Surface Tension Of Liquid Mixtures Research Articles

A unified surface tension model for multi-component salt, organic, and surfactant solutions.

Despite the fact that the surface tension of liquid mixtures is of great importance in numerous fields and applications, there are no accurate models for calculating the surface tension of solutions containing water, salts, organic, and amphiphilic substances in a mixture. This study presents such a model and demonstrates its capabilities by modelling surface tension data from the literature. The presented equations not only allow to model solutions with ideal mixing behaviour but also non-idealities and synergistic effects can be identified and largely reproduced. In total, 22 ternary systems comprising 1842 data points could be modelled with an overall root mean squared error (RMSE) of 3.09 mN m-1. In addition, based on the modelling of ternary systems, the surface tension of two quaternary systems could be well predicted with RMSEs of 1.66 mN m-1 and 3.44 mN m-1. Besides its ability to accurately fit and predict multi-component surface tension data, the model also allows to analyze the nature and magnitude of bulk and surface non-idealities, helping to improve our understanding of the physicochemical mechanisms that influence surface tension.

Surface tension of liquid mixtures and metal alloys. Positive and negative temperature coefficients in alloys with remarkably high surface density

The effect of temperature on the surface tension is examined in liquid alloys that combine a positive or negative temperature coefficient with gravity limitation of the surface concentration in the surface-active metal constituent. This is a restriction that is likely to occur in alloys where the metal with lower surface tension is much denser than the other component. Since there is a surface tension increase due to diminished segregation, the resultant temperature coefficient will depend on the superposition of two independent effects. Working in the framework of Butler’s thermodynamics for ideal surface phases, equations and methods of analysis are obtained to describe both effects. These developments are illustrated with alloys where the surface density is likely to attain the bulk density at certain compositions, namely the Al–Zn alloys that exhibits a negative temperature coefficient and the Sn–Bi, Ga–Bi, Ga-Pb and Cu–Pb alloys that present composition ranges with positive temperature coefficients. The specific concave down dγ/dT curves of liquid alloys are theoretically predicted. Furthermore, good estimates are obtained for systems with positive and negative temperature coefficients, except within a 50 K interval of phase transitions, or for systems showing large deviations from ideal behaviour.

Examination of the Butler Equation for the Surface Tension of Liquid Mixtures.

The classical Butler equation used to describe surface tension and the surface composition of liquid mixtures is revisited. A straightforward derivation is presented, separating basic chemical thermodynamics and assumptions proper to Butler’s model. This model is shown to conceal an approximation not recognized by other researchers. The shortcoming identified consists of not allowing surface standard values to vary with surface tension by virtue of the changing composition. A more rigorous equation is derived and shown to yield the Butler equation in case of incompressible surface phases. It is concluded that the Butler equation slightly overestimates ideal surface tensions. Butler’s surface-phase concentrations of the surface-active component are also slightly overestimated in the surface-active component dilute range, being just underestimated at higher concentrations. Despite this, Butler’s model stands as a very good standard due to its versatility.

Surface tension of liquid mixtures and metal alloys. Thermodynamic conditions for the occurrence of a positive temperature coefficient

The atypical increase of surface tension when the temperature of a liquid alloy increases, is addressed using Butler’s thermodynamic model for an ideal surface phase. A rigorous expression for this temperature coefficient at fixed bulk alloy composition, requiring only pure-metal density and surface tension data and no arbitrary simplifying assumptions, is worked out. This theoretical development predicts the occurrence of positive temperature coefficients whenever a combination involving large difference of pure-metal surface tensions, temperatures close to the alloy melting point and molar surface area of the surface-active metal larger than that of the other component, is met. The proposed method is applied to the alloys Cu–Sn, Cu–In, Ag–Bi, Ag–Pb and Ag–Sn for which experimentally measured positive temperature coefficients have been reported. An acceptable agreement between theoretical and experimental values is documented. This theoretical approach predicts a negative temperature coefficient of the surface tension at fixed surface-phase composition, which is in fact the typical behaviour for this dependence. It is concluded that the temperature and composition ranges over which a certain binary alloy may exhibit positive temperature coefficient of the surface tension can be established beforehand using the proposed methodology.

