Vapor Surface Tension Research Articles

Path dependence of surface–tension scaling in binary mixtures

A mean-field free-energy functional for an n-component mixture with an integral non-local interaction is introduced and then written explicitly for a binary mixture. We use this functional to calculate the liquid–vapor surface tension with parameters chosen to model CO 2/ n–C 4H 10 and CO 2/ n–C 10H 22, and we examine the scaling of the surface tension as a function of the difference in density between the liquid and vapor phases as various critical points are approached. Each critical point is approached on either a constant-temperature or constant-pressure path; we investigate the path dependence of the scaling behavior. For the constant-temperature paths in the CO 2/ n–C 4H 10 mixture, we compare our calculated results with experimental data. We find no significant dependence of the scaling on the path to the critical point. We note that the asymptotic scaling holds for a larger range of densities the higher the temperature of the critical point.

Characterization of adsorbed protein layers by low-rate dynamic liquid–fluid contact angle measurements using axisymmetric drop shape analysis (part II)

Inverse low-rate dynamic contact angles were measured using captive air bubbles in conjunction with axisymmetric drop shape analysis (ADSA) to study the wettability of adsorbed protein layers in their highly hydrated state at the stationary end point of the adsorption process. The initial surface state of smooth fluorohydrocarbon polymer films, used as substrates for the adsorption of two human plasma proteins (albumin, fibrinogen) from phosphate buffered saline, has also been studied by low-rate dynamic contact angle measurements using sessile liquid drops or captive air bubbles. The solid–vapour surface tension of the dry polymer film calculated from the equation-of-state approach for solid–liquid interfacial tensions was found to be 14.1 mJ m −2, from the mean advancing water contact angle of 114.9±0.9°. Concerning the receding contact angles of the sessile liquid drops, a time dependence was revealed probably due to the modification of the polymer surface by the liquids. After the protein adsorption the physicochemical state of the solid–liquid interface is changed from a hydrophobic to a hydrophilic state observed by the decrease of the inverse advancing and receding contact angles. Differences in the overall hydrophobicity/hydrophilicity of the adsorbed protein layers could be revealed depending on the type of protein and on the concentration of the protein solution.

Contact angle measurement and contact angle interpretation

Recent progress in the correlation of contact angles with solid surface tensions are summarized. The measurements of meaningful contact angles in terms of surface energetics are also discussed. It is shown that the controversy with respect to measurement and interpretation of contact angles are due to the fact that some (or all) of the assumptions made in all energetic approaches are violated when contact angles are measured and processed. For a large number of polar and non-polar liquids on different solid surfaces, the liquid–vapor surface tension times cosine of the contact angle, γ lv cosθ, is shown to depend only on the liquid–vapor surface tension γ lv , and the solid–vapor surface tension γ sv when the appropriate experimental techniques and procedures are used. Equations which follow these experimental patterns and which allow the determination of solid surface tensions from contact angles are discussed. Universality of these experimental contact angle patterns is illustrated; other reasons which may cause data to deviate from the patterns slightly are discussed. It is found that surface tension component approaches do not reflect physical reality. Assuming the fact that solid surface tension is constant for one and the same solid surface, experimental contact angle patterns are employed to deduce a functional relationship to be used in conjunction with Young's equation for determining solid surface tensions. The explicit form of such a relation is obtained by modifying Berthelot's rule together with experimental data; essentially constant solid surface tension values are obtained, independent of liquid surface tension and molecular structure. A new combining rule is also derived based on an expression similar to one used in molecular theory; such a combining rule should allow a better understanding of the molecular interactions between unlike solid–liquid pairs from like pairs. Existing static contact angles for 34 different types of solid surfaces from Zisman et al. are evaluated in terms of their solid surface tensions using experimental contact angle patterns. A FORTRAN computer program has been implemented to automate these procedures. It is found that literature contact angles do not have to be discarded completely; they can be used to determine solid surface tensions, with caution. The surface tensions for the 34 solid surfaces from Zisman et al. are also reported.

