Prediction Of Surface Tension Research Articles

Calculation the surface tension of heptane, eicosane, docosane, tetracosane, and their asymmetric mixtures

A method to calculate and predict the surface tension of n-alkanes including heptane, eicosane, docosane, tetracosane, and their asymmetric mixtures has been proposed. Reduced coordinates, σ ∗ and T ∗ , where σ ∗ is the reduced surface tension and T ∗ is the reduced temperature, are introduced for the prediction of surface tension. According to the phenomenological scaling and considering the law of corresponding states correlation, these reduced coordinates result in a single curve for the surface tension as a function of temperature. In the correlation the melting temperature, T m , is applied as the corresponding temperature for these substances and their mixtures. The relationship between σ ∗ and T ∗ has a linear form and is expressed by σ ∗ = a + b T ∗ , where a and b are temperature-independent constants. With this relationship the predicted values of surface tension of these substances and their mixtures are in good agreement with experimental ones. %AAD, percent average absolute deviation, for these four pure n-alkanes is 1.02% and for their four asymmetric mixtures is less than 0.70%.

Phase equilibrium calculations for confined fluids, including surface tension prediction models

Phase equilibrium calculations for fluids confined inside capillary tubes or porous media are formulated using the isofugacity equations. In this situation, the phase pressures are not equal and it is assumed that they are related by the Laplace equation. With this formulation, existing procedures for phase equilibrium calculations can be readily modified to include capillary effects. In this paper, we review some of the main authors who have studied the behavior of fluids inside porous media and perform bubble- and dew-point calculations for pure components and mixtures, using the Peng-Robinson equation of state to model the coexisting phases and several planar surface tension models. Comparisons with results from the literature indicate that the proposed formulation is adequate for representing phase equilibrium inside capillary tubes.

A nonadditive methanol force field: Bulk liquid and liquid-vapor interfacial properties via molecular dynamics simulations using a fluctuating charge model

We study the bulk and interfacial properties of methanol via molecular dynamics simulations using a CHARMM (Chemistry at HARvard Molecular Mechanics) fluctuating charge force field. We discuss the parametrization of the electrostatic model as part of the ongoing CHARMM development for polarizable protein force fields. The bulk liquid properties are in agreement with available experimental data and competitive with existing fixed-charge and polarizable force fields. The liquid density and vaporization enthalpy are determined to be 0.809 g/cm3 and 8.9 kcal/mol compared to the experimental values of 0.787 g/cm3 and 8.94 kcal/mol, respectively. The liquid structure as indicated by radial distribution functions is in keeping with the most recent neutron diffraction results; the force field shows a slightly more ordered liquid, necessarily arising from the enhanced condensed phase electrostatics (as evidenced by an induced liquid phase dipole moment of 0.7 D), although the average coordination with two neighboring molecules is consistent with the experimental diffraction study as well as with recent density functional molecular dynamics calculations. The predicted surface tension of 19.66+/-1.03 dyn/cm is slightly lower than the experimental value of 22.6 dyn/cm, but still competitive with classical force fields. The interface demonstrates the preferential molecular orientation of molecules as observed via nonlinear optical spectroscopic methods. Finally, via canonical molecular dynamics simulations, we assess the model's ability to reproduce the vapor-liquid equilibrium from 298 to 423 K, the simulation data then used to obtain estimates of the model's critical temperature and density. The model predicts a critical temperature of 470.1 K and critical density of 0.312 g/cm3 compared to the experimental values of 512.65 K and 0.279 g/cm3, respectively. The model underestimates the critical temperature by 8% and overestimates the critical density by 10%, and in this sense is roughly equivalent to the underlying fixed-charge CHARMM22 force field.

A new state model of liquid–vapor interfaces—to yield analytical expression for surface tension

Based on the van der Waals fluid model, a simple equation of state, unique for non-uniform fluids, is developed. It is applied to the liquid–vapor interface, to derive the density profile in the interfacial region. The density profile is used in conjunction with the gradient theory, to yield an expression for the surface tension of a saturated fluid as a function of temperature and fluid properties. The non-dimensionalized influence parameter of the gradient theory is assigned best-fit values, which are of a unity order of magnitude, as expected. The predicted surface tension values are in good agreement with experimental data, for a variety of fluids.

