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Diewald F, Heier M, Horsch M, Kuhn C, Langenbach K, Hasse H, Müller R. Three-dimensional phase field modeling of inhomogeneous gas-liquid systems using the PeTS equation of state. J Chem Phys 2018; 149:064701. [PMID: 30111148 DOI: 10.1063/1.5035495] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Recently, an equation of state (EoS) for the Lennard-Jones truncated and shifted (LJTS) fluid has become available. As it describes metastable and unstable states well, it is suited for predicting density profiles in vapor-liquid interfaces in combination with density gradient theory (DGT). DGT is usually applied to describe interfaces in Cartesian one-dimensional scenarios. In the present work, the perturbed LJ truncated and shifted (PeTS) EoS is implemented into a three-dimensional phase field (PF) model which can be used for studying inhomogeneous gas-liquid systems in a more general way. The results are compared with the results from molecular dynamics simulations for the LJTS fluid that are carried out in the present work and good agreement is observed. The PF model can therefore be used to overcome the scale limit of molecular simulations. A finite element approach is applied for the implementation of the PF model. This requires the first and second derivatives of the PeTS EoS which are calculated using hyper-dual numbers. Several tests and examples of applications of the new PeTS PF model are discussed.
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Affiliation(s)
- Felix Diewald
- Institute of Applied Mechanics, Technische Universität Kaiserslautern, 67653 Kaiserslautern, Germany
| | - Michaela Heier
- Laboratory of Engineering Thermodynamics, Technische Universität Kaiserslautern, 67653 Kaiserslautern, Germany
| | - Martin Horsch
- Laboratory of Engineering Thermodynamics, Technische Universität Kaiserslautern, 67653 Kaiserslautern, Germany
| | - Charlotte Kuhn
- Computational Mechanics, Technische Universität Kaiserslautern, 67653 Kaiserslautern, Germany
| | - Kai Langenbach
- Laboratory of Engineering Thermodynamics, Technische Universität Kaiserslautern, 67653 Kaiserslautern, Germany
| | - Hans Hasse
- Laboratory of Engineering Thermodynamics, Technische Universität Kaiserslautern, 67653 Kaiserslautern, Germany
| | - Ralf Müller
- Institute of Applied Mechanics, Technische Universität Kaiserslautern, 67653 Kaiserslautern, Germany
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Richard D, Speck T. Crystallization of hard spheres revisited. II. Thermodynamic modeling, nucleation work, and the surface of tension. J Chem Phys 2018; 148:224102. [DOI: 10.1063/1.5025394] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- David Richard
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
| | - Thomas Speck
- Institut für Physik, Johannes Gutenberg-Universität Mainz, Staudingerweg 7-9, 55128 Mainz, Germany
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Langenbach K, Heilig M, Horsch M, Hasse H. Study of homogeneous bubble nucleation in liquid carbon dioxide by a hybrid approach combining molecular dynamics simulation and density gradient theory. J Chem Phys 2018; 148:124702. [DOI: 10.1063/1.5022231] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Affiliation(s)
- K. Langenbach
- Laboratory of Engineering Thermodynamics, University of Kaiserslautern, Kaiserslautern D-67663, Germany
| | - M. Heilig
- ROM, Digitalization in Research and Development, BASF SE, Ludwigshafen D-67056, Germany
| | - M. Horsch
- Laboratory of Engineering Thermodynamics, University of Kaiserslautern, Kaiserslautern D-67663, Germany
| | - H. Hasse
- Laboratory of Engineering Thermodynamics, University of Kaiserslautern, Kaiserslautern D-67663, Germany
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Planková B, Vinš V, Hrubý J. Predictions of homogeneous nucleation rates for n-alkanes accounting for the diffuse phase interface and capillary waves. J Chem Phys 2017; 147:164702. [PMID: 29096481 DOI: 10.1063/1.5008612] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Abstract
Homogeneous droplet nucleation has been studied for almost a century but has not yet been fully understood. In this work, we used the density gradient theory (DGT) and considered the influence of capillary waves (CWs) on the predicted size-dependent surface tensions and nucleation rates for selected n-alkanes. The DGT model was completed by an equation of state (EoS) based on the perturbed-chain statistical associating fluid theory and compared to the classical nucleation theory and the Peng-Robinson EoS. It was found that the critical clusters are practically free of CWs because they are so small that even the smallest wavelengths of CWs do not fit into their finite dimensions. The CWs contribute to the entropy of the system and thus decrease the surface tension. A correction for the effect of CWs on the surface tension is presented. The effect of the different EoSs is relatively small because by a fortuitous coincidence their predictions are similar in the relevant range of critical cluster sizes. The difference of the DGT predictions to the classical nucleation theory computations is important but not decisive. Of the effects investigated, the most pronounced is the suppression of CWs which causes a sizable decrease of the predicted nucleation rates. The major difference between experimental nucleation rate data and theoretical predictions remains in the temperature dependence. For normal alkanes, this discrepancy is much stronger than observed, e.g., for water. Theoretical corrections developed here have a minor influence on the temperature dependency. We provide empirical equations correcting the predicted nucleation rates to values comparable with experiments.
