Liquid-vapor Interfacial Tension Research Articles

Corresponding-States Modeling of the Speed of Sound of Long-Chain Hydrocarbons

Models based on the corresponding-states principle have been extensively used for several equilibrium and transport properties of different pure and mixed fluids. Some limitations, however, have been encountered with regard to its application to long chain or polar molecules. Following previous studies, where it was shown that the corresponding-states principle could be used to predict thermophysical properties such as vapor–liquid interfacial tension, vapor pressure, liquid density, viscosity, and thermal conductivity of long-chain alkanes, the application of the corresponding-states principle to the estimation of speeds of sound, with a special emphasis on the less studied heavier n-alkane members, is presented. Results are compared with more than four thousand experimental data points as a function of temperature and pressure for n-alkanes ranging from ethane up to n-hexatriacontane. Average deviations are less than 2%, demonstrating the reliability of the proposed model for the estimation of speeds of sound.

Spreading Characteristics and Microscale Evaporative Heat Transfer in an Ultrathin Film Containing a Binary Mixture

Abstract Using image-analyzing interferometry, the thickness profile, in the range of δ0 (adsorbed thickness) <δ<3μm, at the leading edge of a moving ultrathin film with phase change, was measured for a mixture of pentane-octane and compared to that of pure pentane. An improved data-analysis procedure was used to enhance the use of the measured thickness profile. There were significant differences between these two systems, demonstrating the presence of large Marangoni interfacial shear stresses with the mixture. A control volume model was developed to evaluate the differences between the pure fluid and the mixture. The disjoining pressure at the leading edge was found to control fluid flow in the evaporating pure system. However, due to Marangoni stresses, the effect of disjoining pressure on the mixture was found to be small at steady state for the fluxes studied. With an upstream bulk mixture of 2% octane and 98% pentane, a shear stress due to the gradient of the liquid-vapor interfacial surface tension resulting from distillation controlled fluid flow in the contact line region. The average curvature of the evaporating pseudo-steady state pure system was significantly larger (smaller length and larger apparent contact angle at δ=0.1μm) than the isothermal value, whereas the reverse occurred for the mixture. Using a continuum model, a comparison of numerically obtained Marangoni stresses and local evaporative heat flux profiles between the two systems was also made.

Mixtures of charged colloid and neutral polymer: Influence of electrostatic interactions on demixing and interfacial tension

The equilibrium phase behavior of a binary mixture of charged colloids and neutral, nonadsorbing polymers is studied within free-volume theory. A model mixture of charged hard-sphere macroions and ideal, coarse-grained, effective-sphere polymers is mapped first onto a binary hard-sphere mixture with nonadditive diameters and then onto an effective Asakura-Oosawa model [S. Asakura and F. Oosawa, J. Chem. Phys. 22, 1255 (1954)]. The effective model is defined by a single dimensionless parameter-the ratio of the polymer diameter to the effective colloid diameter. For high salt-to-counterion concentration ratios, a free-volume approximation for the free energy is used to compute the fluid phase diagram, which describes demixing into colloid-rich (liquid) and colloid-poor (vapor) phases. Increasing the range of electrostatic interactions shifts the demixing binodal toward higher polymer concentration, stabilizing the mixture. The enhanced stability is attributed to a weakening of polymer depletion-induced attraction between electrostatically repelling macroions. Comparison with predictions of density-functional theory reveals a corresponding increase in the liquid-vapor interfacial tension. The predicted trends in phase stability are consistent with observed behavior of protein-polysaccharide mixtures in food colloids.

Interfacial tensions near critical endpoints: experimental checks of EdGF theory

Predictions of the extended de Gennes–Fisher local-functional theory for the universal scaling functions of interfacial tensions near critical endpoints are compared with experimental data. Various observations of the binary mixture isobutyric acid + water are correlated to facilitate an analysis of the experiments of Nagarajan, Webb and Widom who observed the vapour–liquid interfacial tension as a function of both temperature and density. Antonow's rule is confirmed and, with the aid of previously studied universal amplitude ratios, the crucial analytic ‘background’ contribution to the surface tension near the endpoint is estimated. The residual singular behaviour thus uncovered is consistent with the theoretical scaling predictions and confirms the expected lack of symmetry in (T−Tc ). A searching test of theory, however, demands more precise and extensive experiments; furthermore, the analysis highlights a previously noted but surprising, threefold discrepancy in the magnitude of the surface tension of isobutyric acid + water relative to other systems.

