General approach for solving the density gradient theory in the interfacial tension calculations

Abstract

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Tolman lengths and rigidity constants of multicomponent fluids: Fundamental theory and numerical examples

“…It is challenging to achieve a numerically robust implementation of SGT, and developing various approaches for this is an active research area. [55][56][57] To ensure a correct implementation, the code has been subjected to the following consistency checks:…”

Modeling Interfacial Properties with Spot-DGT-ePC-SAFT for Binary Mixtures Including Ionic Liquid-Based Systems

“…Several algorithms have been proposed to solve eq rigorously, ,, which was termed as the full DGT in this work, such as the reference fluid theory, the stabilized algorithm, etc.…”

“…Several theoretical models have been developed to study the microscopic structure of the interfacial phase. Among them, density gradient theory (DGT) has been widely accepted as a promising model to describe the interfacial properties of fluids, due to its accuracy and simplicity in the calculation. − DGT with the influence parameters of pure substances adjusted from their surface tensions can be used to predict other interfacial properties (density profile, interfacial adsorption, and interfacial thickness) for pure system and the interfacial properties of their mixtures. − However, the work on the IL-containing mixtures is still limited, and the only work was conducted by Oliveira et al, where the soft-statistical associating fluid theory (SAFT) was combined with DGT. Furthermore, IL–CO 2 is an important system for developing an IL-based technology for CO 2 separation, while the theoretical model based on DGT for such a system has not been available.…”

“…Principally, DGT (i.e., full DGT) can be extended to the mixtures for common substances. − ,− However, for the IL-based systems, the extension can be a challenge due to the characterization of ILs with negligible vapor pressures. For example, in ePC-SAFT, the ionic term was used to describe the long-range electrostatic force between the cation and anion with a significant contribution, even at a very low density, leading to that the equilibrium vapor phase of ILs cannot be found at the packing fraction higher than 10 –12 and the mole fraction of IL greater than 10 –10 . , This is reasonable considering the negligible vapor pressure of ILs, and numerically, for a pure IL, this is not a serious problem in solving DGT. , While for IL-based mixtures, if the equilibrium composition cannot be solved, a serious numerical problem will be generated when calculating the density profile of vapor–liquid interphase because the local chemical potential does not equal the bulk chemical potential when approaching to the vapor phase.…”

Phasepy: A Python based framework for fluid phase equilibria and interfacial properties computation

“…If any of the correction parameter β ij is different from zero, it is necessary to solve the system of Equations ) and () as a boundary value problem (BVP) with a finite interfacial length. Different approaches have been proposed to solve this problem, for example, Cornelisse 16 used finite differences, Liang and Michelsen 75 proposed a minimization procedure using orthogonal collocation and Mu et al 76 whose introduced an auxiliary time variable to the system. Those approaches require to solve a system of n ⋅ c equations, where n is the number of interior points to solve and c is the number of components of the mixture.…”