0
Research Papers

Evaluations of Molecular Dynamics Methods for Thermodiffusion in Binary Mixtures

[+] Author and Article Information
Seyedeh H. Mozaffari

Department of Mechanical and Industrial Engineering,
Ryerson University,
350 Victoria Street,
Toronto, ON M5B 2K3, Canada
e-mail: s2mozaff@ryerson.ca

Seshasai Srinivasan

Assistant Professor
School of Engineering Practice and Technology,
McMaster University,
1280 Main Street West,
Hamilton, ON L8S 4L8, Canada;
Department of Mechanical Engineering, McMaster University,
1280 Main Street West,
Hamilton, ON L8S 4L8, Canada;
Adjunct Professor
Department of Mechanical and Industrial Engineering,
Ryerson University,
350 Victoria Street,
Toronto, ON M5B 2K3, Canada
e-mail: ssriniv@mcmaster.ca

M. Ziad Saghir

Professor
Department of Mechanical and
Industrial Engineering,
Ryerson University,
350 Victoria Street,
Toronto, ON M5B 2K3, Canada
e-mail: zsaghir@ryerson.ca

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received May 31, 2016; final manuscript received September 27, 2016; published online April 11, 2017. Assoc. Editor: Pedro Mago.

J. Thermal Sci. Eng. Appl 9(3), 031011 (Apr 11, 2017) (9 pages) Paper No: TSEA-16-1153; doi: 10.1115/1.4035939 History: Received May 31, 2016; Revised September 27, 2016

The objective of this paper is to investigate the behavior of two well-known boundary-driven molecular dynamics (MD) approaches, namely, reverse nonequilibrium molecular dynamics (RNEMD) and heat exchange algorithm (HEX), as well as introducing a modified HEX model (MHEX) that is more accurate and computationally efficient to simulate the mass and heat transfer mechanism. For this investigation, the following binary mixtures were considered: one equimolar mixture of argon (Ar) and krypton (Kr), one nonequimolar liquid mixture of hexane (nC6) and decane (nC10), and three nonequimolar mixtures of pentane (nC5) and decane. In estimating the Thermodiffusion factor in these mixtures using the three methods, it was found that consistent with the findings in the literature, RNEMD predictions have the largest error with respect to the experimental data. Whereas, the MHEX method proposed in this work is the most accurate, marginally outperforming the HEX method. Most importantly, the computational efficiency of MHEX method is the highest, about 7% faster than the HEX method. This makes it more suitable for integration with multiscale computational models to simulate thermodiffusion in a large system such as an oil reservoir.