Influence of thermodynamic and thermophysical properties of water-based working fluids for bubble pump operated vapour absorption refrigerator

Miniaturization of the absorption refrigerator requires an air cooled absorber and condenser and replacement of the customary solution pump by a bubble pump. The operating pressures in the bubble pump operated two fluid vapour absorption refrigerator have to be very low (vacuum) so as to make use of the hydrostatic principle to maintain the required pressure difference between the condenser and evaporator. Hence, only water and alcohol based working fluid combinations are found suitable. Thermodynamic properties, such as specific heat and heat of mixing, and thermophysical properties, such as vapour pressure, density, viscosity, surface tension and solubility, are necessary for the overall performance evaluation of such a refrigerator. In this paper, sixteen water based working combinations have been analyzed and compared with reference to the solution density governing the hydrostatic height, viscosity and specific heat affecting the heat and mass transfer and solubility to avoid crystallization.

Measuring and interpreting contact angles: a complex issue

Low-rate dynamic contact angles of 30 liquids on a FC-725-coated wafer surface were measured by an automated axisymmetric drop shape analysis-profile (ADSA-P). Surprisingly, results indicate that FC-725 behaves differently in some respects from what one would expect for non-polar surfaces: only nine liquids yield essentially constant contact angles whereas the others show slip/stick contact angle behaviour. In the worst case, the contact angle increases from ca 50 to 160° at essentially constant three-phase contact radius. These angles should be disregarded for the interpretation in terms of surface energetics since there is no guarantee that Young's equation is applicable. If one employs a conventional goniometer-sessile drop technique, such contact angle behaviour cannot be easily seen in all cases. These results indicate that the claim from van Oss et al. [Langmuir 4 (1988) 884] that liquids with the same contact angles do not have the same surface tensions is misleading. If the meaningful contact angles are plotted as the liquid–vapour surface tension times cosine of the contact angle versus the liquid–vapour surface tension, that is, γ lv cos θ versus γ lv, a smooth curve emerges. Thus, intermolecular forces (or surface tension components) do not have an additional and independent effect on the contact angles, in good agreement with the results from other studies on non-polar and polar polymers.

Low-Rate Dynamic Contact Angles on Poly(methyl methacrylate) and the Determination of Solid Surface Tensions

Low-rate dynamic contact angles of nine liquids on a poly(methyl methacrylate) (PMMA) polymer are measured by an automated axisymmetric drop shape analysis—profile (ADSA-P). It is found that two liquids dissolved the polymer on contact. From the experimental contact angles of the other seven polar and nonpolar liquids, it is found that the liquid–vapor surface tension times cosine of the contact angle changes smoothly with the liquid–vapor surface tension (i.e., γlνcos θ depends only on γlνfor a given solid surface). The dependence of γlνcos θ on γsνis explicitly illustrated by replacing the solid surface from the PMMA to other methacrylate polymers: such a procedure shifts the curves in a very regular manner. Thus, because of Young's equation, γsldepends only on γlνand γsν. This contact angle pattern is in harmony with those from other inert and noninert (polar and nonpolar) surfaces. The solid–vapor surface tension of PMMA calculated from the equation of state approach for solid–liquid interfacial tensions is found to be 38.5 mJ/m2, with a 95% confidence limit of ±0.5 mJ/m2from the experimental contact angles of the seven liquids.

