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Chaparro G, Müller EA. Simulation and Data-Driven Modeling of the Transport Properties of the Mie Fluid. J Phys Chem B 2024; 128:551-566. [PMID: 38181201 PMCID: PMC10801693 DOI: 10.1021/acs.jpcb.3c06813] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2023] [Revised: 12/14/2023] [Accepted: 12/15/2023] [Indexed: 01/07/2024]
Abstract
This work reports the computation and modeling of the self-diffusivity (D*), shear viscosity (η*), and thermal conductivity (κ*) of the Mie fluid. The transport properties were computed using equilibrium molecular dynamics simulations for the Mie fluid with repulsive exponents (λr) ranging from 7 to 34 and at a fixed attractive exponent (λa) of 6 over the whole fluid density (ρ*) range and over a wide temperature (T*) range. The computed database consists of 17,212, 14,288, and 13,099 data points for self-diffusivity, shear viscosity, and thermal conductivity, respectively. The database is successfully validated against published simulation data. The above-mentioned transport properties are correlated using artificial neural networks (ANNs). Two modeling approaches were tested: a semiempirical formulation based on entropy scaling and an empirical formulation based on density and temperature as input variables. For the former, it was found that a unique formulation based on entropy scaling does not yield satisfactory results over the entire density range due to a divergent and incorrect scaling of the transport properties at low densities. For the latter empirical modeling approach, it was found that regularizing the data, e.g., modeling ρ*D* instead of D*, ln η* instead of η*, and ln κ* instead of κ*, as well as using the inverse of the temperature as an input feature, helps to ease the interpolation efforts of the artificial neural networks. The trained ANNs can model seen and unseen data over a wide range of density and temperature. Ultimately, the ANNs can be used alongside equations of state to regress effective force field parameters from volumetric and transport data.
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Affiliation(s)
- Gustavo Chaparro
- Department of Chemical Engineering,
Sargent Centre for Process Systems Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, U.K.
| | - Erich A. Müller
- Department of Chemical Engineering,
Sargent Centre for Process Systems Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, U.K.
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Rehner P, Bauer G, Gross J. FeO s: An Open-Source Framework for Equations of State and Classical Density Functional Theory. Ind Eng Chem Res 2023. [DOI: 10.1021/acs.iecr.2c04561] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/11/2023]
Affiliation(s)
- Philipp Rehner
- Energy and Process Systems Engineering, Department of Mechanical and Process Engineering, ETH Zurich, Tannenstrasse 3, Zurich 8092, Switzerland
| | - Gernot Bauer
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, Stuttgart 70569, Germany
| | - Joachim Gross
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, Stuttgart 70569, Germany
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Maltby TW, Hafskjold B, Bedeaux D, Kjelstrup S, Wilhelmsen Ø. Local equilibrium in liquid phase shock waves. Phys Rev E 2023; 107:035108. [PMID: 37073064 DOI: 10.1103/physreve.107.035108] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2022] [Accepted: 03/13/2023] [Indexed: 04/20/2023]
Abstract
We have assessed the assumption of local thermodynamic equilibrium in a shock wave by comparing local thermodynamic data generated with nonequilibrium molecular dynamics (NEMD) simulations with results from corresponding equilibrium simulations. The shock had a Mach number approximately equal to 2 in a Lennard-Jones spline liquid. We found that the local equilibrium assumption holds perfectly well behind the wave front, and is a very good approximation in the front itself. This was supported by calculations of the excess entropy production in the shock front with four different methods that use the local equilibrium assumption in different ways. Two of the methods assume local equilibrium between excess thermodynamic variables by treating the shock as an interface in Gibbs's sense. The other two methods are based on the local equilibrium assumption in a continuous description of the shock front. We show for the shock studied in this work that all four methods give excess entropy productions that are in excellent agreement, with an average variance of 3.5% for the nonequilibrium molecular dynamics (NEMD) simulations. In addition, we solved the Navier-Stokes (N-S) equations numerically for the same shock wave using an equilibrium equation of state (EoS) based on a recently developed perturbation theory. The results for the density, pressure, and temperature profiles agree well with the profiles from the NEMD simulations. For instance, the shock waves generated in the two simulations travel with almost the same speed; the average absolute Mach-number deviation of the N-S simulations relative to NEMD is 2.6% in the investigated time interval.
