Corresponding-states and parachor models for the calculation of interfacial tensions

Quantitative Predictions and Experimental Validation of Liquid-Vapor Interfacial Tension in Binary and Ternary Mixtures of Alkanes Using Molecular Dynamics Simulations

Liquid-vapor interfacial properties of alkane mixtures present a challenge for experimental determination, especially under conditions relevant to the energy industry processes. Molecular dynamics (MD) simulations can accurately predict interfacial tensions (IFTs) for complex alkane mixtures under virtually any conditions, thereby alleviating the need for difficult and costly experiments. MD simulations with the CHARMM force field and empirical corrections for the IFT and pressure were used to obtain the IFT for three binary mixtures of ethane (with n-pentane, n-hexane, and n-nonane) and a ternary system (ethane/n-butane/n-decane) under a variety of conditions. The results were thoroughly validated against experimental data from the literature, and new original IFT data were collected using the pendant drop method. The simulations are able to reproduce the experimental IFT to better than 0.5 mN/m or 5% on average and within 1 mN/m or 10% in the worst case. IFTs for the studied three binary and ternary alkane mixtures were predicted for wide ranges of conditions with no known experimental data. Finally, using the MD simulation data, the reliability of the widely used empirical parachor model for predicting IFT was reaffirmed, and the significance of the empirical parameters examined to establish an optimal balance between the accuracy and broad applicability of the model.

Pressure–Surface Tension–Temperature Equation of State for n-Alkanes

Herein, the geometric similitude concept is applied to propose a cubic equation that relates surface tension, saturation pressure, and temperature for n-alkanes. The input properties for each fluid are the molecular mass, pressure, temperature, and compressibility factor at the critical point. The model is applied to temperatures below 0.93·T_c (critical point temperature). A total of 2429 surface tension values have been selected for 32 n-alkanes. The parameters of the model have been obtained with a fit of the surface tension values for 19 pure n-alkanes that are randomly chosen. Then, it is tested for the other 13 pure n-alkanes and used to predict the surface tension for 11 binary and 4 ternary mixtures. These predictions are compared with the reported experimental data. For pure n-alkanes, the overall absolute average deviation is 2.4%, including the correlation and testing sets. No additional adjustable coefficients are used for mixtures, yielding an overall absolute average deviation of 2.98% for the binary systems and 7.97% for the ternary ones. The results show that the model is accurate enough for predictions and that the highest deviations are due to the lack of agreement in the values of surface tension of pure fluids obtained from different sources.

Molecular Dynamics Simulations of the Vapor-Liquid Equilibria in CO2/n-Pentane, Propane/n-Pentane, and Propane/n-Hexane Binary Mixtures

Molecular dynamics (MD) simulations were used to study vapor-liquid equilibrium interfacial properties of n-alkane and n-alkane/CO₂ mixtures over a wide range of pressure and temperature conditions. The simulation methodology, based on CHARMM molecular mechanics force field with long-range Lennard-Jones potentials, was first validated against experimental interfacial tension (IFT) data for two pure n-alkanes (n-pentane and n-heptane). Subsequently, liquid-vapor equilibria of CO₂/n-pentane, propane/n-pentane, and propane/n-hexane mixtures were investigated at temperatures from 296 to 403 K and pressures from 0.2 to 6 MPa. The IFT, liquid and vapor phase densities, and molecular compositions of the liquid and vapor phases and of the interface were analyzed. The calculated mixture IFTs were in excellent agreement with experiments. Likewise, calculated phase densities closely matched values obtained from the equation of state (EOS) fitted to the experimental data. Examination of the density profiles, particularly in the liquid-vapor transition regions, provided a molecular-level rationalization for the observed trends in the IFT as a function of both molecular composition and temperature. Finally, two variants of the empirical parachor model commonly used for predicting the IFT, the Weinaug-Katz and Hugill-Van Welsenes equations, were tested for their accuracy in reproducing the MD simulation results. The IFT prediction accuracies of both equations were nearly identical, implying that the simpler Weinaug-Katz model is sufficient to describe the IFT of the studied systems.