Low-rate Dynamic Contact Angles on Poly(methyl methacrylate/n-butyl methacrylate) and the Determination of Solid Surface Tensions

Low-rate dynamic contact angles of 12 liquids on a poly(methyl methacrylate/n-butyl methacrylate) P(MMA/nBMA) copolymer are measured by an automated axisymmetric drop shape analysis-profile (ADSA-P). It is found that 6 liquids yield non-constant contact angles, and/or dissolve the polymer on contact. From the experimental contact angles of the remaining 6 liquids, it is found that the liquid- vapour surface tension times the cosine of the contact angle changes smoothly with the liquid-vapour surface tension, i.e., γiv cos θ depends only on γiv for a given solid surface (or solid surface tension). This contact angle pattern is in harmony with those from other inert and noninert (polar and non-polar) surfaces [34-42, 51 -53]. The solid-vapour surface tension calculated from the equation-of-state approach for solid -liquid interfacial tensions [14] is found to be 34.4 mJ/m2, with a 95% confidence limit of \\pm 0.8mJ/m2, from the experimental contact angles of the 6 liquids.

Low-rate dynamic contact angles on poly( n -butyl methacrylate) and the determination of solid surface tensions

Low-rate dynamic contact angles of 22 liquids on a poly(n-butyl methacrylate) (PnBMA) polymer are measured by an automated axisymmetric drop shape analysis-profile (ADSA-P). It is found that 16 liquids yielded non-constant contact angles, and/or dissolved the polymer on contact. From the experimental contact angles of the remaining 6 liquids, it is found that the liquid–vapor surface tension times cosine of the contact angle changes smoothly with the liquid–vapor surface tension, i.e. γlv cos θ depends only on γlv for a given solid surface (or solid surface tension). This contact angle pattern is in harmony with those from other inert and non-inert (polar and non-polar) surfaces [34–37, 45–47]. The solid–vapor surface tension calculated from the equation-of-state approach for solid-liquid interfacial tensions [14] is found to be 28.8 mJ/m2, with a 95% confidence limit of ±0.5 mJ/m2, from the experimental contact angles of the 6 liquids.

Comparison of methanol-based working fluid combinations for a bubble pump-operated vapour absorption refrigerator

Miniaturization of an alcohol-based absorption refrigerator requires an air-cooled absorber and condenser and the replacement of customary solution pumps by the bubble pump. Evaluation of such a refrigerator requires thermodynamic (specific heat and heat of mixing) and thermophysical (vapour pressure, density, viscosity, surface tension and solubility) properties of refrigerant–absorbent solution. These property correlations for five alcohol-based working combinations, majority of them obtained by curve fitting, have been complied and presented in this paper along with their validity ranges and percentage of error. The working fluids have been analyzed and compared with reference to the solution density governing the hydrostatic height, viscosity and specific heat affecting the heat and mass transfer and solubility to avoid crystallization. Further the variations of performance parameters like cut-off temperature, circulation ratio, coefficient of performance and efficiency ratio of these working fluids with respect to various operating conditions are discussed. © 1998 John Wiley & Sons, Ltd.

Valveless pumping using traversing vapor bubbles in microchannels

Pumping of fluids in microchannels using the movement of a single or multiple vapor bubble(s) is proposed, analyzed, and demonstrated. The pumping mechanism requires no micromechanical moving parts for actuation by utilizing asymmetric heating which creates a variation in vapor pressure and surface tension due to the heater-induced temperature gradient along the channel. A heat and mass transfer analysis was performed to understand the pumping mechanism and estimate the pumping capability of the micropumping device. To verify the concept and our analysis, a pumping device with a transparent microchannel with a hydraulic diameter of 3.4 μm was fabricated on a silicon wafer using surface micromachining. Experimental results with the first generation device have shown pumping of isopropanol at velocities as high as 160 μm/s (0.5 nl/min flow rate) with a pressure head of approximately 800 Pa.

Wetting and drying of a rigid substrate under variation of the microscopic details

Wetting and drying of a rigid substrate by a Lennard–Jones fluid in molecular dynamics simulations is reported. The size of the substrate particles, being smaller than the fluid particles in former simulations, is now taken to be equal to, respectively, larger than, that of the fluid particles. Recently, for the latter type of system a first-order drying transition has been reported. Like before we find a continuous-like transition for all systems considered. This also holds for substrates with incompletely-filled top layers, the so-called molecularly rough surfaces. All systems studied behave qualitatively alike, but inconsistencies are found in the solid–vapour surface tension on approach of the wetting transition and for the solid–fluid surface tension in general.