Surface tension as a function of temperature and composition for a broad range of mixtures

It is desirable to predict the surface tension of liquid mixtures for a wide range of compositions, temperatures, and pressures, but current state-of-the-art calculations (e.g., density gradient theory) are computationally expensive. We propose a computationally simple—but accurate—semi-empirical mathematical model of surface tension for a wide variety of multicomponent mixtures, including those with a supercritical compound when coupled with an equation of state (by introducing a reduced mole fraction scaled by a critical composition). Our predictions for binary systems with one supercritical component are an average of 0.22 mN/m away from literature experimental data (466 data points), and those for systems with two subcritical components (293–333 K) are within 0.09 mN/m (236 data points). We make predictions for methanol + ethanol + water using binary coefficients within an average of 0.71 mN/m (196 data points). Given its computational simplicity and wide applicability, the proposed model will be useful for many applications.

Prediction of the surface tension of binary liquid mixtures of associating compounds using the Cubic Plus Association (CPA) equation of state

Abstract Accurate knowledge of the surface tension of liquid mixtures is of considerable importance in the development of chemical processes that involve mass and heat transfer across phase interfaces. Despite the significant progress made in the development of advanced equations of state (EOS) for accurate representation of thermophysical properties, as well as sophisticated models for the thermodynamic equilibrium of highly non-ideal mixtures, they nonetheless have been to a large extent underrepresented in the prediction and correlation of the surface tension of such systems. In the current work, a modified version of the Butler equation is adopted alongside the Cubic Plus Association (CPA) EOS, with the objective of predicting and correlating the surface tension of binary liquid mixtures of associating compounds. In doing so, the experimental data of aqueous and non-aqueous mixtures of alcohols, glycols, acids, and phenol, comprised of 238 data points belonging to 18 binary mixtures are studied. It is shown that by incorporation of an association term based on the Wertheim's first-order thermodynamic perturbation theory, the CPA EOS can satisfactorily predict the values of surface tension with an AARD of only 9.78%, compared with deviations of 73.87% and 28.38% obtained for the Soave-Redlich-Kwong (SRK) and Peng-Robinson (PR) EOSs, respectively. Also, a major advantage of the proposed model is its inherent capability to simultaneously estimate the composition of the surface phase alongside the mixture surface tension. In addition, with only one adjusted binary parameter, AARDs of 5.29%, 7.09%, and 11.02% are obtained for the correlation of the experimental data using the CPA, SRK, and PR EOSs, respectively.

Surface Tension Prediction of Organic Binary Liquid Mixtures

Equations have been reported in the literature to predict the surface tension of binary liquid mixtures. However, the equations involve large number of variables and are very complex. In the present article an attempt is made to propose an empirical equation to predict the surface tension of binary organic liquid mixtures. A simple equation, ‘Hadkar Equation’, has been proposed and was used to calculate the surface tension of binary liquid mixtures that have already been reported in the literature and was found to give the results close to the reported values. To verify the utility of the equation for the prediction of surface tension of liquid mixture, the surface tension of a few organic binary liquid mixtures was determined using drop weight method. The ‘Hadkar Equation’, was found to be useful in the prediction of surface tension of organic binary liquids having weak force of attraction.

Prediction of the Surface Tension, Surface Concentration and the Relative Gibbs Adsorption Isotherm of Non-ideal Binary Liquid Mixtures

Surface properties of binary mixtures of 1,2-ethanediol, 1,2-propanediol and 1,4-butanediol with acetonitrile have been measured by the surface tension method at T = 298.15 K and atmospheric pressure. The surface tension has been predicted based on the Suarez method. This method combines a model for the description of surface tension of liquid mixtures by using the UNIFAC group contribution method for calculation of activity coefficients. Also, the results have been discussed in terms of surface concentration and lyophobicity using the extended Langmuir isotherm. The results provide information on the molecular interactions between the unlike molecules that exist at the surface and the bulk phase. Finally, experimental values of the surface tension have been correlated by the Redlich–Kister and Wang–Chen polynomial equations over the whole mole fraction range.

Application of the UNIFAC model for prediction of surface tension and thickness of the surface layer in the binary mixtures

Surface properties of binary mixtures of (alkanol with acetonitrile) have been measured by surface tension method at T = 298.15 K and atmospheric pressure. The UNIFAC method is used for calculation activity coefficients of surface and bulk phases. Also, the surface tension has been predicted based on the Suarez method. This method combines a model for the description of surface tension of liquid mixtures with a UNIFAC group contribution method for the calculation of activity coefficient. Two techniques for calculation of molar surface areas, based on Paquette areas and Rasmussen areas are tested. On comparing the computed values of surface tension by the present approaches with experimental data, satisfactory results have been observed. In addition, the relative Gibbs adsorption and the surface mole fraction have been evaluated using this model. It is possible to calculate the thickness of liquid–vapor interfaces starting from surface tension data. A novel procedure is developed to obtain the thickness of liquid–vapor interfaces as a function of composition in binary systems.