Mixed adsorption and surface tension prediction of nonideal ternary surfactant systems

To deal with the mixed adsorption of nonideal ternary surfactant systems, the regular solution approximation for nonideal binary surfactant systems is extended and a pseudo-binary system treatment is also proposed. With both treatments, the compositions of the mixed monolayer and the solution concentrations required to produce given surface tensions can be predicted based only on the γ-LogC curves of individual surfactants and the pair interaction parameters. Conversely, the surface tensions of solutions with different bulk compositions can be predicted by the surface tension equations for mixed surfactant systems. Two ternary systems: SDS/Hyamine 1622/AEO7, composed of homogeneous surfactants, and AES/DPCl/AEO9, composed of commercial surfactants, in the presence of excess NaCl, are examined for the applicability of the two treatments. The results show that, in general, the pseudo-binary system treatment gives better prediction than the extended regular solution approximation, and the applicability of the latter to typical anionic/cationic/nonionic nonideal ternary surfactant systems seems to depend on the combined interaction parameter, \( {\mathop {(\beta }\nolimits_{an}^s } + {\mathop \beta \nolimits_{cn}^s })/2 - {\mathop \beta \nolimits_{ac}^s }/4 \): the more it deviates from zero, the larger the prediction difference. If \( {\mathop {(\beta }\nolimits_{an}^s } + {\mathop \beta \nolimits_{cn}^s })/2 - {\mathop \beta \nolimits_{ac}^s }/4 \)→0, good agreements between predicted and experimental results can be obtained and both treatments, though differently derived, are interrelated and tend to be equivalent.

Liquid-vapor interface of square-well fluids of variable interaction range.

Properties of the liquid-vapor interface of square-well fluids with ranges of interaction lambda=1.5, 2.0, and 3.0 are obtained by Monte Carlo simulations and from square-gradient theories that combine the Carnahan-Starling equation of state for hard spheres with the second and third virial coefficients. The predicted surface tensions show good agreement with the simulation results for lambda=2 and for lambda=3 in a temperature range reasonably close to the critical point, 0.8</=T/T(c)</=0.95. As expected, the surface tension increases with the range of interaction and decreases monotonically with temperature. A comparison between theory and simulation results is also given for the width of the interface and for the coexistence curves for the different interaction ranges.

Prediction of multicomponent liquid adsorption using excess quantities: III. Calculations for the liquid/air interface

The utilization of excess quantities as the basis of a thermodynamic approach can simplify the prediction of multicomponent data from binary ones. Whereas in Part II the excess formalism was applied to the prediction of liquid phase adsorption on solids, in this paper, the liquid/air interface is investigated. In order to show the generality of the suggested approach, thermodynamic equations are developed in analogy to Part II. Surface tensions are predicted by different excess models and compared with experimental data. From predicted surface tensions, ternary adsorption isotherms on the liquid/air interface are calculated.

Theoretical prediction of surface tension of ternary liquid system (nitrogen + oxygen + argon) at elevated temperature and different pressure

The surface tension of a ternary liquid mixture of nitrogen, oxygen, and argon has been calculated by a new approach using critical constants P c , V c , and T c at temperatures ranging from 90 to 110 K and pressure up to 865 kPa. New formalism has been made by modifying the Brock–Bird relation. The computed values are compared with the experimental findings. Satisfactory results have been obtained.