Surface Tension of Decane Binary and Ternary Mixtures with Eicosane, Docosane, and Tetracosane

A tensiometer operating on the Wilhelmy plate method was employed to measure liquid-vapor interfacial tensions of three binary mixtures and one ternary mixture of decane with eicosane, docosane, and tetracosane. Tensions of binary mixtures n-C10H22 + n-C20H42, n-C10H22 + n-C22H46, and n-C10H22 + n-C24H50 and the ternary n-C10H22 + n-C20H42 + n-C24H50 were measured from 293.15 K (or above the solution melting temperature) up to 343.15 K. An average absolute deviation of 1.3% was obtained in comparison with pure component literature data. No mixture information for the reported systems was found in the literature. Results were modeled with a recently proposed corresponding states model. The average absolute deviation was found to be 1.2%.

Scaling for interfacial tensions near critical endpoints

Parametric scaling representations are obtained and studied for the asymptotic behavior of interfacial tensions in the full neighborhood of a fluid (or Ising-type) critical endpoint, i.e., as a function both of temperature and of density/order parameter or chemical potential/ordering field. Accurate nonclassical critical exponents and reliable estimates for the universal amplitude ratios are included naturally on the basis of the "extended de Gennes-Fisher" local-functional theory. Serious defects in previous scaling treatments are rectified and complete wetting behavior is represented; however, quantitatively small, but unphysical residual nonanalyticities on the wetting side of the critical isotherm are smoothed out "manually." Comparisons with the limited available observations are presented elsewhere but the theory invites new, searching experiments and simulations, e.g., for the vapor-liquid interfacial tension on the two sides of the critical endpoint isotherm for which an amplitude ratio -3.25+/-0.05 is predicted.

Simultaneous prediction of interfacial tension and phase equilibria in binary mixtures: An approach based on cubic equations of state with improved mixing rules

Vapor–liquid interfacial tensions of miscible mixtures have been predicted by applying the gradient theory to an improved Peng–Robinson equation of state. The modified Huron–Vidal mixing rule model has been considered for fitting vapor–liquid equilibrium data of miscible polar and non-polar mixtures and, then, for predicting the interfacial tension of these mixtures. According to results, an accurate and globally stable fitting of the vapor–liquid equilibrium data results on a physically coherent prediction of interfacial tensions in the full concentration range. In addition, we present a criteria based on the geometry of the grand potential function along the interface for assessing the predictive value of the GT. Calculations for subcritical binary mixtures are presented and compared to experimental data and the Parachor method for demonstrating the potential of the unified approach suggested in this work.

Liquid–vapor interfacial tension of blood plasma, serum and purified protein constituents thereof

A systematic study of water–air (liquid–vapor, LV) interfacial tension γ lv of blood plasma and serum derived from four different mammalian species (human, bovine, ovine and equine) reveals nearly identical concentration-dependence ( d γ lv d ln C B ; where C B is plasma/serum dilution expressed in v/v concentration units). Comparison of results to a previously-published survey of purified human-blood proteins further reveals that d γ lv d ln C B of plasma and serum is surprisingly similar to that of purified protein constituents. It is thus concluded that any combination of blood-protein constituents will be substantially similar because d γ lv d ln C B of individual proteins are very similar. Experimental results are further interpreted in terms of a recently-developed theory emphasizing the controlling role of water in protein adsorption. Accordingly, the LV interphase saturates with protein adsorbed from bulk solution at a fixed weight-volume concentration (∼436 mg/mL) independent of protein identity or mixture. As a direct consequence, d γ lv d ln C B of purified proteins closely resembles that of mixed solutions and does not depend on the relative proportions of individual proteins comprising a mixture. Thus variations in the plasma proteome between species are not reflected in d γ lv d ln C B nor is serum different from plasma in this regard, despite being depleted of coagulation proteins (e.g. fibrinogen). A comparison of pendant-drop and Wilhelmy-balance tensiometry as tools for assessing protein γ lv shows that measurement conditions employed in the typical Wilhelmy plate approach fails to achieve the steady-state adsorption state that is accessible to pendant-drop tensiometry.