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Affiliation(s)
- Barbora Planková
- Institute of Thermomechanics of the Czech Academy of Sciences, v. v. i., Dolejškova 5, 182 00 Prague, Czech Republic
| | - Václav Vinš
- Institute of Thermomechanics of the Czech Academy of Sciences, v. v. i., Dolejškova 5, 182 00 Prague, Czech Republic
| | - Jan Hrubý
- Institute of Thermomechanics of the Czech Academy of Sciences, v. v. i., Dolejškova 5, 182 00 Prague, Czech Republic
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Celný D, Vinš V, Planková B, Hrubý J. Mathematical modeling of planar and spherical vapor–liquid phase interfaces for multicomponent fluids. EPJ WEB OF CONFERENCES 2016. [DOI: 10.1051/epjconf/201611402011] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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6
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Bruot N, Caupin F. Curvature Dependence of the Liquid-Vapor Surface Tension beyond the Tolman Approximation. PHYSICAL REVIEW LETTERS 2016; 116:056102. [PMID: 26894721 DOI: 10.1103/physrevlett.116.056102] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/04/2015] [Indexed: 06/05/2023]
Abstract
Surface tension is a macroscopic manifestation of the cohesion of matter, and its value σ_{∞} is readily measured for a flat liquid-vapor interface. For interfaces with a small radius of curvature R, the surface tension might differ from σ_{∞}. The Tolman equation, σ(R)=σ_{∞}/(1+2δ/R), with δ a constant length, is commonly used to describe nanoscale phenomena such as nucleation. Here we report experiments on nucleation of bubbles in ethanol and n-heptane, and their analysis in combination with their counterparts for the nucleation of droplets in supersaturated vapors, and with water data. We show that neither a constant surface tension nor the Tolman equation can consistently describe the data. We also investigate a model including 1/R and 1/R^{2} terms in σ(R). We describe a general procedure to obtain the coefficients of these terms from detailed nucleation experiments. This work explains the conflicting values obtained for the Tolman length in previous analyses, and suggests directions for future work.
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Affiliation(s)
- Nicolas Bruot
- Institut Lumière Matière, UMR5306 Université Claude Bernard Lyon 1-CNRS, Université de Lyon, Institut Universitaire de France, 69622 Villeurbanne cedex, France
| | - Frédéric Caupin
- Institut Lumière Matière, UMR5306 Université Claude Bernard Lyon 1-CNRS, Université de Lyon, Institut Universitaire de France, 69622 Villeurbanne cedex, France
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Wilhelmsen Ø, Bedeaux D, Reguera D. Communication: Tolman length and rigidity constants of water and their role in nucleation. J Chem Phys 2015; 142:171103. [DOI: 10.1063/1.4919689] [Citation(s) in RCA: 40] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Øivind Wilhelmsen
- Department of Chemistry, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
| | - Dick Bedeaux
- Department of Chemistry, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
| | - David Reguera
- Departament de Física Fonamental, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain
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Magnanelli E, Wilhelmsen Ø, Bedeaux D, Kjelstrup S. Extending the nonequilibrium square-gradient model with temperature-dependent influence parameters. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:032402. [PMID: 25314452 DOI: 10.1103/physreve.90.032402] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2014] [Indexed: 06/04/2023]
Abstract
Nonequilibrium interface phenomena play a key role in crystallization, hydrate formation, pipeline depressurization, and a multitude of other examples. Square gradient theory extended to the nonequilibrium domain is a powerful tool for understanding these processes. The theory gives an accurate prediction of surface tension at equilibrium, only with temperature-dependent influence parameters. We extend in this work the nonequilibrium square gradient model to have temperature-dependent influence parameters. The extension leads to thermodynamic quantities which depend on temperature gradients. Remarkably the Gibbs relation proposed in earlier work is still valid. Also for the extended framework, the "Gibbs surface" described by excess variables is found to be in local equilibrium. The temperature-dependent influence parameters give significantly different interface resistivities (∼9%-50%), due to changed density gradients and additional terms in the enthalpy. The presented framework facilitates a more accurate description of transport across interfaces with square gradient theory.
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Affiliation(s)
- Elisa Magnanelli
- Department of Chemistry, Norwegian University of Science and Technology, Trondheim, Norway
| | - Øivind Wilhelmsen
- Department of Chemistry, Norwegian University of Science and Technology, Trondheim, Norway
| | - Dick Bedeaux
- Department of Chemistry, Norwegian University of Science and Technology, Trondheim, Norway
| | - Signe Kjelstrup
- Department of Chemistry, Norwegian University of Science and Technology, Trondheim, Norway
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9
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Vinš V, Planková B, Hrubý J, Celný D. Density gradient theory combined with the PC-SAFT equation of state used for modeling the surface tension of associating systems. EPJ WEB OF CONFERENCES 2014. [DOI: 10.1051/epjconf/20146702129] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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10
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Wilhelmsen Ø, Bedeaux D, Kjelstrup S, Reguera D. Thermodynamic stability of nanosized multicomponent bubbles/droplets: The square gradient theory and the capillary approach. J Chem Phys 2014; 140:024704. [DOI: 10.1063/1.4860495] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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11
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Carreón-Calderón B. Theoretical study of vapor-liquid homogeneous nucleation using stability analysis of a macroscopic phase. J Chem Phys 2012; 137:144104. [PMID: 23061836 DOI: 10.1063/1.4757384] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
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.
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Affiliation(s)
- Bernardo Carreón-Calderón
- Programa de Aseguramiento de la Producción de Hidrocarburos, Instituto Mexicano del Petróleo, Eje Central Lázaro Cárdenas Norte 152, San Bartolo Atepehuacan, Gustavo A. Madero, 07730 D.F., México
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12
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Napari I, Julin J, Vehkamäki H. Performance of some nucleation theories with a nonsharp droplet-vapor interface. J Chem Phys 2010; 133:154503. [DOI: 10.1063/1.3502643] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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13
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Ghosh D, Bergmann D, Schwering R, Wölk J, Strey R, Tanimura S, Wyslouzil BE. Homogeneous nucleation of a homologous series of n-alkanes (CiH2i+2, i=7–10) in a supersonic nozzle. J Chem Phys 2010; 132:024307. [DOI: 10.1063/1.3274629] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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14
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Tóth GI, Gránásy L. Crystal Nucleation in the Hard-Sphere System Revisited: A Critical Test of Theoretical Approaches. J Phys Chem B 2009; 113:5141-8. [DOI: 10.1021/jp8097439] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Gyula I. Tóth
- Research Institute for Solid State Physics and Optics, H-1525 Budapest, POB 49, Hungary
| | - László Gránásy
- Brunel Centre for Advanced Solidification Technology, Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom
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15
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Julin J, Napari I, Merikanto J, Vehkamäki H. Equilibrium sizes and formation energies of small and large Lennard-Jones clusters from molecular dynamics: A consistent comparison to Monte Carlo simulations and density functional theories. J Chem Phys 2008; 129:234506. [DOI: 10.1063/1.3040245] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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