Water+esters+methanol: experimental data, correlation and prediction of surface and interfacial tensions at 303.15 K and atmospheric pressure

For the ternary system water+ ethyl propionate + methanol , and the constituent binaries, the surface tension at 303.15 K and atmospheric pressure was measured over the whole miscible composition range. The liquid interfacial tension was determined in the liquid–liquid equilibrium range at the same conditions of temperature and pressure. Correlation of the excess surface tension of the above mentioned binary and ternary systems as well as for the ternary water+ ethyl butyrate + methanol and constituent binaries, was performed with empirical and thermodynamic-based models. The interfacial tension was correlated with the equation of Fu et al. The prediction of the surface tension of the binary and ternary systems was made using the model of Sprow and Prausnitz. The models of Fu et al. and Li et al. were also applied to predict the surface tension in the ternary systems. The liquid interfacial tension of the ternary systems was correlated and predicted using the relations proposed by Li and Fu and Fu et al., respectively, with satisfactory results.

Prediction of Surface Tension in Molten Metallic and Ionic Systems

The so-called excess surface tension model was proposed for molten metallic and ionic systems in the present study. The surface tension, σ, in a binary system was regarded as the summation of σ 1 and σ E to respectively represent the contributions of the linear and non-linear behaviour of the solution. The excess surface tension, σ E , was correlated with mole fraction and temperature as: σ E = A 0 + A 1 (x 1 - x 2 ) + A 2 (x 1 - x 2 ) 2 and A j =A j,0 +A j, 1 , j=0, 1, 2 The model predicted results for some molten binary alloys, slags and salts; in addition, ternary slags with a specified mass percent ratio of two components are provided to show the model's validity and applicability. The predicted surface tension values in these systems have been found to be in reasonable agreement with the corresponding experimental data.

Study on Surface Tension for Non-polar and Associating Fluids Based on Density Functional Theory

A method for the prediction of surface tension of non-polar and associating fluids has been developed based on the density functional theory (DFT). The WCA perturbation theory and the SAFT are used to establish the equation of state (EOS). The adjustable parameters are correlated by simultaneously fitting the saturated vapor pressure and the liquid density data with the EOS. The local density approximation (LDA) is applied to the reference term and the mean field approximation (MFA) is used for perturbation term. The density profile is obtained by minimizing the grand potential functional. The surface thickness is calculated by “10%-to-90%-width” method. By use of the regressed parameters in EOS and the obtained density profile, the surface tensions for 13 non-polar fluids and 10 associating fluids are predicted satisfactorily.

Lagrangian theorem-based density functional approach free of adjustable parameter

An adjustable parameter associated with an recently proposed Lagrangian theorem-based density functional theory (DFT) approach is found to be a constant 0.5 by applying the non-uniform first-order direct correlation function (DCF) from the Lagrangian theorem-based DFT approach to an exact relation between the zero wave vector Fourier transform of the bulk DCFs and their density derivatives. The new parameter-free DFT approach is comparable or even more accurate in predicting density distribution than the original DFT approach. Based on functional integral procedure, a numerical procedure from approximation for non-uniform first-order DCF to non-uniform excess Helmholtz free energy is proposed, the predicted surface tension of a hard wall-hard sphere interface as a function of the bulk hard sphere fluid density from the original DFT approach and its parameter-free version is in very good agreement with the available simulation data.

Surface tension and thermodynamic properties of liquid Ag-Bi solutions

With the maximum bubble pressure method, the density and surface tension were measured for five Ag-Bi liquid alloys (XBi = 0.05, 0.15, 0.25, 0.5, and 0.75), as well as for pure silver. The experiments were performed in the temperature range 544-1443 K. Linear dependences of both density and surface tension versus temperature were observed, and therefore the experimental data were described by linear equations. The density dependence on concentration and temperature was derived using the polynomial method. A similar dependence of surface tension on temperature and concentration is presented. Next, the Gibbs energy of formation of solid Bi2O3, as well as activities of Bi in liquid Ag-Bi alloys, were determined by a solidstate electromotive force (emf) technique using the following galvanic cells: Ni, NiO, Pt/O �2 /W, AgXBi(1�X), Bi2O3(s). The Gibbs energy of formation of solid Bi2O3 from pure elements was derived: G 0�Bi2O3) = �598 148 + 309.27T [J mol �1 ] and G 0�Bi2O3) = �548 009 + 258.94T [J mol �1 ]; the temperature and the heat of the → transformation for this solid oxide were calculated as 996 K and 50.1 4J·m ol �1 . Activities of Bi in the liquid alloys were determined in the temperature range from 860-1075 K, for five Ag-Bi alloys (XAg= 0.2, 0.35, 0.5, 0.65, 0.8), and a Redlich-Kister polynomial expansion was used to describe the thermodynamic properties of the liquid phase. Using Thermo-Calc software, the Ag-Bi phase diagram was calculated. Finally, thermodynamic data were used to predict surface tension behavior in the Ag-Bi binary system.