Modeling vapor–liquid interfaces with the gradient theory in combination with the CPA equation of state

With the final purpose of describing the important aqueous + hydrocarbon liquid–liquid interfaces, the gradient theory was combined with the Cubic-Plus-Association equation of state (CPA EOS), taking advantage of the correct representation of interfacial tensions provided by the gradient theory and the correct phase equilibrium of water + hydrocarbon systems already obtained from CPA.In this work, preliminary studies involving the vapor–liquid interfacial tensions of some selected associating and non-associating pure components (water, ethanol, n-butane, n-pentane, n-hexane, n-heptane) are presented and discussed.The good description of equilibrium properties such as vapor pressure and liquid and vapor phase densities is shown in the full range of the vapor–liquid saturation line. For non-associating components, results are compared with those from the Soave–Redlich–Kwong and Peng–Robinson equations of state.A correlation for the influence parameter is presented from which surface tensions can be obtained in a broad temperature range with average errors smaller than 1%.

Catalytic nanomotors: autonomous movement of striped nanorods.

Rod-shaped particles, 370 nm in diameter and consisting of 1 microm long Pt and Au segments, move autonomously in aqueous hydrogen peroxide solutions by catalyzing the formation of oxygen at the Pt end. In 2-3% hydrogen peroxide solution, these rods move predominantly along their axis in the direction of the Pt end at speeds of up to 10 body lengths per second. The dimensions of the rods and their speeds are similar to those of multiflagellar bacteria. The force along the rod axis, which is on the order of 10(-14) N, is generated by the oxygen concentration gradient, which in turn produces an interfacial tension force that balances the drag force at steady state. By solving the convection-diffusion equation in the frame of the moving rod, it was found that the interfacial tension force scales approximately as SR(2)gamma/muDL, where S is the area-normalized oxygen evolution rate, gamma is the liquid-vapor interfacial tension, R is the rod radius, mu is the viscosity, D is the diffusion coefficient of oxygen, and L is the length of the rod. Experiments in ethanol-water solutions confirmed that the velocity depends linearly with the product Sgamma, and scaling experiments showed a strong dependence of the velocity on R and L. The direction of motion implies that the gold surface is hydrophobic under the conditions of the experiment. Tapping-mode AFM images of rods in air-saturated water show soft features that are not apparent in images acquired in air. These features are postulated to be nanobubbles, which if present in hydrogen peroxide solutions, would account for the observed direction of motion.

Mixology of Protein Solutions and the Vroman Effect

Mixing rules stipulating both concentration and distribution of proteins adsorbed to the liquid-vapor (LV) interphase from multicomponent aqueous solutions are derived from a relatively straightforward protein-adsorption model. Accordingly, proteins compete for space within an interphase separating bulk-vapor and bulk-solution phases on a weight, not molar, concentration basis. This results in an equilibrium weight-fraction distribution within the interphase that is identical to bulk solution. However, the absolute interphase concentration of any particular protein adsorbing from an m-component solution is 1/mth that adsorbed from a pure, single-component solution of that protein due to competition with m - 1 constituents. Applied to adsorption from complex biological fluids such as blood plasma and serum, mixing rules suggest that there is no energetic reason to expect selective adsorption of any particular protein from the mixture. Thus, dilute members of the plasma proteome are overwhelmed at the hydrophobic LV surface by the 30 classical plasma proteins occupying the first 5 decades of physiological concentration. Mixing rules rationalize the experimental observations that (i) concentration-dependent liquid-vapor interfacial tension, gammalv, of blood plasma and serum (comprised of about 490 different proteins) cannot be confidently resolved, even though serum is substantially depleted of coagulable proteins (e.g., fibrinogen), and (ii) gammalv of plasma is startlingly similar to that of purified protein constituents. Adsorption-kinetics studies of human albumin (66.3 kDa) and IgM (1000 kDa) binary mixtures revealed that relatively sluggish IgM molecules displace faster-moving albumin molecules adsorbing to the LV surface. This Vroman-effect-like process leads to an equilibrium gammalv reflecting the linear combination of weight/volume concentrations at the surface predicted by theory. Thus, the Vroman effect is interpreted as a natural outcome of protein reorganization to achieve an equilibrium interphase composition dictated by a firm set of mixing rules.

