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Theoretical and numerical study of nanoporous evaporation with receded liquid surface: effect of Knudsen number

Published online by Cambridge University Press:  04 October 2021

Ran Li Open the ORCID record for Ran Li [Opens in a new window] ,
Jiahao Wang  and
Guodong Xia
Ran Li*
Affiliation:
MOE Key Laboratory of Enhanced Heat Transfer and Energy Conservation, Beijing Key Laboratory of Heat Transfer and Energy Conversion, Beijing University of Technology, Beijing 100124, China
Jiahao Wang
Affiliation:
MOE Key Laboratory of Enhanced Heat Transfer and Energy Conservation, Beijing Key Laboratory of Heat Transfer and Energy Conversion, Beijing University of Technology, Beijing 100124, China
Guodong Xia*
Affiliation:
MOE Key Laboratory of Enhanced Heat Transfer and Energy Conservation, Beijing Key Laboratory of Heat Transfer and Energy Conversion, Beijing University of Technology, Beijing 100124, China
*
† Email addresses for correspondence: liran@bjut.edu.cn, xgd@bjut.edu.cn
† Email addresses for correspondence: liran@bjut.edu.cn, xgd@bjut.edu.cn
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Abstract

The liquid evaporation from nanoscale pores has attracted much attention from researchers due to its importance in water treatment and device cooling related applications. It is crucial to investigate the receded liquid case as the vapour flow resistance in a nanopore has high impacts on the evaporation rate. This paper proposed a semi-empirical analysis on nanoporous evaporation with a receded liquid surface under the influence of the Knudsen number. The vapour flow dynamics in a nanopore was examined considering the multiple reflections of vapour molecules. We calculated the value of pore transmissivity based on transitional gas flow correlation which incorporated the effect of the Knudsen number. Direct simulation Monte Carlo method was employed to provide validation for the present model. The vapour density jump near the liquid surface and the pressure ratio between the far field and saturation value were predicted by our model with good precision. It was shown that the vapour flow resistance in the nanopore accounted for more than 90 % of the total resistance in present cases. With increasing Knudsen number, the pressure ratio gradually drops and reaches an asymptotic level. This suggested a relatively higher evaporation resistance in free molecular regimes. The present work revealed the importance of the Knudsen number in nanoporous evaporation with receded liquids, providing insights into the governing factors under various Knudsen regimes.

JFM classification

Phase change: Condensation/evaporation Rarefied Gas Flow: Kinetic theory Micro-/Nano-fluid dynamics: Non-continuum effects

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 928 , 10 December 2021 , A9
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© The Author(s), 2021. Published by Cambridge University Press