Influência da temperatura, da massa molar e da distribuição de massa molar na tensão superficial de PS, PP e PE: experimento e teoria

Neste trabalho a influência da temperatura, da massa molar (&lt;IMG SRC="/img/revistas/po/v13n1/15069x34.gif" WIDTH=11 HEIGHT=11&gt;n) e da distribuição de massa molar (MWD) na tensão superficial de poliestireno (PS) foi avaliada utilizando o método da gota pendente. A influência da temperatura na tensão superficial de polipropileno isotático (i-PP) e de polietileno de baixa densidade (PELBD) também foi estudada aqui. As teorias de Patterson-Rastogi e Dee-Sauer foram utilizadas em conjunção com a teoria de equação de estado de Flory, Orwoll, e Vrij (FOV) para prever a tensão superficial (gama) utilizando dados de pressão-volume-temperatura (PVT) dos polímeros. Ambas teorias prevêem que a tensão superficial diminui linearmente com o aumento da temperatura e aumenta com a massa molar concordando com os resultados experimentais. Entretanto, ambas teorias subestimam a mudança de entropia de formação de superfície por unidade de área a volume constante para sistemas poliméricos de baixa massa molar e polidisperso e subestimam o efeito da distribuição de massa molar na tensão superficial

Prediction of surface properties of metals from the law of corresponding states

The schema, previously developed by the author, for the prediction of surface tension of liquid metals (LM) from the corresponding states (CS) principle has been extended to solid metals (SM). As in the case of LM, the reduced formula for surface tension of SM has been obtained by scaling ε and a characterizing the interatomic potential, with the melting point T m(0) at atmospheric pressure and the atomic volume Ω sm 2/3(0) T m at the melting point as macroscopic parameters. CS rules derived for the surface tension, its temperature derivatives, and also the specific surface energy are discussed and compared with the experimental data and with the counterpart rules for LM. It is shown that pressure dependence of the surface tension can be described by pressure dependence of the scaling parameters T m( p) and Ω m (p) .

Prediction of interfacial tension between an organic solvent and aqueous solutions of mixed-electrolytes

The recently proposed approach for representing and predicting surface tension of aqueous electrolyte solutions [Chem. Eng. Sci. 56 (2001) 2879] is extended to the prediction of interfacial tension between an organic solvent and aqueous multi-electrolyte solutions. The method of Meissner was adopted in all the calculations of activity coefficient of electrolytes. Model parameters were determined by correlating interfacial tensions reported in the literature for 11 single electrolytes, including 10 inorganic salts and one inorganic acid at isothermal conditions. The correlation yielded an overall average absolute percentage deviation (AAPD) of 0.42. Using these model parameters, the proposed approach was successfully applied to the prediction of interfacial tensions available in the literature for aqueous FeCl 3–HCl, NiCl 2–FeCl 3–HCl and NiCl 2–CoCl 2–FeCl 3–HCl solutions with an AAPD of 5.73.

Prediction of surface tension for pure non-polar fluids based on density functional theory

A method for the prediction of surface tension of non-polar fluids has been developed based on the density functional theory. The Barker–Henderson perturbation theory and statistical associating fluid theory are used to establish an equation of state (EOS). The parameters m, σ and ε/ k of the EOS are correlated by simultaneously fitting the saturated vapor pressure and the liquid density data. The surface region of a pure liquid is divided into many extreme thin layers. The chemical potentials of different layers in the surface region are equal and lead to a constant by optimizing the surface thickness. The density profile is obtained from the optimized surface thickness and a hyperbolic tangent function. By use of the regressed parameters in the EOS, the surface tensions for 18 pure non-polar fluids are predicted and the results are satisfactory.