Wavelength dependence of liquid-vapor interfacial tension of Ga.

The wave-vector dependence of the liquid-vapor interfacial tension of Ga, gamma(q), has been determined from diffuse x-ray scattering measurements. The ratio gamma(q)/gamma(0)=1 for q<0.05 A(-1) decreases to 0.5 near q=0.22 A(-1), and increases strongly for larger q. The observed form for gamma(q)/gamma(0) is consistent with the prediction from the Mecke-Dietrich theory when the known stratified liquid-vapor interfacial density profile of Ga and a pseudopotential based pair interaction with appropriate asymptotic (r--> infinity ) behavior are used. The detailed behavior of gamma(q)/gamma(0) depends on the particular forms of both the interfacial density profile and the asymptotic falloff of the atomic pair interaction.

Scaled interfacial activity of proteins at the liquid-vapor interface.

A principal conclusion drawn from observations of time- and concentration-dependent liquid-vapor (LV) interfacial tension gamma(lv) of a diverse selection of proteins ranging from albumin to ubiquitin spanning nearly three decades in molecular weight (MW) is that concentration scaling substantially alters perception of protein interfacial activity as measured by reduction in gamma(lv). Proteins appear more similar than dissimilar on a weight/volume basis, whereas molarity scaling reveals a "Traube-rule" ordering by MW, suggesting that adsorption is substantially driven by solution concentration rather than diversity in protein amphilicity. Scaling as a ratio-to-physiological-concentration demonstrates that certain proteins exhibit the full possible range of interfacial activity at and well-below physiological concentration, whereas others are only weakly surface active within this range, requiring substantially higher solution concentration to achieve reduction in gamma(lv). Important among this latter category of proteins are the blood factors XII and XIIa, assumed by the classical biochemical mechanism of plasma coagulation to adsorb to procoagulant surfaces, even in the presence of overwhelming concentrations of other blood constituents such as albumin and immunoglobulin that are shown by this work to be among the class of highly surface-active proteins at physiologic concentration. A comparison of pendant drop and Wilhelmy balance tensiometry as tools for assessing protein interfacial activity shows that measurement conditions employed in the typical Wilhelmy plate approach fails to achieve the steady-state adsorption condition that is accessible to pendant drop tensiometry.

Surface tension and vapor–liquid phase coexistence of the square-well fluid

Vapor–liquid interfacial tension of square-well (SW) fluids is calculated using three different methods viz., molecular dynamics (MD) with collision-based virial evaluation, Monte Carlo with virial computed by volume perturbation, and Binder’s density-distribution method in conjunction with grand-canonical transition-matrix Monte Carlo (GC-TMMC). Three values of the SW attractive well range parameter were studied: λ=1.5, 1.75, and 2.0, respectively. The results from MD and GC-TMMC methods are in very good mutual agreement, while the volume-perturbation method yields data of unacceptable quality. The results are compared with predictions from the statistical associating fluid theory (SAFT), and SAFT is shown to give a good estimate for the systems studied. Liquid and vapor coexistence densities and saturation pressure are determined from analysis of GC-TMMC data and the results are found to agree very well with the established literature data.

Interfacial tension behavior of binary and ternary mixtures of partially miscible Lennard-Jones fluids: A molecular dynamics simulation

By means of extensive equilibrium molecular dynamics simulations we have investigated the behavior of the interfacial tension γ of two immiscible symmetrical Lennard-Jones fluids. This quantity is studied as function of reduced temperature T*=kBT/ε in the range 0.6⩽T*⩽3.0. We find that, unlike the monotonic decay obtained for the liquid-vapor interfacial tension, for the liquid–liquid interface, γ(T) has a maximum at a specific temperature. We also investigate the effect that surfactantlike particles have on the thermodynamic as well as the structural properties of the liquid–liquid interface. It is found that γ decays monotonically as the concentration of the surfactantlike particles increases.

