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Molecular kinetic modelling of non-equilibrium evaporative flows

Published online by Cambridge University Press:  18 September 2024

Shaokang Li Open the ORCID record for Shaokang Li [Opens in a new window] ,
Wei Su Open the ORCID record for Wei Su [Opens in a new window] ,
Baochao Shan Open the ORCID record for Baochao Shan [Opens in a new window] ,
Zuoxu Li Open the ORCID record for Zuoxu Li [Opens in a new window] ,
Livio Gibelli Open the ORCID record for Livio Gibelli [Opens in a new window]  and
Yonghao Zhang Open the ORCID record for Yonghao Zhang [Opens in a new window]
Shaokang Li
Affiliation:
School of Engineering, The University of Edinburgh, Edinburgh EH9 3FB, UK
Wei Su
Affiliation:
Division of Emerging Interdisciplinary Areas, The Hong Kong University of Science and Technology, Hong Kong, PR China Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, PR China
Baochao Shan
Affiliation:
School of Engineering, The University of Edinburgh, Edinburgh EH9 3FB, UK
Zuoxu Li
Affiliation:
Center for Interdisciplinary Research in Fluids, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China
Livio Gibelli*
Affiliation:
School of Engineering, The University of Edinburgh, Edinburgh EH9 3FB, UK
Yonghao Zhang*
Affiliation:
Center for Interdisciplinary Research in Fluids, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China School of Engineering Science, University of Chinese Academy of Sciences, Beijing 101408, PR China
*
†Email addresses for correspondence: livio.gibelli@ed.ac.uk, yonghao.zhang@imech.ac.cn
†Email addresses for correspondence: livio.gibelli@ed.ac.uk, yonghao.zhang@imech.ac.cn
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Abstract

Recent years have seen the emergence of new technologies that exploit nanoscale evaporation, ranging from nanoporous membranes for distillation to evaporative cooling in electronics. Despite the increasing depth of fundamental knowledge, there is still a lack of simulation tools capable of capturing the underlying non-equilibrium liquid–vapour phase changes that are critical to these and other such technologies. This work presents a molecular kinetic theory model capable of describing the entire flow field, i.e. the liquid and vapour phases and their interface, while striking a balance between accuracy and computational efficiency. In particular, unlike previous kinetic models based on the isothermal assumption, the proposed model can capture the temperature variations that occur during the evaporation process, yet does not require the computational resources of more complicated mean-field kinetic approaches. We assess the present kinetic model in three test cases: liquid–vapour equilibrium, evaporation into near-vacuum condition, and evaporation into vapour. The results agree well with benchmark solutions, while reducing the simulation time by almost two orders of magnitude on average in the cases studied. The results therefore suggest that this work is a stepping stone towards the development of an accurate and efficient computational approach to optimising the next generation of nanotechnologies based on nanoscale evaporation.

JFM classification

Micro-/Nano-fluid dynamics: Non-continuum effects Phase change: Condensation/evaporation Rarefied Gas Flow: Kinetic theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 994 , 10 September 2024 , A16
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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References