FIGURES IN THIS ARTICLE
<>
Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Srinivasan, S. , and Saghir, M. Z. , 2013, Thermodiffusion in Multicomponent Mixtures, Springer, New York, Chap. 1.
Huang, F. , Chakraborty, P. , Lundstrom, C. C. , Holmden, C. , Glessner, J. J. G. , Kieffer, S. W. , and Lesher, C. E. , 2010, “ Isotope Fractionation in Silicate Melts by Thermal Diffusion,” Nature, 464(7287), pp. 396–400. [CrossRef] [PubMed]
Halder, A. , Dhall, A. , and Datta, A. K. , 2011, “ Modeling Transport in Porous Media With Phase Change: Applications to Food Processing,” ASME J. Heat Transfer, 133(3), p. 031010. [CrossRef]
Würger, A. , 2009, “ Molecular-Weight Dependent Thermal Diffusion in Dilute Polymer Solutions,” Phys. Rev. Lett., 102(7), pp. 1–4. [CrossRef]
You, Y. , 2002, “ A Global Ocean Climatological Atlas of the Turner Angle: Implications for Double-Diffusion and Water–Mass Structure,” Deep-Sea Res., Part I, 49(11), pp. 2075–2093. [CrossRef]
Suárez, F. , Tyler, S. W. , and Childress, A. E. , 2010, “ A Fully Coupled, Transient Double-Diffusive Convective Model for Salt-Gradient Solar Ponds,” Int. J. Heat Mass Transfer, 53(9–10), pp. 1718–1730. [CrossRef]
Montel, F. , 1993, “ Phase Equilibria Needs for Petroleum Exploration and Production Industry,” Fluid Phase Equilib., 84(C), pp. 343–367. [CrossRef]
Srinivasan, S. , and Saghir, M. Z. , 2011, “ Experimental Approaches to Study Thermodiffusion—A Review,” Int. J. Therm. Sci., 50(7), pp. 1125–1137. [CrossRef]
Platten, J. K. , 2006, “ The Soret Effect: A Review of Recent Experimental Results,” J. Appl. Mech., 73(5), pp. 5–15. [CrossRef]
Faissat, B. , Knudsen, K. , Stenby, E. , and Montel, F. , 1994, “ Fundamental Statements About Thermal Diffusion for a Multicomponent Mixture in a Porous Medium,” Fluid Phase Equilib., 100(C), pp. 209–222. [CrossRef]
Ziad Saghir, M. , and Eslamian, M. , 2009, “ A Critical Review of Thermodiffusion Models: Role and Significance of the Heat of Transport and the Activation Energy of Viscous Flow,” J. Non-Equilib. Thermodyn., 34(2), pp. 97–131.
Kohler, W. E. , and Halbritter, J. , 1975, “ Kinetic Theory of Thermal Diffusion in a Magnetic Field,” Z. Naturforsch., 30(9), pp. 1114–1121.
Kox, A. J. , Van Leeuwen, W. A. , and De Groot, S. R. , 1976, “ On Relativistic Kinetic Gas Theory. XVII. Diffusion and Thermal Diffusion in a Binary Mixture of Hard Spheres,” Physica A, 84(1), pp. 165–174. [CrossRef]
Dougherty, E. L. , and Drickamer, H. G. , 1955, “ A Theory of Thermal Diffusion in Liquids,” J. Chem. Phys., 23(2), pp. 295–309. [CrossRef]
Guy, A. , 1986, “ Prediction of Thermal Diffusion in Binary Mixtures of Nonelectrolyte Liquids by the Use of Nonequilibrium Thermodynamics,” Int. J. Thermophys., 7(3), pp. 563–572. [CrossRef]
Firoozabadi, A. , Ghorayeb, K. , and Shukla, K. , 2000, “ Theoretical Model of Thermal Diffusion Factors in Multicomponent Mixtures,” AIChE J., 46(5), pp. 892–900. [CrossRef]
Eslamian, M. , and Saghir, M. Z. , 2012, “ Estimation of Thermodiffusion Coefficients in Ternary Associating Mixtures,” Can. J. Chem. Eng., 90(4), pp. 936–943. [CrossRef]
Srinivasan, S. , and Saghir, M. Z. , 2011, “ Thermodiffusion in Ternary Hydrocarbon Mixtures: Part 1—n-Dodecane/Isobutylbenzene/Tetralin,” J. Non-Equilib. Thermodyn., 36(3), pp. 243–258. [CrossRef]
Srinivasan, S. , and Saghir, M. Z. , 2012, “ Thermodiffusion in Ternary Hydrocarbon Mixtures: Part 2—n-decane/isobutylbenzene/tetralin,” J. Non-Equilib. Thermodyn., 37(1), pp. 99–113. [CrossRef]
Mortimer, R. , and Eyring, H. , 1980, “ Elementary Transition State Theory of Soret and Dufour Effects,” Proc. Natl. Acad. Sci., 77(4), pp. 1728–1731. [CrossRef]
Bielenberg, J. , and Brenner, H. , 2005, “ A Hydrodynamic/Brownian Motion Model of Thermal Diffusion in Liquids,” Physica A, 356(2–4), pp. 279–293. [CrossRef]
