- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Velocity distribution function of spontaneously evaporating atoms

Sergiu Busuioc1, Livio Gibelli1,*, Duncan A. Lockerby2, and James E. Sprittles3

  • 1School of Engineering, The University of Edinburgh, Edinburgh, EH9 3FB, United Kingdom
  • 2School of Engineering, University of Warwick, Coventry CV4 7AL, United Kingdom
  • 3Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom

  • *livio.gibelli@ed.ac.uk
PDF

Phys. Rev. Fluids 5, 103401 – Published 12 October, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.103401

Abstract

Numerical solutions of the Enskog-Vlasov equation are used to determine the velocity distribution function of atoms spontaneously evaporating into near-vacuum conditions. It is found that an accurate approximation is provided by a half-Maxwellian including a drift velocity combined with different characteristic temperatures for the velocity components normal and parallel to the liquid-vapor interface. The drift velocity and the temperature anisotropy reduce as the liquid bulk temperature decreases but persist for relatively low temperatures corresponding to a vapor behavior which is only slightly nonideal. Deviations from the undrifted isotropic half-Maxwellian are shown to be consequences of collisions in the liquid-vapor interface which preferentially backscatter atoms with lower normal-velocity component.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (39)

  1. J. Safarian and T. A. Engh, Vacuum evaporation of pure metals, Metall. Mater. Trans. A 44, 747 (2013).
  2. Y. Li and S.-L. Xu, DSMC simulation of vapor flow in molecular distillation, Vacuum 110, 40 (2014).
  3. S. S. Sazhin, Modelling of fuel droplet heating and evaporation: Recent results and unsolved problems, Fuel 196, 69 (2017).
  4. B. John, R. Enright, J. E. Sprittles, L. Gibelli, D. R. Emerson, and D. A. Lockerby, Numerical investigation of nanoporous evaporation using direct simulation monte carlo, Phys. Rev. Fluids 4, 113401 (2019).
  5. M. Chang, Z. Lee, S. Park, and S. Park, Characteristics of flash boiling and its effects on spray behavior in gasoline direct injection injectors: A review, Fuel 271, 117600 (2020).
  6. J. S. Rowlinson and B. Widom, Molecular Theory of Capillarity (Courier, North Chelmsford, MA, 2013).
  7. Y. Sone, Kinetic theoretical studies of the half-space problem of evaporation and condensation, Transport Theor. Stat. 29, 227 (2000).
  8. A. H. Persad and C. A. Ward, Expressions for the evaporation and condensation coefficients in the hertz-knudsen relation, Chem. Rev. 116, 7727 (2016).
  9. G. Fang and C. A. Ward, Temperature measured close to the interface of an evaporating liquid, Phys. Rev. E 59, 417 (1999).
  10. P. D. Crout, An application of kinetic theory to the problems of evaporation and sublimation of monatomic gases, J. Math. Phys. 15, 1 (1936).
  11. E. Bird and Z. Liang, Transport phenomena in the Knudsen layer near an evaporating surface, Phys. Rev. E 100, 043108 (2019).
  12. T. Tsuruta, H. Tanaka, and T. Masuoka, Condensation/evaporation coefficient and velocity distributions at liquid–vapor interface, Int. J. Heat Mass 42, 4107 (1999).
  13. R. Meland, A. Frezzotti, T. Ytrehus, and B. Hafskjold, Nonequilibrium molecular-dynamics simulation of net evaporation and net condensation, and evaluation of the gas-kinetic boundary condition at the interphase, Phys. Fluids 16, 223 (2004).
  14. J.-F. Xie, S. S. Sazhin, and B.-Y. Cao, Molecular dynamics study of the processes in the vicinity of the n-dodecane vapour/liquid interface, Phys. Fluids 23, 112104 (2011).
  15. J.-F. Xie, S. S. Sazhin, and B.-Y. Cao, Molecular dynamics study of condensation/evaporation and velocity distribution of n-dodecane at liquid-vapour phase equilibria, J. Therm. Sci. Tech-Jpn. 7, 288 (2012).
