In this work, the classic density functional approach is applied to describe the interfacial structure and properties of the dissolved gas and liquid in the presence of a hydrophobic wall. In the theoretical approach, the modified fundamental measure theory is adopted for the hard-sphere reference term, and the weighted density approximation is applied for the attractive term. The vapor−liquid phase coexistence curve and the interfacial tensions of Lennard-Jones binary mixtures are first calculated. The results are in good agreement with the corresponding simulation data, indicating that the approach is suitable to study the inhomogeneous properties of fluid mixtures. The density profiles of dissolved gas and liquid in the vicinity of the hydrophobic surface are then calculated. It is shown that distinctive gas enrichment and liquid depletion occur in the interfacial region, and the effects can be reinforced as the dispersion potential and molecule diameter of the gas increase. Based on the supersaturation induced by the gas enrichment and liquid depletion, the free energy barriers of bubble nucleation on the solid wall are approximately estimated for different gases to analyze the probability of spontaneous bubble nucleation near the hydrophobic surface.
We present a three-dimensional density functional approach to investigate heterogeneous nucleation behaviors of Lennard-Jones fluid on solid walls. In the theoretical calculation, fast Fourier transforms to compute the convolutions of Euler-Lagrange equation enables a high-efficient algorithm in three-dimensional space. The density distributions of a growing nucleus are presented to account for the nucleation process. Accordingly, the structures of nucleated droplet and surrounding supersaturated vapor on different walls are analyzed, and the corresponding free energy barriers and the critical radii are obtained to evaluate the difficulty of droplet formation. Since the theoretical approach is strictly constructed in three-dimensional space, and the liquid-solid, vapor-solid, and vapor-liquid interfacial tensions as well as the vapor-liquid-solid line tension are entirely integrated into the excess free energy expression, the present approach provides a flexible and efficient tool for studying heterogeneous nucleation.
Due to its complexity, line tension is usually neglected or indirectly estimated in studying heterogeneous nucleation. In this work, we try to provide a direct and quantitative description of it. Within a three-dimensional density functional framework, the total excess free energy and individual energies at different two-phase interfaces are calculated during the droplet or bubble nucleation in binary fluids, and the line tension and contact angle are determined simultaneously. Meanwhile, the contact angle can also be measured directly from the spatial configuration of droplet or bubble. Comparing the calculated and measured contact angles, one can see that a good agreement is achieved for bubble and droplet at solvophilic and solvophobic walls. It is shown that line tension provides a considerable modification of contact angle prediction that is of great importance in engineering applications. V C 2013 American Institute of Chemical Engineers AIChE J, 59: [4390][4391][4392][4393][4394][4395][4396][4397][4398] 2013
In this work, a weighted density functional theory has been used to study the equilibrium and metastable processes for argon. In the theoretical approach, the two- and three-body interactions of the fluid molecules are considered simultaneously, and the renormalization group transformation is applied to address the long-range fluctuations inside the critical region. The global phase equilibria, planar and curvature-dependent surface tensions, critical radius, and nucleation rates of argon are investigated systematically. The results are in good agreement with the experimental data. Meanwhile, this work applies a methodology for calculating the curved surface tension in local supersaturated environments, showing that the Tolman length is negligible far from the critical region. Near the critical point, however, the Tolman length becomes positive and appears to diverge.
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