Aoki, K., Sone, Y. & Yamada, T. 1990 Numerical analysis of gas flows condensing on its plane condensed phase on the basis of kinetic theory. Phys. Fluids A 2 (10), 1867–1878.Google Scholar
Aursand, E. & Ytrehus, T. 2019 Comparison of kinetic theory evaporation models for liquid thin-films. Intl J. Multiphase Flow 116, 67–79.Google Scholar
Brutin, D., Sobac, B., Loquet, B. & Sampol, J. 2011 Pattern formation in drying drops of blood. J. Fluid Mech. 667, 85–95.Google Scholar
Busuioc, S. & Gibelli, L. 2020 Mean-field kinetic theory approach to Langmuir evaporation of polyatomic liquids. Phys. Fluids 32 (9), 093314.Google Scholar
Cercignani, C. & Lampis, M. 1988 Kinetic theory of a dense gas of rough spheres. J. Stat. Phys. 53, 655.Google Scholar
Chapman, S. & Cowling, T.G. 1970 The Mathematical Theory of Non-Uniform Gases: An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases. Cambridge University Press.Google Scholar
Chen, T., Wu, L., Wang, L. & Chen, S. 2023 Rarefaction effects in head-on collision of two near-critical droplets. Intl J. Multiphase Flow 164, 104451.Google Scholar
Dong, Y., Poredoš, P., Ma, Q. & Wang, R. 2022 High-yielding and stable desalination via photothermal membrane distillation with free-flow evaporation channel. Desalination 543, 116103.Google Scholar
Frezzotti, A. 1999 Monte Carlo simulation of the heat flow in a dense hard sphere gas. Eur. J. Mech. (B/Fluids) 18 (1), 103–119.Google Scholar
Frezzotti, A. 2007 A numerical investigation of the steady evaporation of a polyatomic gas. Eur. J. Mech. (B/Fluids) 26 (1), 93–104.Google Scholar
Frezzotti, A. 2011 Boundary conditions at the vapor–liquid interface. Phys. Fluids 23 (3), 030609.Google Scholar
Frezzotti, A. & Barbante, P. 2017 Kinetic theory aspects of non-equilibrium liquid–vapor flows. Mech. Engng Rev. 4 (2), 16–00540.Google Scholar
Frezzotti, A., Barbante, P. & Gibelli, L. 2019 Direct simulation Monte Carlo applications to liquid–vapor flows. Phys. Fluids 31 (6), 062103.Google Scholar
Frezzotti, A. & Gibelli, L. 2003 A kinetic model for equilibrium and non-equilibrium structure of the vapor–liquid interface. In AIP Conference Proceedings (ed. A.D. Ketsdever & E.P. Muntz), vol. 663, pp. 980–987. American Institute of Physics.Google Scholar
Frezzotti, A., Gibelli, L., Lockerby, D.A. & Sprittles, J.E. 2018 Mean-field kinetic theory approach to evaporation of a binary liquid into vacuum. Phys. Rev. Fluids 3 (5), 054001.Google Scholar
Frezzotti, A., Gibelli, L. & Lorenzani, S. 2005 Mean field kinetic theory description of evaporation of a fluid into vacuum. Phys. Fluids 17 (1), 012102.Google Scholar
Graur, I.A., Gatapova, E.Y., Wolf, M. & Batueva, M.A. 2021 Non-equilibrium evaporation: 1D benchmark problem for single gas. Intl J. Heat Mass Transfer 181, 121997.Google Scholar
Grmela, M. 1971 Kinetic equation approach to phase transitions. J. Stat. Phys. 3, 347–364.Google Scholar
He, X. & Doolen, G.D. 2002 Thermodynamic foundations of kinetic theory and lattice Boltzmann models for multiphase flows. J. Stat. Phys. 107, 309–328.Google Scholar
Hertz, H. 1882 Ueber die Verdunstung der Flüssigkeiten, insbesondere des Quecksilbers, im luftleeren Raume. Ann. Phys. 253 (10), 177–193.Google Scholar
Heyes, D.M. & Santos, A. 2016 Chemical potential of a test hard sphere of variable size in a hard-sphere fluid. J. Chem. Phys. 145 (21), 214504.Google Scholar
Huang, R., Wu, H. & Adams, N.A. 2021 Mesoscopic lattice Boltzmann modeling of the liquid–vapor phase transition. Phys. Rev. Lett. 126 (24), 244501.Google Scholar
John, B., Enright, R., Sprittles, J.E., Gibelli, L., Emerson, D.R. & Lockerby, D.A. 2019 Numerical investigation of nanoporous evaporation using direct simulation Monte Carlo. Phys. Rev. Fluids 4 (11), 113401.Google Scholar
John, B., Gibelli, L., Enright, R., Sprittles, J.E., Lockerby, D.A. & Emerson, D.R. 2021 Evaporation from arbitrary nanoporous membrane configurations: an effective evaporation coefficient approach. Phys. Fluids 33 (3), 032022.Google Scholar
Karkheck, J. & Stell, G. 1981 Kinetic mean-field theories. J. Chem. Phys. 75 (3), 1475–1487.Google Scholar
Khayet, M. 2011 Membranes and theoretical modeling of membrane distillation: a review. Adv. Colloid Interface Sci. 164 (1–2), 56–88.Google Scholar
