluating surface tension of solids by additive approaches

The validity and the accuracy of both the Owens and Wendt and the Lifshitz-van der Waals/acid-base (LW/AB) methods for the determination of surface tensions of solids have been examined for a wide variety of situations. In each case, the allowed range of contact angles that result in positive values of all the square roots of the surface tension components of the solid has first been determined. Then the maximum relative errors in the surface tensions of solids that result from errors in contact angle measurements have been calculated within the allowed range. For both methods, it has been found that the maximum relative errors are minimal if one of the liquids is apolar. In the case of the LW/AB method, minimal errors are obtained if, in addition, the other two liquids are monopolar with different polarities. However, the more similar are the properties of the liquids, the narrower is the allowed range, and the larger are the maximum relative errors.

Super-hydrophobicity fundamentals: implications to biofouling prevention

The theory of wetting on super-hydrophobic surfaces is presented and discussed, within the general framework of equilibrium wetting and contact angles. Emphasis is put on the implications of super-hydrophobicity to the prevention of biofouling. Two main lines of thought are discussed, viz. i) "mirror imaging" of the Lotus effect, namely designing a surface that repels biological entities by being super-hydrophilic, and ii) designing a surface that minimises the water-wetted area when submerged in water (by keeping an air film between the water and the surface), so that the suspended biological entities have a low probability of encountering the solid surface.

Drops down the hill: theoretical study of limiting contact angles and the hysteresis range on a tilted plate

The limiting inclination angle (slip angle), for which a two-dimensional water drop may be at equilibrium on a chemically heterogeneous surface, is exactly calculated for a variety of cases. The main conclusion is that, in the cases studied, the contact angles at the upper and lower contact line do not always simultaneously equal the receding and advancing contact angles, respectively. On a hydrophobic surface, the lowest contact angle (at the upper contact line) tends to be approximately equal to the receding contact angle, while the highest contact angle (at the lower contact line) may be much lower than the advancing contact angle. For hydrophilic surfaces, the opposite is true. These conclusions imply that the hysteresis range cannot in general be measured by analyzing the shape of a drop on an inclined plane. Also, the limiting inclination angle cannot in general be calculated from the classical equation based only on the advancing and receding contact angles.

Contact angle measurement on rough surfaces

A new method for the measurement of apparent contact angles at the global energy minimum on real surfaces has been developed. The method consists of vibrating the surface, taking top-view pictures of the drop, monitoring the drop roundness, and calculating the contact angle from the drop diameter and weight. The use of the new method has been demonstrated for various rough surfaces, all having the same surface chemistry. In order to establish the optimal vibration conditions, the proper ranges for the system parameters (i.e., drop volume, vibration time, frequency of vibration, and amplitude of vibration) were determined. The reliability of the method has been demonstrated by the fact that the ideal contact angles of all surfaces, as calculated from the Wenzel equation using the measured apparent contact angles, came out to be practically identical. This ideal contact angle has been compared with three methods of calculation from values of advancing and receding contact angles.

The Lotus effect: superhydrophobicity and metastability

To learn how to mimic the Lotus effect, superhydrophobicity of a model system that resembles the Lotus leaf is theoretically discussed. Superhydrophobicity is defined by two criteria: a very high water contact angle and a very low roll-off angle. Since it is very difficult to calculate the latter for rough surfaces, it is proposed here to use the criterion of a very low wet (solid-liquid) contact area as a simple, approximate substitute for the roll-off angle criterion. It is concluded that nature employs metastable states in the heterogeneous wetting regime as the key to superhydrophobicity on Lotus leaves. This strategy results in two advantages: (a) it avoids the need for high steepness protrusions that may be sensitive to breakage and (b) it lowers the sensitivity of the superhydrophobic states to the protrusion distance.