Condensation of Refrigerants in Horizontal Microfin Tubes. Numerical Analysis of Heat Transfer for Annular Flow Regime.

A method for predicting the local heat transfer coefficient is presented for film condensation of vapor in a spirally grooved horizontal microfin-tube. Based on the flow observation study performed by the present authors, film flow model between fins in the annular flow regime is proposed. For the fin surface, laminar condensate film controlled by the combined effects of vapor shear and surface tension forces is analyzed. While, in the groove, thick condensate film driven by the vapor shear force is taken into consideration. A parameter which accounts for the transition from annular-to stratified flow regimes is also derived. The present and previous local heat transfer data for fluorocarbon refrigerants in the annular flow regime are found by the present numerical analysis to have a mean absolute deviation of 15.1 percent.

A Predictive Model for Condensation in Small Hydraulic Diameter Tubes Having Axial Micro-Fins

A semiempirical model is proposed to predict the condensation coefficient inside small hydraulic diameter extruded aluminum tubes having microgrooves. The model accounts for the effects of vapor shear and surface tension forces. Surface tension force is effective in enhancing the condensation coefficient as long as the fin tips are not flooded by condensate. This enhancement increases as mass velocity is reduced. At high mass velocity the flow is vapor shear controlled and the surface tension contribution is very small. The surface tension effect is strongly affected by the fin geometry. A smaller fin tip radius provides a higher surface tension drainage force. A large cross sectional area in the interfin region will allow the surface tension enhancement to occur at lower vapor quality. Separate models are developed for the surface tension and vapor shear controlled regimes and the models are combined in the form of an asymptotic equation. The vapor shear model is based on use of an equivalent mass velocity and the heat-momentum transfer analogy. The surface tension model is analytically based. The model is validated by predicting the authors data for two tube geometries using R-12 and R-134a, and the model predicts 95 percent of the condensation data within ±16 percent.

Contact Angles of Liquid Drops on Low-Energy Solid Surfaces

There have been many experiments that have determined the wetting behavior of liquids on low-energy solid surfaces. These experiments show that, in general, the contact angle, θ, measured through the liquid, increases with increasing liquid–vapor surface tension, σlv. Surprisingly, in experiments with some such surfaces, the contact angle of a drop appears to depend almost entirely on the liquid–vapor surface tension and very little on the other properties of the liquid. To gain some insight into this phenomenon, we have used a generalized van der Waals theory to model a diverse series of liquids on a low-energy substrate and to calculate the corresponding surface tensions and contact angles. We find that it is indeed possible to reproduce behavior similar to that seen in experiments, with the data for cos θ plotted versus σlvfalling in a narrow band which could almost be interpreted as a smooth curve. The width of the band in our calculation depends on the ranges of the model parameters and on the details of the molecular interactions.

Are the (Solid−Liquid) Kelvin Equation and the Theory of Interfacial Tension Components Commensurate?

The theory of interfacial tensions, ITC theory, developed over the last half-century from contact angle and wetting studies, has proven to be reliable in many fields of physical and biophysical chemistry. However, interfacial tensions for curved solid surfaces in liquids, estimated in various ways from the Kelvin equation (itself, of course, a very successful theory), give very different results from those estimated by ITC theory. That is, a clear distinction must be made between the Kelvin equation parameter (KEP) of classical freezing theory and the contact angle parameter (CAP) of ITC theory. The difference between KEPs and CAPs is to some degree caused by the incorrect application of addition rules, Antonow's rule, for example, but a more profound discrepancy remains even when correct addition rules are used. One source of a discrepancy in measures of solid−vapor surface tension has been known since Gibbs, but has often not been acted upon, and does not appear to have been routinely quantified. Discre...