Thermodynamic investigation of the surface tension of liquid mixtures of cis-decaline with either methyl–acetate or n-pentyl–acetate in the temperature range from 283.15 to 303.15 K

Surface tensions (σ) and densities (ρ) of binary liquid mixtures of cis-decaline with either methyl–acetate (MAC) or n-pentyl–acetate (PAC) were measured over the entire composition range at the temperatures 283.15, 288.15, 298.15 and 303.15 K. The excess surface tensions (σE ) and the excess molar volumes (VE ) were calculated. The σE and VE values were fitted by the Redlich–Kister polynomial equation and the Ak coeffients as well as the standard deviations (d) between the calculated and the experimental excess parameters were derived. The σ values were further used for the calculation of the surface entropy (SS ) and the surface enthalpy (HS ) per unit surface area. The lyophobicity (β) and the surface mole fraction () of the surfactant component (either MAC or PAC) were also derived using the extended Langmuir model. The results were used for the characterisation of the molecular interactions at the surface and the bulk-phase region.

Experimental and theoretical study of surface tension of binary mixtures of (n-alkyl acetates + heptane, benzene, and toluene)

Surface properties of binary mixtures of (n-alkyl acetates + heptane, benzene, and toluene) have been measured by surface tension method at T = 298.15 K and atmospheric pressure. Also, the surface tension has been predicted based on the Suarez method. This method combines a model for the description of surface tension of liquid mixtures with a group contribution method for the calculation of activity coefficient. The mean relative standard deviations obtained from the comparison of experimental (measured) and calculated surface tension values for the eight binary systems are less than 1.5%, which leads to concluding that the model shows a good accuracy in different situations in comparison with other predicted equations. In addition, the relative Gibbs adsorption and the surface mole fraction have been evaluated using this model. The surface tension deviations were calculated from experimental results and have been fitted to the Redlich–Kister type polynomial relation.

Equation of State Coupled with Scaled Particle Theory for Surface Tensions of Liquid Mixtures

A new statistical mechanics model is developed to calculate the surface tensions of liquid mixtures, based on an equation of state for chain fluids and the scaled particle theory. Transferrable molecular parameters fitted to experimental phase equilibrium properties are used in this model. The feasibility of the model has been systematically tested in the correlations of 62 binary mixtures and in the predictions of 7 binary and 5 ternary mixtures, including nonassociating, self-associating, and cross-associating systems with overall average absolute relative deviations of 0.31%, 0.86%, and 0.92%, respectively. The accuracy of the new model makes it particularly well-suited in the calculation of surface tensions for a wide range of complex liquid mixtures.

Surface Tension of o-Xylene + Acetic Acid and m-Xylene + Acetic Acid Binary Mixtures from 303.15 K to 343.15 K

The surface tension of liquid mixtures is an important physical property in heat and mass transfer at an interface. A differential maximum bubble pressure tensiometer is described. Evaluation of the apparatus with standard chemicals had shown that the apparatus is convenient and reliable. The surface tensions of o-xylene +acetic acid and m-xylene + acetic acid were measured from 303.15 K to 343.15 K over the entire range of concentration. The data were correlated as a function of temperature and mole fraction. The average deviation is less than 1 %.

Surface segregation and surface tension of liquid mixtures

A model has been developed in which surfaces are treated as separate phases with a thickness corresponding to a monolayer. It is argued that the surface tension of liquids is a measure of the excess surface chemical potential of the surface atoms relative to the bulk atoms. Equations for the calculation of the surface composition and surface tension of liquid mixtures are developed. Using only the surface tension and molar volume data of the pure components, excellent correspondence between calculated and experimental surface tension values was obtained. The method was also tested on liquid systems showing immiscibility. The surface coverage calculated from the present model is compared with that calculated using Gibbs adsorption equation. The surface coverage of the solute species increases with increasing solute concentration. However, depending on the surface properties of the system, the excess surface coverage may pass through a maximum value and then decrease with increasing solute concentration.

Empirical expression for predicting surface tension of liquid mixtures

Donnees theoriques et comparaison aux donnees experimentales relatives a des liquides organiques polaires et non polaires

Surface tensions and surface heats of mixing of mixtures containing bromobenzene at 293.15 and 303.15 K

Surface tensions of mixtures of bromobenzene with cyclohexane, benzene,o-, m-, andp-xylene have been determined by the capillary rise method at 293.15 and 303.15 K. The data have been used to check the various theories of surface tension of liquid mixtures. The surface heats of mixing have been computed at 293.15 K as a function of composition.