A molecular model for representing surface tension for polar liquids

An expression based on molecular thermodynamic considerations was developed for representing surface tensions of pure polar liquids and their mixtures. Contributions to surface tension from hard spheres, dispersion, and polar–polar interactions were considered and assumed to be additive in the development. The Davis theory (J. Chem. Phys. 62 (1975) 3412, Adv. Chem. Phys. 49 (1982) 357) and the simplified radial distribution function expression of Xu and Hu (Fluid Phase Equilibria 30 (1986) 221) were adopted in the model development. Two pair-potential parameters, size and energy, were used for each pure fluid. In addition, one adjustable parameter was used for each binary system, but two adjustable parameters were required for binary systems containing water. The average absolute percentage deviations obtained for arbitrarily selected 22 pure polar compounds, 12 non-aqueous binary polar systems and four binary aqueous systems (excluding ethanol + water and 1-propanol + water) are 0.59, 0.58 and 2.40, respectively. In addition, the proposed approach was extended to mixtures containing polar and non-polar compounds with reasonably good results. Feasibility of the proposed model for predicting surface tension for multicomponent (ternary) mixtures was demonstrated.

Surface tension prediction for hydrocarbons and its application to level swell modelling

In this article, methods for estimating surface tension are considered where the specific gravity and normal boiling point are known such as when the composition is expressed using petroleum fractions. This is of interest as surface tension is an important parameter in the calculation of outflow conditions from a two-phase vessel undergoing level swell. A new improved correlation for the parachor is presented and the improved accuracy of the surface tension and bubble rise velocity compared to when the original parachor correlation is used is assessed. Finally the sensitivity of outflow predictions to changes in the surface tension is presented for a depressurising vessel containing pentane. For the vessel depressurisation simulation where the original parachor correlation is used, two-phase venting is maintained for two–three times as long compared to when the actual parachor or improved parachor correlation is used to estimate the surface tension. This has an impact on the error in predicting the mass flow rate as a source condition for other consequence models and also in vent sizing calculations.

Dynamic Surface Tensions of Aqueous Surfactant Mixtures: Experimental Investigation

We present an experimental investigation of the interfacial behavior of aqueous solutions of two nonionic surfactants and their binary mixture. Specifically, we measure both the equilibrium surface tensions (using the Wilhelmy plate method) and the dynamic surface tensions (using the pendant bubble technique) of aqueous solutions of two nonionic alkyl ethoxylate surfactants, dodecyl penta(ethylene oxide) (C12E5) and decyl octa(ethylene oxide) (C10E8), as well as of their binary mixture. These measurements are then compared with the predictions made using recently developed molecular-thermodynamic theories of the equilibrium and the dynamic interfacial behaviors of nonionic surfactant mixtures and are found to be in good agreement. The main advantage of the equilibrium and the dynamic interfacial theories adopted here is that they are based on the molecular characteristics of the surfactants, and as such, the required number of experimentally determined parameters can be reduced significantly. Indeed, no experimental measurements, neither of the equilibrium nor of the dynamic type, need to be conducted on the mixed surfactant solutions. In addition to the complete prediction of the dynamic surface tensions and the dynamic surface concentrations, the theoretical framework also includes a simplified time scale analysis of the dynamic interfacial behavior that allows “quick” insight into the relationship between the molecular structure of a surfactant and its dynamic interfacial behavior. The experimental measurements also show that the simplified time scale analysis of the dynamic interfacial behavior provides an approximate, yet quantitatively accurate, description of the rate of adsorption, measured through the dynamic surface tension, of the single nonionic surfactants as well as of a surfactant component in the binary mixture of nonionic surfactants.