Wetting Transition at the Liquid−Air Interface of Methanol−Alkane Mixtures

Wetting transition (Tw) and consolute (CT) temperatures close to the upper critical solution temperature (UCST) have been determined for methanol + n-alkane mixtures where n = 6−12. Tw and the CT were also measured for noninteger n values, i.e., for mixtures of methanol + a binary mixture of two normal alkanes. The liquid−vapor surface tension (σLV) and the liquid−liquid interfacial tension (σLL) were measured at 25 °C. For all mixtures studied the methanol rich-phase is denser than the alkane rich-phase. It is found that while the CT increases continuously, the Tw first increases and then decreases as a function of n. This is the first time that, for a homologous series of mixtures, this behavior has been found. For 6 ≤ n ≤ 8.25 the observed wetting transition was from partial wetting to nonwetting (the alkane rich-phase intrudes between the methanol rich-phase and the vapor) while for 8.5 ≤ n ≤ 12 the transition was from partial to total wetting (the methanol-rich phase intrudes between the alkane rich-...

Density functional theory of nucleation: A semiempirical approach

We present a semiempirical approach to the density functional theory of gas–liquid nucleation, in which the same experimental properties used in classical nucleation theory (equilibrium vapor pressure, liquid density, and surface tension) are used to fit three adjustable parameters in the intermolecular potential. This approach allows direct comparison of nucleation rates with experimental data. Agreement with results on nonane from three different experimental groups is reasonable, although the comparison clearly reveals the scatter in those results and suggests that further experimental measurements by different groups on the same systems would be very valuable. For water and the n-alcohols, this version of density functional theory gives results quite close to classical nucleation theory, implying that it is not a good approximation to describe polar fluids by effective spherically symmetric potentials.

Structure and thermodynamics of the liquid–vapor interface of fluorocarbons and semifluorinated alkane diblocks: A molecular dynamics study

We use molecular dynamics simulations to predict the equilibrium liquid–vapor interface structure and surface tension of two liquids, one comprised of short fluorocarbon–hydrocarbon diblock chains and the other of short fluorocarbon chains. Larger Lennard-Jones diameters and shallower well depths distinguish the perfluoromethyl segments from the methyl ones. In this model, realistic bond angle potentials, torsional potentials, and bond lengths describe the intramolecular interactions. At high temperatures, the density profile of the copolymer melt decays monotonically from the bulk liquid density to the vapor density and the structure of the free surface is similar to that of homopolymer melts. Increasing the chain length or decreasing the temperature causes the fluorocarbon segments to segregate to the free surface. Consequently, the constraint of connectivity between the two blocks results in oscillatory density profiles and a rich structure. Our model predicts that a copolymer can have a lower surface tension than either homopolymer of similar length. We also find that the simple Lennard-Jones based model is deficient in that it fails to explain the surface tension differences between decane and perfluorodecane.

Mechanical vibrations of freely suspended smectic liquid-crystal films.

The low-frequency vibrations of freely suspended smectic liquid-crystal films are analyzed. The characteristic frequencies for very thin films can be used for the determination of the smectic-liquid-crystal--vapor surface tension. In thick films one can also determine from the vibrational frequencies the compressional elastic constant B for smectic liquid crystals.

Molecular dynamics of the surface tension of a drop

The curvature dependence of the liquid–vapor surface tension is described in the limit of small curvatures by Tolman’s length. Measurements of it, either experimentally or in a simulation, have not yet given a clear idea of its magnitude, even its sign is being debated. Previous attempts to relate Tolman’s length to a pressure tensor have led to ill-defined expressions. From an analysis of the pressure difference over the interface of a liquid drop, a pressure tensor expression is obtained for Tolman’s length that does not suffer from the previously encountered inconsistencies. This pressure difference is studied in a simulation of liquid drops, leading to an estimate of Tolman’s length. It appears to be small and bounds are given on it.