Brenner, H. , 2006, “ Elementary Model of Thermal Diffusion in Liquids and Gases,” Phys. Rev. E, 74(3), p. 036306. [CrossRef]
Kempers, L. M. , 1989, “ A Thermodynamic Theory of the Soret Effect in a Multicomponent Liquid,” J. Chem. Phys., 90(11), pp. 6541–6548. [CrossRef]
Srinivasan, S. , and Saghir, M. Z. , 2010, “ Significance of Equation of State and Viscosity on the Thermodiffusion Coefficients of a Ternary Hydrocarbon Mixture,” J. High Temp. High Pressures, 39(1), pp. 65–81.
Srinivasan, S. , and Saghir, M. Z. , 2014, “ Computational Evaluation of Micro-Scale and Macro-Scale Error Sources in a Thermodiffusive Cell,” J. Comput. Sci., 5(5), pp. 767–776. [CrossRef]
Srinivasan, S. , and Saghir, M. Z. , 2011, “ Impact of the Vibrations on Soret Separation in Binary and Ternary Mixtures,” Fluid Dyn. Mater. Process., 7(2), pp. 201–216.
Srinivasan, S. , and Saghir, M. Z. , 2010, “ Thermo-Solutal-Diffusion in High Pressure Liquid Mixtures in the Presence of Micro-Vibrations,” Int. J. Therm. Sci., 49(9), pp. 1613–1624. [CrossRef]
Parsa, A. , Srinivasan, S. , and Saghir, M. Z. , 2013, “ Impact of Density Gradients on the Fluid Flow Inside a Vibrating Cavity Subjected to Soret Effect,” Can. J. Chem. Eng., 91(3), pp. 550–559. [CrossRef]
Srinivasan, S. , and Saghir, M. Z. , 2014, “ Predicting Thermodiffusion in an Arbitrary Binary Liquid Hydrocarbon Mixtures Using Artificial Neural Networks,” Neural Comput. Appl., 25(5), pp. 1193–1203. [CrossRef]
Srinivasan, S. , and Saghir, M. Z. , 2014, “ A Neurocomputing Model to Calculate the Thermo-Solutal Diffusion in Liquid Hydrocarbon mixtures,” Neural Comput. Appl., 24(2), pp. 287–299. [CrossRef]
Srinivasan, S. , and Saghir, M. Z. , 2012, “ Estimating the Thermotransport Factor in Binary Metal Alloys Using Artificial Neural Networks,” Appl. Math. Model., 37(5), pp. 2850–2869. [CrossRef]
Schoen, M. , and Hoheisel, C. , 1984, “ The Mutual Diffusion Coefficient D12 in Liquid Model Mixture—A Molecular Dynamics Study based on Lennard–Jones (12-6) Potentials. II. Lorentz–Berthelot Mixtures,” Mol. Phys., 52(5), pp. 1029–1042. [CrossRef]
Babaei, H. , Keblinski, P. , and Khodadadi, J. M. , 2012, “ Equilibrium Molecular Dynamics Determination of Thermal Conductivity for Multi-Component Systems,” J. Appl. Phys., 112(5), p. 054310. [CrossRef]
Alaghemandi, M. , Algaer, E. , Bohm, M. C. , and Muller-Plathe, F. , 2009, “ The Thermal conductivity and Thermal Rectification of Carbon Nanotubes Studied Using Reverse Non-Equilibrium Molecular Dynamics Simulations,” Nanotechnology, 20(11), p. 115704. [CrossRef] [PubMed]
Wheeler, D. R. , Fuller, N. G. , and Rowley, R. L. , 1997, “ Non-Equilibrium Molecular Dynamics Simulation of the Shear Viscosity of Liquid Methanol: Adaptation of Ewald Sum to Lees–Edwards Boundary Conditions,” Mol. Phys., 92(1), pp. 55–62. [CrossRef]
Guevara-Carrion, G. , Vrabec, J. , and Hasse, H. , 2012, “ Prediction of Transport Properties of Liquid Ammonia and Its Binary Mixture With Methanol by Molecular simulation,” Int. J. Thermophys., 33(3), pp. 449–468. [CrossRef]
MacGowan, D. , and Evans, D. J. , 1986, “ Heat and Mass Transfer in Binary Liquid Mixtures,” Phys. Rev. A, 34(3), pp. 2133–2141. [CrossRef]
Paolini, G. V. , and Ciccotti, G. , 1987, “ Cross Thermotransport in Liquid Mixtures by Non-Equilibrium Molecular Dynamics,” Phys. Rev. A, 35(12), pp. 5156–5166. [CrossRef]
Evans, D. J. , 1982, “ Homogeneous NEMD Algorithm for Thermal Conductivity—Application of Non-Canonical Linear Response Theory,” Phys. Lett. A, 91(9), pp. 457–460. [CrossRef]
HafskJold, B. , Ikeshoji, T. , and Ratkje, S. K. , 1993, “ On the Molecular Mechanism of Thermal Diffusion in Liquids,” Mol. Phys., 80(6), pp. 1389–1412. [CrossRef]
Ikeshoji, T. , and HafskJold, B. , 1994, “ Non-Equilibrium Molecular Dynamics Calculation of Heat Conduction Liquid and Through Liquid–Gas Interface,” Mol. Phys., 81(2), pp. 251–261. [CrossRef]
Müller-Plathe, F. , 1997, “ A Simple Non-Equilibrium Molecular Dynamics Method for Calculating the Thermal Conductivity,” J. Chem. Phys., 106(14), pp. 6082–6085. [CrossRef]
Müller-Plathe, F. , and Reith, D. , 1999, “ Cause and Effect Reversed in Non-Equilibrium Molecular Dynamics: An Easy Route to Transport Coefficients,” Comput. Theor. Polym. Sci., 9(3–4), pp. 203–209. [CrossRef]
Galliero, G. , Srinivasan, S. , and Saghir, M. Z. , 2010, “ Estimation of Thermodiffusion in Ternary Alkane Mixtures Using Molecular Dynamics Simulations and an Irreversible Thermodynamic Theory,” High Temp. High Pressure, 38, pp. 315–328.
Galliero, G. , Bugel, M. , Duguay, B. , and Montel, F. , 2007, “ Mass Effect on Thermodiffusion Using Molecular Dynamics,” J. Non-Equilib. Thermodyn., 32(3), pp. 251–258. [CrossRef]
Galliero, G. , Colombani, J. , Bopp, P. A. , Duguay, B. , Caltagirone, J. P. , and Montel, F. , 2006 “ Thermal Diffusion in Micropores by Molecular Dynamics Computer Simulations,” Physica A, 361(2), pp. 494–510. [CrossRef]
Colombani, J. , Galliero, G. , Duguay, B. , Caltagirone, J. P. , Montel, F. , and Bopp, P. A. , 2003, “ Molecular Dynamics Study of Thermal Diffusion in a Binary Mixture of Alkanes Trapped in a Slit Pore,” Philos. Mag., 83(17–18), pp. 2087–2095. [CrossRef]
Galliero, G. , and Volz, S. , 2008, “ Thermodiffusion in Model Nanofluids by Molecular Dynamics Simulations,” J. Chem. Phys., 128(6), p. 064505. [CrossRef] [PubMed]
Galliero, G. , and Montel, F. , 2008, “ Nonisothermal Gravitational Segregation by Molecular Dynamics Simulations,” Phys. Rev. E, 78(4), p. 041203. [CrossRef]
De Groot, S. R. , and Mazur, P. , 1961, Thermodiffusion in Multicomponent Mixtures, Dover Publications, New York, Chap. 4.
Bird, R. B. , Stewart, W. E. , and Lightfoot, E. N. , 2007, Transport Phenomena, Wiley, New York, Chap. 24.
Gallero, G. , Dugyay, B. , Caltagirone, J. P. , and Montel, F. , 2003, “ On Thermal Diffusion in Binary and Ternary Lennard–Jones Mixtures by Non-Equilibrium Molecular Dynamics,” Philos. Mag., 83(18), pp. 2097–2108. [CrossRef]
Allen, M. P. , and Tildesley, D. J. , 1987, Computer Simulation of Liquids, Oxford Science Publication, Oxford, UK, Chap. 1.
NIST, 2007, “ NIST Thermophysical Properties of Hydrocarbon Mixtures Database,” SUPERTRAPP Software, Version 3.2, National Institute of Standards and Technology, Gaithersburg, MD.
Miller, N. A. T. , Daivis, P. J. , Snook, I. K. , and Todd, B. D. , 2013, “ Computation of Thermodynamic and Transport Properties to Predict Thermophoretic Effects in an Argon–Krypton Mixture,” J. Chem. Phys., 139(14), p. 144504. [CrossRef] [PubMed]
Srinivasan, S. , de Mezquia, D. A. , Bou-Ali, M. M. , and Saghir, M. Z. , 2011, “ Thermodiffusion and Molecular Diffusion in Binary n-Alkane Mixtures: Experiments and Numerical Analysis,” Philos. Mag., 91(34), pp. 4332–4344. [CrossRef]
Perronace, A. , Leppla, C. , Leroy, F. , Rousseau, B. , and Wiegand, S. , 2002, “ Soret and Mass Diffusion Measurements and Molecular Dynamics Simulations of N-Pentane–N-Decane Mixtures,” J. Chem. Phys., 116(9), pp. 3718–3729. [CrossRef]
Polyakov, P. , Müller, F. , and Wiegand, S. , 2008, “ Reverse Nonequilibrium Molecular Dynamics Calculation of the Soret Coefficient in Liquid Heptane/Benzene Mixtures,” J. Phys. Chem. B, 112(47), pp. 14999–15004. [CrossRef] [PubMed]
Furtado, F. A. , Silveira, A. J. , Abreu, C. A. , and Tavares, F. W. , 2015, “ Non-Equilibrium Molecular Dynamics Used to Obtain Soret Coefficients of Binary Hydrocarbon Mixtures,” Br. J. Chem. Eng., 32(3), pp. 683–698. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Schematic view of simulation box