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Affiliation(s)
- Tage W Maltby
- PoreLab, Department of Chemistry, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
| | - Bjørn Hafskjold
- PoreLab, Department of Chemistry, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
| | - Dick Bedeaux
- PoreLab, Department of Chemistry, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
| | - Signe Kjelstrup
- PoreLab, Department of Chemistry, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
| | - Øivind Wilhelmsen
- PoreLab, Department of Chemistry, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
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Walker PJ. Toward Advanced, Predictive Mixing Rules in SAFT Equations of State. Ind Eng Chem Res 2022. [DOI: 10.1021/acs.iecr.2c03464] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Affiliation(s)
- Pierre J. Walker
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California91125, United States
- Department of Chemical Engineering, Imperial College London, LondonSW7 2AZ, United Kingdom
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Bråten V, Zhang DT, Hammer M, Aasen A, Schnell SK, Wilhelmsen Ø. Equation of state for confined fluids. J Chem Phys 2022; 156:244504. [DOI: 10.1063/5.0096875] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Fluids confined in small volumes behave differently than fluids in bulk systems. For bulk systems, a compact summary of the system’s thermodynamic properties is provided by equations of state. However, there is currently a lack of successful methods to predict the thermodynamic properties of confined fluids by use of equations of state, since their thermodynamic state depends on additional parameters introduced by the enclosing surface. In this work, we present a consistent thermodynamic framework that represents an equation of state for pure, confined fluids. The total system is decomposed into a bulk phase in equilibrium with a surface phase. The equation of state is based on an existing, accurate description of the bulk fluid and uses Gibbs’ framework for surface excess properties to consistently incorporate contributions from the surface. We apply the equation of state to a Lennard-Jones spline fluid confined by a spherical surface with a Weeks–Chandler–Andersen wall-potential. The pressure and internal energy predicted from the equation of state are in good agreement with the properties obtained directly from molecular dynamics simulations. We find that when the location of the dividing surface is chosen appropriately, the properties of highly curved surfaces can be predicted from those of a planar surface. The choice of the dividing surface affects the magnitude of the surface excess properties and its curvature dependence, but the properties of the total system remain unchanged. The framework can predict the properties of confined systems with a wide range of geometries, sizes, interparticle interactions, and wall–particle interactions, and it is independent of ensemble. A targeted area of use is the prediction of thermodynamic properties in porous media, for which a possible application of the framework is elaborated.
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Affiliation(s)
- Vilde Bråten
- Department of Materials Science and Engineering, Norwegian University of Science and Technology, NTNU, Trondheim NO-7491, Norway
| | - Daniel Tianhou Zhang
- Department of Chemistry, Norwegian University of Science and Technology, NTNU, Trondheim NO-7491, Norway
| | - Morten Hammer
- PoreLab, Department of Chemistry, Norwegian University of Science and Technology, NTNU, Trondheim NO-7491, Norway
- Gas Technology, PoreLab, SINTEF Energy Research, Trondheim NO-7465, Norway
| | - Ailo Aasen
- Gas Technology, PoreLab, SINTEF Energy Research, Trondheim NO-7465, Norway
| | - Sondre Kvalvåg Schnell
- Department of Materials Science and Engineering, Norwegian University of Science and Technology, NTNU, Trondheim NO-7491, Norway
| | - Øivind Wilhelmsen
- PoreLab, Department of Chemistry, Norwegian University of Science and Technology, NTNU, Trondheim NO-7491, Norway
- Gas Technology, PoreLab, SINTEF Energy Research, Trondheim NO-7465, Norway
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van Westen T, Gross J. Double-Hard-Sphere perturbation theory: a perturbation theory that is less dependent on the value of the hard-sphere diameter. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2059410] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Thijs van Westen
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Stuttgart, Germany
| | - Joachim Gross
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Stuttgart, Germany
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van Westen T, Hammer M, Hafskjold B, Aasen A, Gross J, Wilhelmsen Ø. Perturbation theories for fluids with short-ranged attractive forces: A case study of the Lennard-Jones spline fluid. J Chem Phys 2022; 156:104504. [DOI: 10.1063/5.0082690] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
It is generally not straightforward to apply molecular-thermodynamic theories to fluids with short-ranged attractive forces between their constituent molecules (or particles). This especially applies to perturbation theories, which, for short-ranged attractive fluids, typically must be extended to high order or may not converge at all. Here, we show that a recent first-order perturbation theory, the uv-theory, holds promise for describing such fluids. As a case study, we apply the uv-theory to a fluid with pair interactions defined by the Lennard-Jones spline potential, which is a short-ranged version of the LJ potential that is known to provide a challenge for equation-of-state development. The results of the uv-theory are compared to those of third-order Barker–Henderson and fourth-order Weeks–Chandler–Andersen perturbation theories, which are implemented using Monte Carlo simulation results for the respective perturbation terms. Theoretical predictions are compared to an extensive dataset of molecular simulation results from this (and previous) work, including vapor–liquid equilibria, first- and second-order derivative properties, the critical region, and metastable states. The uv-theory proves superior for all properties examined. An especially accurate description of metastable vapor and liquid states is obtained, which might prove valuable for future applications of the equation-of-state model to inhomogeneous phases or nucleation processes. Although the uv-theory is analytic, it accurately describes molecular simulation results for both the critical point and the binodal up to at least 99% of the critical temperature. This suggests that the difficulties typically encountered in describing the vapor–liquid critical region are only to a small extent caused by non-analyticity.
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Affiliation(s)
- Thijs van Westen
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, D-70569 Stuttgart, Germany
| | - Morten Hammer
- Department of Gas Technology, SINTEF Energy Research, NO-7465 Trondheim, Norway
| | - Bjørn Hafskjold
- Porelab, Department of Chemistry, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
| | - Ailo Aasen
- Department of Gas Technology, SINTEF Energy Research, NO-7465 Trondheim, Norway
| | - Joachim Gross
- Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, D-70569 Stuttgart, Germany
| | - Øivind Wilhelmsen
- Porelab, Department of Chemistry, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
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