Rapid Determination of Interfacial Tensions in Nanopores: Experimental Nanofluidics and Theoretical Models

A rapid and accurate determination of interfacial tensions (IFTs) in nanopores is scientifically and practically significant, while most existing experimental measurements are restricted to the micrometer scale and theoretical calculations are relatively limited. In this study, six series of the IFT measurement tests for the binary CO₂-C₁₀, C₁-C₁₀, and N₂-C₁₀ mixtures are conducted at temperatures ( T) of 25.0 and 53.0 °C in a self-manufactured nanofluidic system. Moreover, a nanoscale-extended equation-of-state model considering the effects of the confinement, intermolecular interactions, and disjoining pressure and a semianalytical correlation are proposed to calculate the IFTs of the three mixtures in bulk phase and nanopores. Third, a new Tolman length formulation is developed for the IFT corrections in nanopores. Overall, the calculated IFTs from the two theoretical methods agree well with the measured results for most cases in nanopores. On the other hand, effects of the pore scale, temperature, pressure, and fluid composition on the IFTs of the three mixtures are effectively validated and specifically investigated. One suggestion comes from this work that the two theoretical methods for calculating the IFTs are better to be applied concurrently to minimize errors. Another important future work is to include more pore surface parameter (e.g., wettability) into the theoretical model.

Theoretical study of vapor-liquid homogeneous nucleation using stability analysis of a macroscopic phase

Stability analysis is generally used to verify that the solution to phase equilibrium calculations corresponds to a stable state (minimum of the free energy). In this work, tangent plane distance analysis for stability of macroscopic mixtures is also used for analyzing the nucleation process, reconciling thus this analysis with classical nucleation theories. In the context of the revised nucleation theory, the driving force and the nucleation work are expressed as a function of the Lagrange multiplier corresponding to the mole fraction constraint from the minimization problem of stability analysis. Using a van der Waals fluid applied to a ternary mixture, Lagrange multiplier properties are illustrated. In particular, it is shown how the Lagrange multiplier value is equal to one on the binodal and spinodal curves at the same time as the driving force of nucleation vanishes on these curves. Finally, it is shown that, on the spinodal curve, the nucleation work from the revised and generalized nucleation theories are characterized by two different local minima from stability analysis, irrespective of any interfacial tension models.

Comparison of united-atom potentials for the simulation of vapor-liquid equilibria and interfacial properties of long-chain n-alkanes up to n-C100

Canonical ensemble molecular dynamics (MD) simulations are reported which compute both the vapor-liquid equilibrium properties (vapor pressure and liquid and vapor densities) and the interfacial properties (density profiles, interfacial tensions, entropy and enthalpy of surface formation) of four long-chained n-alkanes: n-decane (n-C(10)), n-eicosane (n-C(20)), n-hexacontane (n-C(60)), and n-decacontane (n-C(100)). Three of the most commonly employed united-atom (UA) force fields for alkanes (SKS: Smit, B.; Karaborni, S.; Siepmann, J. I. J. Chem. Phys. 1995,102, 2126-2140; J. Chem. Phys. 1998,109, 352; NERD: Nath, S. K.; Escobedo, F. A.; de Pablo, J. J. J. Chem. Phys. 1998, 108, 9905-9911; and TraPPE: Martin M. G.; Siepmann, J. I. J. Phys. Chem. B1998, 102, 2569-2577.) are critically appraised. The computed results have been compared to the available experimental data and those fitted using the square gradient theory (SGT). In the latter approach, the Lennard-Jones chain equation of state (EoS), appropriately parametrized for long hydrocarbons, is used to model the homogeneous bulk phase Helmholtz energy. The MD results for phase equilibria of n-decane and n-eicosane exhibit sensible agreement both to the experimental data and EoS correlation for all potentials tested, with the TraPPE potential showing the lowest deviations. However, as the molecular chain increases to n-hexacontane and n-decacontane, the reliability of the UA potentials decreases, showing notorious subpredictions of both saturated liquid density and vapor pressure. Based on the recommended data and EoS results for the heaviest hydrocarbons, it is possible to attest, that in this extreme, the TraPPE potential shows the lowest liquid density deviations. The low absolute values of the vapor pressure preclude the discrimination among the three UA potentials studied. On the other hand, interfacial properties are very sensitive to the type of UA potential thus allowing a differentiation of the potentials. Comparing the interfacial tension MD results to the available experimental data and SGT results, the TraPPE model exhibits the lowest deviations for all hydrocarbons.