Khodabandeh, R. & Furberg, R. 2010 Heat transfer, flow regime and instability of a nano- and micro-porous structure evaporator in a two-phase thermosyphon loop. Intl J. Therm. Sci. 49 (7), 1183–1192.Google Scholar
Knudsen, M. 1915 Die maximale verdampfungsgeschwindigkeit des quecksilbers. Ann. Phys. 352 (13), 697–708.Google Scholar
Kremer, G.M. 2010 An Introduction to the Boltzmann Equation and Transport Processes in Gases. Springer Science & Business Media.Google Scholar
Labuntsov, D.A. & Kryukov, A.P. 1979 Analysis of intensive evaporation and condensation. Intl J. Heat Mass Transfer 22 (7), 989–1002.Google Scholar
Li, R., Wang, J. & Xia, G. 2021 Theoretical and numerical study of nanoporous evaporation with receded liquid surface: effect of Knudsen number. J. Fluid Mech. 928, A9.Google Scholar
Li, R., Yan, Z. & Xia, G. 2023 Effect of inter-pore interference on liquid evaporation rates from nanopores by direct simulation Monte Carlo. Phys. Fluids 35 (3), 032015.Google Scholar
Luo, L. 1998 Unified theory of lattice Boltzmann models for nonideal gases. Phys. Rev. Lett. 81 (8), 1618.Google Scholar
Luo, L. 2000 Theory of the lattice Boltzmann method: lattice Boltzmann models for nonideal gases. Phys. Rev. E 62 (4), 4982.Google Scholar
Meland, R. & Ytrehus, T. 2003 Evaporation and condensation Knudsen layers for nonunity condensation coefficient. Phys. Fluids 15 (5), 1348–1350.Google Scholar
Ohashi, K., Kobayashi, K., Fujii, H. & Watanabe, M. 2020 Evaporation coefficient and condensation coefficient of vapor under high gas pressure conditions. Sci. Rep. 10 (1), 8143.Google Scholar
Persad, A.H. & Ward, C.A. 2016 Expressions for the evaporation and condensation coefficients in the Hertz–Knudsen relation. Chem. Rev. 116 (14), 7727–7767.Google Scholar
Pinto, G., Silva, F., Porteiro, J., Míguez, J. & Baptista, A. 2018 Numerical simulation applied to PVD reactors: an overview. Coatings 8 (11), 410.Google Scholar
Schrage, R.W. 1953 A Theoretical Study of Interphase Mass Transfer. Columbia University Press.Google Scholar
Shan, B., Su, W., Gibelli, L. & Zhang, Y. 2023 Molecular kinetic modelling of non-equilibrium transport of confined van der Waals fluids. J. Fluid Mech. 976, A7.Google Scholar
Sibold, D. & Urbassek, H.M. 1993 Monte Carlo study of Knudsen layers in evaporation from elemental and binary media. Phys. Fluids A: Fluid Dyn. 5 (1), 243–256.Google Scholar
de Sobrino, L. 1967 On the kinetic theory of a van der Waals gas. Can. J. Phys. 45 (2), 363–385.Google Scholar
Sone, Y., Aoki, K., Sugimoto, H. & Yamada, T. 1988 Steady evaporation and condensation on a plane condensed phase. Theor. Appl. Mech. 19 (3), 89–93.Google Scholar
Su, W., Gibelli, L., Li, J., Borg, M. & Zhang, Y. 2023 Kinetic modeling of nonequilibrium flow of hard-sphere dense gases. Phys. Rev. Fluids 8 (1), 013401.Google Scholar
Takata, S., Matsumoto, T. & Hattori, M. 2021 Kinetic model for the phase transition of the van der Waals fluid. Phys. Rev. E 103 (6), 062110.Google Scholar
Takata, S. & Noguchi, T. 2018 A simple kinetic model for the phase transition of the van der Waals fluid. J. Stat. Phys. 172, 880–903.Google Scholar
Vaartstra, G., Lu, Z., Lienhard, J.H. & Wang, E.N. 2022 Revisiting the Schrage equation for kinetically limited evaporation and condensation. Trans. ASME J. Heat Transfer 144 (8), 080802.Google Scholar
Vaartstra, G., Zhang, L., Lu, Z., Díaz-Marín, C.D., Grossman, J. & Wang, E. 2020 Capillary-fed, thin film evaporation devices. J. Appl. Phys. 128 (13), 130901.Google Scholar
Wang, J., Xia, G. & Li, R. 2022 Numerical analysis of evaporation from nanopores using the direct simulation Monte Carlo method. J. Mol. Liq. 347, 118348.Google Scholar
Wang, P., Wu, L., Ho, M.T., Li, J., Li, Z. & Zhang, Y. 2020 The kinetic Shakhov–Enskog model for non-equilibrium flow of dense gases. J. Fluid Mech. 883, A48.Google Scholar
Yang, Y., Cui, G. & Lan, C.Q. 2019 Developments in evaporative cooling and enhanced evaporative cooling – a review. Renew. Sust. Energ. Rev. 113, 109230.Google Scholar
Ytrehus, T. 1997 Molecular-flow effects in evaporation and condensation at interfaces. Multiphase Sci. 9 (3), 205–327.Google Scholar
Zhang, Y., Xu, A., Qiu, J., Wei, H. & Wei, Z. 2020 Kinetic modeling of multiphase flow based on simplified Enskog equation. Front. Phys. 15, 1–13.Google Scholar