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References

Berman, A.S. 1965 Free molecule transmission probabilities. J. Appl. Phys. 36 (10), 3356.CrossRefGoogle Scholar
Bird, G.A. 1994. Axially symmetric flows. In Molecular Gas Dynamics and the Direct Simulation of Gas Flows, 2nd edn. pp. 372–373. Clarendon Press.Google Scholar
Canbazoglu, F.M., Fan, B., Vemuri, K. & Bandaru, P.R. 2018 Enhanced solar thermal evaporation of ethanol–water mixtures, through the use of porous media. Langmuir 34 (36), 10523–10528.CrossRefGoogle ScholarPubMed
Carrier, O., Shahidzadeh-Bonn, N., Zargar, R., Aytouna, M., Habibi, M., Eggers, J. & Bonn, D. 2016 Evaporation of water: evaporation rate and collective effects. J. Fluid Mech. 798, 774–786.CrossRefGoogle Scholar
Clausing, P. 1932 The flow of highly rarefied gases through tubes of arbitrary length. Ann. Phys. 12 (5), 961.CrossRefGoogle Scholar
Davis, D.H. 1960 Monte Carlo calculation of molecular flow rates through a cylindrical elbow and pipes of other shapes. J. Appl. Phys. 31 (7), 1169–1176.CrossRefGoogle Scholar
Dushman, S. 1922 Production and Measurement of High Vacuum, pp. 32. General Electric CO.Google Scholar
Fang, G. & Ward, C.A. 1999 Temperature measured close to the interface of an evaporating liquid. Phys. Rev. E 59 (1), 417–428.CrossRefGoogle Scholar
Ghim, D., Wu, X., Suazo, M. & Jun, Y.-S. 2021 Achieving maximum recovery of latent heat in photothermally driven multi-layer stacked membrane distillation. Nano Energy 80, 105444.CrossRefGoogle Scholar
Gong, B., Yang, H., Wu, S., Xiong, G., Yan, J., Cen, K., Bo, Z. & Ostrikov, K. 2019 Graphene array-based anti-fouling solar vapour gap membrane distillation with high energy efficiency. Nano-Micro Lett. 11 (1), 51.CrossRefGoogle ScholarPubMed
Gusarov, A.V. & Smurov, I. 2002 Gas-dynamic boundary conditions of evaporation and condensation: numerical analysis of the Knudsen layer. Phys. Fluids 14 (12), 4242–4255.CrossRefGoogle Scholar
Han, X., Wang, W., Zuo, K., Chen, L., Yuan, L., Liang, J., Li, Q., Ajayan, P.M., Zhao, Y. & Lou, J. 2019 Bio-derived ultrathin membrane for solar driven water purification. Nano Energy 60, 567–575.CrossRefGoogle Scholar
Hanks, D.F., Lu, Z., Sircar, J., Kinefuchi, I., Bagnall, K.R., Salamon, T.R., Antao, D.S., Barabadi, B. & Wang, E.N. 2020 High heat flux evaporation of low surface tension liquids from nanoporous membranes. ACS Appl. Mater. Interfaces 12 (6), 7232–7238.CrossRefGoogle ScholarPubMed
Hu, H. & Sun, Y. 2016 Effect of nanostructures on heat transfer coefficient of an evaporating meniscus. Intl J. Heat Mass Transfer 101, 878–885.CrossRefGoogle Scholar
Jatukaran, A., Zhong, J., Persad, A.H., Xu, Y., Mostowfi, F. & Sinton, D. 2018 Direct visualization of evaporation in a two-dimensional nanoporous model for unconventional natural gas. ACS Appl. Nano Mater. 1 (3), 1332–1338.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle Scholar
Karniadakis, G., Beskok, A., Aluru, N., Antman, S.S., Marsden, J.E. & Sirovich, L. 2005 a Governing equations and slip models. In Microflows and Nanoflows: Fundamentals and Simulation (eds. Karniadakis, G., Beskok, A., Aluru, N., Antman, S. S., Marsden, J. E. & Sirovich, L.). Springer New York.Google Scholar
Karniadakis, G., Beskok, A., Aluru, N., Antman, S.S., Marsden, J.E. & Sirovich, L. 2005 b Pressure-driven flows. In Microflows and Nanoflows: Fundamentals and Simulation (eds. Karniadakis, G., Beskok, A., Aluru, N., Antman, S. S., Marsden, J. E. & Sirovich, L.). Springer New York.Google Scholar
Labuntsov, D.A. & Kryukov, A.P. 1979 Analysis of intensive evaporation and condensation. Intl J. Heat Mass Transfer 22 (7), 989–1002.CrossRefGoogle Scholar