Determination of the crystal growth mechanism of KCl in ethanol–water system

The mechanism of crystal growth of KCl in ethanol–water system is studied by Nielsen's map-model, and the growth rate is estimated by the induction time (nucleation rate, growth rate) function in a salting-out crystallization system. In the experiments, the induction time and the particle size distribution of the final product were measured, and the solid–liquid interfacial tension was calculated from the induction period data. The map of rate control of crystal-growth for the KCl–ethanol–water salting out system was constructed by taking into consideration that the liquid–vapour interfacial tension varied with the variation of the ethanol concentration, and, as a consequence, the solid–liquid interfacial tension varied as well. As a result, diffusion controlled crystal growth was obtained as a rate-determining step for supersaturation ratios 0.01<0.45. For determining the crystal growth rate, the nucleation rate was estimated from the experimental average particle number and induction period, applying the assumption that all nuclei were born during the induction period. The results, obtained by using linear and non-linear regressions, have appeared to be in good agreement with the data published in the literature.

Recovery of Residual Lubricating Oil from Waste Clay by Flotation

The waste clay produced from refining waste lubricating oil contains about 30% oil. Laboratory research has been carried out on the selective separation of oil by flotation using linear barium alkyl benzene sulfonates as a collector. The behaviour of this collector at the solution-air interface is studied; the critical micelle concentration (CMC), efficiency (Π), and effectiveness (P c20) of the collector are determined. The effects of collector concentration and addition mode are investigated. The liquid-vapour interfacial tension was controlled by methanol. The selectivity achieved by the use of methanol is explained in terms of critical surface tension of floatability and CMC. In addition the physico-chemical characteristics of the recovered oil at optimum conditions are determined.

The protective effect of specific medium additives with respect to bubble rupture

A significant degree of cell damage is observed during suspension cell culture with air sparging. Protective agents can be added to the culture medium to protect the cells from damage. It has been observed that cells tend to adhere to air-medium interfaces and cell damage is mainly due to this cell-bubble interaction; protective additives have been found to prevent this cell adhesion to the bubble surfaces. In this article, it is demonstrated that the interfacial tension between the air and medium is related to the effectiveness of the protective additives to prevent adhesion of cells to this interface. Five different types of additives (Pluronic F-68, Methocels, dextran, Polyvinyl alcohol, and polyethylene glycols) were studied in an effort to determine their protective characteristics. Liquid-vapor interfacial tensions of the culture medium, with and without the additives, were measured by two different techniques (maximum bubble pressure method and Wilhelmy plate method). In addition, visualization techniques showed that in the presence of certain protective additives cells do not adhere to the bubble surface. Results obtained from these experiments indicate that the additives which rapidly lower the liquid-vapor interfacial tension of the culture medium also prevent adhesion of cells to the bubble surface. Experiments have also been conducted to determine the number of cells killed due to bubble rupture, and it was observed that this number is related to the amount of cells adhering to the bubble surface.

Surface tension of helium at the superfluid critical end-point

The singularity in the vapor-liquid interfacial tension, ∑(T), of helium at the transition to superfluidity is analyzed theoretically. The universal amplitude ratio R σξ + =K+(ξ 0 + )d−1/k B Tλ , where K+ and K− are the amplitudes of the |T−Tλ|µ singularity in ∑, with μ=1.34 3 , is known from recent work to first order in e=4−d for the general n-vector model in d dimensions. Extrapolation to d=3 for n=2 indicates R σξ + =0.05−0.08, which is shown to be consistent with the experimental data. Further analysis of the experiments establishes that the universal ratio Q=K+/K − exceeds 0.35, and is consistent with the recent prediction Q≃0.9; this demonstrates the inadequacies of earlier theoretical treatments. The existence in the observed surface tension of an anomalous, negative contribution of unknown origin at a few millikelvin beneath Tλ is stressed.

Volterra integro-differential equation and the aging effect at a liquid interface.

The aging of a liquid surface is made evident through the surface-mass-density variation with time. By using the surface-mass conservation law together with the solution of the diffusion equation, we find, for dilute solutions, that surface-mass changes with time following a Volterra integro-differential equation of the second kind. The solution of this equation, for a semi-infinite fluid, together with the two-dimensional equation of state for a dilute gas, allows us to find the surface-tension variation with time. The result is compared with a recent experimental dynamic measurement of the liquid-vapor interfacial tension for aqueous solutions of a nonionic detergent.