Grahic Jump Location
Fig. 5

Average dimensionless temperature distribution in middle layers for nonequimolar nC6–nC10 mixture using the HEX, RNEMD (with swapping time = 20 time-step), and MHEX algorithms

Grahic Jump Location
Fig. 6

Average mole fraction trend of nC10 in middle layers for nonequimolar nC6–nC10 mixture using the HEX, RNEMD (with swapping time = 20 time-step) and MHEX algorithms

Grahic Jump Location
Fig. 7

Average mole fraction trend of nC6 in middle layers for nonequimolar nC6–nC10 mixture using the HEX, RNEMD (with swapping time = 20 time-step), and MHEX algorithms

Grahic Jump Location
Fig. 2

Dimensionless temperature distribution inside the simulation box for equimolar mixture of Ar–Kr using the HEX, RNEMD (with swapping time = 20 time-step) and MHEX algorithms

Grahic Jump Location
Fig. 3

Kr concentration profile inside the simulation box for equimolar mixture of Ar–Kr using the HEX, RNEMD (with swapping time = 20 time-step) and MHEX algorithms

Grahic Jump Location
Fig. 4

Ar concentration profile inside the simulation box for equimolar mixture of Ar–Kr using the HEX, RNEMD (with swapping time = 20 time-step) and MHEX algorithms

Grahic Jump Location
Fig. 8

Average dimensionless temperature distribution in middle layers for nC5–nC10 mixture with an initial uniform mole fraction of nC5 = 0.8, using the HEX, and MHEX algorithms

Grahic Jump Location
Fig. 9

Average mole fraction trend of nC10 in middle layers for nC5–nC10 mixture with an initial uniform mole fraction of nC5 = 0.8, using the HEX, and MHEX algorithms

Grahic Jump Location
Fig. 11

Thermodiffusion factor versus velocity swapping time for RNEMD method

Grahic Jump Location
Fig. 10

Average mole fraction trend of nC5 in middle layers for nC5–nC10 mixture with an initial uniform mole fraction of nC5 = 0.8, using the HEX, and MHEX algorithms

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In