Li, J., Zhou, G., Tian, T. & Li, X. 2021 a A new cooling strategy for edge computing servers using compact looped heat pipe. Appl. Thermal Engng 187, 116599.CrossRefGoogle Scholar
Li, R., Wang, J. & Xia, G. 2021 b New model for liquid evaporation and vapor transport in nanopores covering the entire Knudsen regime and arbitrary pore length. Langmuir 37 (6), 2227–2235.CrossRefGoogle ScholarPubMed
Lu, Z., Kinefuchi, I., Wilke, K.L., Vaartstra, G. & Wang, E.N. 2019 A unified relationship for evaporation kinetics at low Mach numbers. Nat. Commun. 10 (1), 2368.CrossRefGoogle ScholarPubMed
Lu, Z., Narayanan, S. & Wang, E.N. 2015 Modeling of evaporation from nanopores with nonequilibrium and nonlocal effects. Langmuir 31 (36), 9817–9824.CrossRefGoogle ScholarPubMed
Marek, R. & Straub, J. 2001 Analysis of the evaporation coefficient and the condensation coefficient of water. Intl J. Heat Mass Transfer 44 (1), 39–53.CrossRefGoogle Scholar
Millán-Merino, A., Fernández-Tarrazo, E. & Sánchez-Sanz, M. 2021 Theoretical and numerical analysis of the evaporation of mono- and multicomponent single fuel droplets. J. Fluid Mech. 910, A11.CrossRefGoogle Scholar
Morris, S.J.S. 2003 The evaporating meniscus in a channel. J. Fluid Mech. 494, 297–317.CrossRefGoogle Scholar
Narayanan, S., Fedorov, A.G. & Joshi, Y.K. 2011 Interfacial transport of evaporating water confined in nanopores. Langmuir 27 (17), 10666–10676.CrossRefGoogle ScholarPubMed
Ota, M. & Taniguchi, H. 1993 Transmission probabilities of gas molecules through finite length tubes in transition ranges. Vacuum 44 (5), 685–688.CrossRefGoogle Scholar
Plimpton, S.J. & Gallis, M.A. 2015 SPARTA Direct Simulation Monte Carlo (DSMC) Simulator. Available at: http://sparta.sandia.gov.Google Scholar
Schrage, R.W. 1953 A Theoretical Study of Interphase Mass Transfer, pp. 1–25. Columbia University Press.CrossRefGoogle Scholar
Shahidzadeh-Bonn, N., Rafaï, S., Azouni, A.Z.A. & Bonn, D. 2006 Evaporating droplets. J. Fluid Mech. 549, 307–313.CrossRefGoogle Scholar
Shen, C. 2005 Rarefied Gas Dynamics-Fundamentals, Simulations and Micro Flows, pp. 1–100. Springer-Verlag Berlin Heidelberg.Google Scholar
Sone, Y. 2000 Kinetic theoretical studies of the half-space problem of evaporation and condensation. Transp. Theory Stat. Phys. 29 (3–5), 227–260.CrossRefGoogle Scholar
Sone, Y., Ohwada, T. & Aoki, K. 1989 Evaporation and condensation on a plane condensed phase: numerical analysis of the linearized Boltzmann equation for hard-sphere molecules. Phys. Fluids A: Fluid Dyn. 1 (8), 1398–1405.CrossRefGoogle Scholar
Vaartstra, G., Zhang, L., Lu, Z., Díaz-Marín, C.D., Grossman, J.C. & Wang, E.N. 2020 Capillary-fed, thin film evaporation devices. J. Appl. Phys. 128 (13), 130901.CrossRefGoogle Scholar
Wang, Q., Shi, Y. & Chen, R. 2020 Transition between thin film boiling and evaporation on nanoporous membranes near the kinetic limit. Intl J. Heat Mass Transfer 154, 119673.CrossRefGoogle Scholar
Wu, J.S., Lee, W.S., Lee, F. & Wong, S.C. 2001 Pressure boundary treatment in internal gas flows at subsonic speed using the DSMC method. AIP Conf. Proc. 585 (1), 408–416.CrossRefGoogle Scholar
Xia, G., Wang, J., Zhou, W., Ma, D. & Wang, J. 2020 Orientation effects on liquid-vapor phase change heat transfer on nanoporous membranes. Intl Commun. Heat Mass Transfer 119, 104934.CrossRefGoogle Scholar
Yen, S.M. 1973 Numerical solutions of non-linear kinetic equations for a one-dimensional evaporation- condensation problem. Comput. Fluids 1 (4), 367–377.CrossRefGoogle Scholar
Ytrehus, T. & Østmo, S. 1996 Kinetic theory approach to interphase processes. Intl J. Multiphase Flow 22 (1), 133–155.CrossRefGoogle Scholar
Zhou, F., Liu, Y. & Dede, E.M. 2019 Design, fabrication, and performance evaluation of a hybrid wick vapor chamber. J. Heat Transfer 141 (8), 081802.CrossRefGoogle Scholar