  16. M. Kon, K. Kobayashi, and M. Watanabe, Method of determining kinetic boundary conditions in net evaporation/condensation, Phys. Fluids 26, 072003 (2014).
  17. K. Kobayashi, K. Sasaki, M. Kon, H. Fujii, and M. Watanabe, Kinetic boundary conditions for vapor–gas binary mixture, Microfluid. Nanofluid. 21, 53 (2017).
  18. V. V. Zhakhovskii and S. I. Anisimov, Molecular-dynamics simulation of evaporation of a liquid, J. Exp. Theor. Phys. 84, 734 (1997).
  19. T. Ishiyama, T. Yano, and S. Fujikawa, Molecular dynamics study of kinetic boundary condition at an interface between argon vapor and its condensed phase, Phys. Fluids 16, 2899 (2004).
  20. A. Frezzotti, L. Gibelli, and S. Lorenzani, Mean field kinetic theory description of evaporation of a fluid into vacuum, Phys. Fluids 17, 012102 (2005).
  21. A. Frezzotti, L. Gibelli, D. A. Lockerby, and J. E. Sprittles, Mean-field kinetic theory approach to evaporation of a binary liquid into vacuum, Phys. Rev. Fluids 3, 054001 (2018).
  22. M. Heinen and J. Vrabec, Evaporation sampled by stationary molecular dynamics simulation, J. Chem. Phys. 151, 044704 (2019).
  23. V. V. Zhakhovsky, A. P. Kryukov, V. Yu. Levashov, I. N. Shishkova, and S. I. Anisimov, Mass and heat transfer between evaporation and condensation surfaces: Atomistic simulation and solution of boltzmann kinetic equation, Proc. Natl. Acad. Sci. U.S.A. 116, 18209 (2019).
  24. A. Frezzotti and P. Barbante, Kinetic theory aspects of non-equilibrium liquid-vapor flows, Mech. Eng. Rev. 4, 16-00540 (2017).
  25. J. Karkheck and G. Stell, Kinetic mean-field theories, J. Chem. Phys. 75, 1475 (1981).
  26. N. F. Carnahan and K. E. Starling, Equation of state for nonattracting rigid spheres, J. Chem. Phys. 51, 635 (1969).
  27. J. Fischer and M. Methfessel, Born-Green-Yvon approach to the local densities of a fluid at interfaces, Phys. Rev. A 22, 2836 (1980).
  28. L. De Sobrino, On the kinetic theory of a van der waals gas, Can. J. Phys. 45, 363 (1967).
  29. M. Grmela, Kinetic equation approach to phase transitions, J. Stat. Phys. 3, 347 (1971).
  30. E. S. Benilov and M. S. Benilov, The enskog–vlasov equation: A kinetic model describing gas, liquid, and solid, J. Stat. Mech. (2019) 103205.
  31. A. Frezzotti, P. Barbante, and L. Gibelli, Direct simulation monte carlo applications to liquid-vapor flows, Phys. Fluids 31, 062103 (2019).
  32. P. Barbante, A. Frezzotti, and L. Gibelli, A kinetic theory description of liquid menisci at the microscale, Kinet. Relat. Mod. 8, 235 (2015).
  33. S. Takata, T. Matsumoto, A. Hirahara, and M. Hattori, Kinetic theory for a simple modeling of a phase transition: Dynamics out of local equilibrium, Phys. Rev. E 98, 052123 (2018).
  34. E. S. Benilov and M. S. Benilov, Energy conservation and h theorem for the enskog-vlasov equation, Phys. Rev. E 97, 062115 (2018).
  35. A. Frezzotti, A particle scheme for the numerical solution of the Enskog equation, Phys. Fluids 9, 1329 (1997).
  36. J. Hirschfelder, R. B. Bird, and C. F. Curtiss, Molecular Theory of Gases and Liquids (Wiley, New York, 1964).
  37. H. C. Andersen, Molecular dynamics simulations at constant pressure and/or temperature, J. Chem. Phys. 72, 2384 (1980).
  38. S. Cheng, J. B. Lechman, S. J. Plimpton, and G. S. Grest, Evaporation of Lennard-Jones fluids, J. Chem. Phys. 134, 224704 (2011).
  39. E. H. Kennard, Kinetic Theory of Gases (McGraw–Hill, New York, 1938).

Outline

Information

Phys. Rev. Fluids 5, 103401– Published 12 October, 2020
  • Received 4 June 2020
  • Accepted 10 September 2020
Crossmark - Check for updates button

©2020 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation