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

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Editors' Suggestion
  • Access by Xinjiang University

Multiscale approach to model steady meniscus evaporation in a wetting fluid

Kishan Bellur1,*, Ezequiel F. Médici1, Chang Kyoung Choi1, James C. Hermanson2, and Jeffrey S. Allen1

  • 1Michigan Technological University, Houghton, Michigan, USA
  • 2University of Washington, Seattle, Washington, USA

  • *ksbellur@mtu.edu
PDF

Phys. Rev. Fluids 5, 024001 – Published 10 February, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.024001

Abstract

Evaporation along a curved liquid vapor interface, such as that of a wetting meniscus, is a classic multiscale problem of vital significance to many fields of science and engineering. However, a complete description of the local evaporative flux over all length scales, especially without arbitrary tuning of boundary conditions, is lacking. A multiscale method to model evaporation from steady meniscus is described such that a need for tuning of boundary conditions and additional assumptions are alleviated. A meniscus submodel is used to compute evaporation flux in the bulk meniscus while a transition film submodel is used to account for enhanced evaporation near the contact line. A unique coupling between the meniscus and transition film submodels ensures smooth continuity of both film and mass flux profiles along the meniscus. The local mass flux is then integrated over the interfacial area to investigate the contribution from the different regions on the surface. The model is evaluated with data from cryoneutron phase-change tests conducted previously at National Institute for Standards and Technology (NIST) [K. Bellur et al., Cryogenics 74, 131 (2016)]. It is found that the peak mass flux in the transition region is two orders of magnitude greater than the flux at the apex. Despite the enhanced evaporation in the thin film region, it was found that 78–95% of the evaporation occurs in the bulk meniscus due to the large area. The bulk meniscus contribution increases with increase in vapor pressure and Bond number but decreases with an increase in thermal conductivity of the substrate. Using a nonuniform temperature boundary suggests that there is a possibility that the adsorbed film may have a nonzero mass flux.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (66)

  1. C. E. Kolb, R. A. Cox, J. P. D. Abbatt, M. Ammann, E. J. Davis, D. J. Donaldson, B. C. Garrett, C. George, P. T. Griffiths, D. R. Hanson, M. Kulmala, G. McFiggans, U. Pöschl, I. Riipinen, M. J. Rossi, Y. Rudich, P. E. Wagner, P. M. Winkler, D. R. Worsnop, and C. D. O' Dowd, An overview of current issues in the uptake of atmospheric trace gases by aerosols and clouds, Atmos. Chem. Phys. 10, 10561 (2010).
  2. H. R. Pruppacher and J. D. Klett, Microphysics of Clouds and Precipitation (Springer Netherlands, Amsterdam, 2010).
  3. M. Mozurkewich, Aerosol growth and the condensation coefficient for water: A review, Aerosol Sci. Technol. 5, 223 (1986).
  4. B. Paul, Compilation of evaporation coefficients, ARS J. 32, 1321 (1962).
  5. D. Singh, X. Guo, A. Alexeenko, J. Y. Murthy, and T. S. Fisher, Modeling of subcontinuum thermal transport across semiconductor-gas interfaces, J. Appl. Phys. 106, 024314 (2009).
  6. V. P. Carey, G. Chen, C. Grigoropoulos, M. Kaviany, and A. Majumdar, A review of heat transfer physics, Nanosc. Microsc. Thermophys. Eng. 12, 1 (2008).
  7. D. Bayer, U. Gross, and K. Raed, A new facility for the experimental investigation on nano heat transfer between gas molecules and ceramic surfaces, in Proceedings of the 32nd International Thermal Conductivity Conference (Purdue University, West Lafayette, Indiana, USA, 2014).
  8. National Research Council, NASA Space Technology Roadmaps and Priorities (National Academies Press, Washington, DC, 2012).
  9. D. Brutin and V. Starov, Recent advances in droplet wetting and evaporation, Chem. Soc. Rev. 47, 558 (2018).
  10. M. A. Saxton, D. Vella, J. P. Whiteley, and J. M. Oliver, Kinetic effects regularize the mass-flux singularity at the contact line of a thin evaporating drop, J. Eng. Math. 106, 47 (2017).
  11. R. W. Schrage, A theoretical study of interphase mass transfer, Ph.D. thesis, Columbia University Press, 1953.
  12. J. Barrett and C. Clement, Kinetic evaporation and condensation rates and their coefficients, J. Colloid Interface Sci. 150, 352 (1992).
  13. V. S. Ajaev, Interfacial Fluid Mechanics (Springer US, New York, 2012).
  14. E. J. Davis, A history and state-of-the-art of accommodation coefficients, Atmos. Res. 82, 561 (2006).
  15. R. Marek and J. Straub, Analysis of the evaporation coefficient and the condensation coefficient of water, Int. J. Heat Mass Transf. 44, 39 (2001).
  16. P. Davidovits, C. E. Kolb, L. R. Williams, J. T. Jayne, and D. R. Worsnop, Update 1 of: Mass accommodation and chemical reactions at gas-liquid interfaces, Chem. Rev. 111, 1323 (2011).
  17. A. H. Persad and C. A. Ward, Expressions for the evaporation and condensation coefficients in the hertz-knudsen relation, Chem. Rev. 116, 7727 (2016).
  18. P. C. Wayner, Y. K. Kao, and L. V. LaCroix, The interline heat-transfer coefficient of an evaporating wetting film, Int. J. Heat Mass Transf. 19, 487 (1976).
  19. J. L. Plawsky, M. Ojha, A. Chatterjee, and P. C. Wayner, Review of the effects of surface topography, surface chemistry, and fluid physics on evaporation at the contact line, Chem. Eng. Commun. 196, 658 (2008).
  20. P. C. Wayner, The effect of interfacial mass transport on flow in thin liquid films, Colloids Surf. 52, 71 (1991).
  21. M. Potash and P. C. Wayner, Evaporation from a two-dimensional extended meniscus, Int. J. Heat Mass Transf. 15, 1851 (1972).
  22. S. DasGupta, I. Y. Kim, and P. C. Wayner, Use of the kelvin-clapeyron equation to model an evaporating curved microfilm, J. Heat Transfer 116, 1007 (1994).
  23. F. W. Holm and S. P. Goplen, Heat transfer in the meniscus thin-film transition region, J. Heat Transfer 101, 543 (1979).
  24. J. A. Schonberg, S. DasGupta, and P. C. Wayner, An augmented young-laplace model of an evaporating meniscus in a microchannel with high heat flux, Exp. Therm. Fluid Sci. 10, 163 (1995).
  25. Shi-Yuan Du and Yao-Hua Zhao, New boundary conditions for the evaporating thin-film model in a rectangular micro channel, Int. J. Heat Mass Transf. 54, 3694 (2011).
  26. S.-K. Wee, K. D. Kihm, D. M. Pratt, and J. S. Allen, Microscale heat and mass transport of evaporating thin film of binary mixture, J. Thermophys. Heat Transf. 20, 320 (2006).
  27. D. L Fritz, Implementation of a phenomenological evaporation model into a porous network simulation for water management in low temperature fuel cells, Ph.D. thesis, Michigan Technological University, 2012.
  28. V. S. Ajaev and O. A. Kabov, Heat and mass transfer near contact lines on heated surfaces, Int. J. Heat Mass Transf. 108, 918 (2017).
  29. Y. Akkuş and Z. Dursunkaya, A new approach to thin film evaporation modeling, Int. J. Heat Mass Transf. 101, 742 (2016).
  30. S. DasGupta, J. A. Schonberg, I. Y. Kim, and P. C. Wayner, Use of the augmented young-laplace equation to model equilibrium and evaporating extended menisci, J. Colloid Interface Sci. 157, 332 (1993).
  31. K. Park, K.-J. Noh, and K.-S. Lee, Transport phenomena in the thin-film region of a micro-channel, Int. J. Heat Mass Transf. 46, 2381 (2003).
  32. S.-K. Wee, K. D. Kihm, and K. P. Hallinan, Effects of the liquid polarity and the wall slip on the heat and mass transport characteristics of the micro-scale evaporating transition film, Int. J. Heat Mass Transf. 48, 265 (2005).
  33. H. Wang, S. V. Garimella, and J. Y. Murthy, Characteristics of an evaporating thin film in a microchannel, Int. J. Heat Mass Transf. 50, 3933 (2007).
  34. H. Wang, S. V. Garimella, and J. Y. Murthy, An analytical solution for the total heat transfer in the thin-film region of an evaporating meniscus, Int. J. Heat Mass Transf. 51, 6317 (2008).
  35. J. L. Plawsky, A. Chatterjee, and P. C. Wayner, Jr., Modeling conact line dynamics in evaporating menisci, in Proceedings of the COMSOL Conference 2009 Boston 2009 Comsol User's Conference (COMSOL, Boston, MA, USA, 2009).
  36. Y. Akkus, A. Koklu, and A. Beskok, Atomic scale interfacial transport at an extended evaporating meniscus, Langmuir 35, 4491 (2019).
  37. V. S. Ajaev and E. Ya Gatapova, Contact line motion over heated substrates with spatially nonuniform wetting properties, J. Phys.: Conf. Ser. 925, 012016 (2017).
  38. C. Sodtke, V. S. Ajaev, and P. Stephan, Dynamics of volatile liquid droplets on heated surfaces: Theory versus experiment, J. Fluid Mech. 610, 343 (2008).
  39. P. C. Stephan and C. A. Busse, Analysis of the heat transfer coefficient of grooved heat pipe evaporator walls, Int. J. Heat Mass Transf. 35, 383 (1992).
  40. S. S. Panchamgam, A. Chatterjee, J. L. Plawsky, and P. C. Wayner, Comprehensive experimental and theoretical study of fluid flow and heat transfer in a microscopic evaporating meniscus in a miniature heat exchanger, Int. J. Heat Mass Transf. 51, 5368 (2008).
  41. L. Biswal, S. K. Som, and S. Chakraborty, Thin film evaporation in microchannels with slope- and curvature-dependent disjoining pressure, Int. J. Heat Mass Transf. 57, 402 (2013).
  42. M. S. Hanchak, M. D. Vangsness, L. W. Byrd, and J. S. Ervin, Thin film evaporation of n-octane on silicon: Experiments and theory, Int. J. Heat Mass Transf. 75, 196 (2014).
  43. Shi-Yuan Du and Yao-Hua Zhao, Numerical study of conjugated heat transfer in evaporating thin-films near the contact line, Int. J. Heat Mass Transf. 55, 61 (2012).
  44. Zhi-Hai Kou, Hong-Tao Lv, W. Zeng, Min-Li Bai, and Ji-Zu Lv, Comparison of different analytical models for heat and mass transfer characteristics of an evaporating meniscus in a micro-channel, Int. Commun. Heat Mass Transfer 63, 49 (2015).
  45. H. K. Dhavaleswarapu, J. Y. Murthy, and S. V. Garimella, Numerical investigation of an evaporating meniscus in a channel, Int. J. Heat Mass Transf. 55, 915 (2012).
  46. H. Wang, J. Y. Murthy, and S. V. Garimella, Transport from a volatile meniscus inside an open microtube, Int. J. Heat Mass Transf. 51, 3007 (2008).
  47. R. Ranjan, J. Y. Murthy, and S. V. Garimella, A microscale model for thin-film evaporation in capillary wick structures, Int. J. Heat Mass Transf. 54, 169 (2011).
  48. Z. Zheng, L. Zhou, X. Du, and Y. Yang, Numerical investigation on conjugate heat transfer of evaporating thin film in a sessile droplet, Int. J. Heat Mass Transf. 101, 10 (2016).
  49. H. Yi, J. Tipton, K. D. Kihm, D. M. Pratt, A. D. Swanson, and S. Rawal, Effect of disjoining pressure (π) on multi-scale modeling for evaporative liquid metal (na) capillary, Int. J. Heat Mass Transf. 78, 137 (2014).
  50. K. Bellur, An Assessment of the Validity of the Kinetic Model for Liquid-Vapor Phase Change by Examining Cryogenic Propellants, Master's thesis, Michigan Technological University, 2016.
  51. J. L. Plawsky, S. S. Panchamgam, S. J. Gokhale, P. C. Wayner, and S. DasGupta, A study of the oscillating corner meniscus in a vertical constrained vapor bubble system, Superlatt. Microstruct. 35, 559 (2004).
  52. L. Zheng, J. L. Plawsky, P. C. Wayner, and S. DasGupta, Stability and oscillations in an evaporating corner meniscus, J. Heat Transf. 126, 169 (2004).
  53. Thao T. T. Nguyen, J. Yu, J. L. Plawsky, P. C. Wayner, D. F. Chao, and R. J. Sicker, Spontaneously oscillating menisci: Maximizing evaporative heat transfer by inducing condensation, Int. J. Therm. Sci. 128, 137 (2018).
  54. K. Bellur, E. F. Médici, M. Kulshreshtha, V. Konduru, D. Tyrewala, A. Tamilarasan, J. McQuillen, J. B. Leão, D. S. Hussey, D. L. Jacobson, J. Scherschligt, J. C. Hermanson, C. K. Choi, and J. S. Allen, A new experiment for investigating evaporation and condensation of cryogenic propellants, Cryogenics 74, 131 (2016).
  55. C. H. Panzarella and M. Kassemi, On the validity of purely thermodynamic descriptions of two-phase cryogenic fluid storage, J. Fluid Mech. 484, 41 (2003).
  56. C. Panzarella and M. Kassemi, One-dimensional model of evaporation and condensation in the presence of a noncondensable gas with applications to cryogenic fluid storage, Int. J. Heat Mass Transf. 52, 3767 (2009).
  57. J. Hartwig and J. McQuillen, Analysis of screen channel LAD bubble point tests in liquid oxygen at elevated temperature, in Proceedings of the 42nd AIAA Thermophysics Conference (American Institute of Aeronautics and Astronautics, Honolulu, Hawaii, USA, 2011).
  58. Bellur, A new technique to determine accommodation coefficients of cryogenic propellants, Ph.D. thesis, Michigan Technological University, 2018.
  59. S. DasGupta, J. A. Schonberg, and P. C. Wayner, Investigation of an evaporating extended meniscus based on the augmented young–laplace equation, J. Heat Transf. 115, 201 (1993).
  60. J. Israelachvili, Intermolecular and Surface Forces (Elsevier, Amsterdam, 2011).
  61. K. Bellur, Vinaykumar Konduru, E. F. Medici, D. S. Hussey, D. L. Jacobson, J. M. LaManna, J. S. Allen, and Chang Kyoung Choi, Visualization of the evaporation and condensation phenomena in cryogenic propellants, J. Flow Vis. Image Process. 23, 137 (2016).
  62. K. Bellur, E. Medici, J. Allen, Chang Kyoung Choi, J. Hermanson, A. Tamilarasan, D. Hussey, D. Jacobson, J. B. Leao, and J. McQuillen, Neutron radiography of condensation and evaporation of hydrogen in a cryogenic condition, J. Heat Transf. 137, 080901 (2015).
  63. K. Bellur, Vinaykumar Konduru, M. Kulshrestha, D. Tyrewala, E. Medici, J. S. Allen, Chang Kyoung Choi, D. S. Hussey, D. C. Jacobson, J. B. Leão, J. McQuillen, J. Hermanson, and A. Tamilarasan, Contact angle measurement of liquid hydrogen (LH2) in stainless steel and aluminum cells, J. Heat Transf. 138, 020904 (2016).
  64. Vinaykumar Konduru, K. Bellur, E. F. Médici, J. S. Allen, Chang Kyoung Choi, D. S. Hussey, D. Jacobson, J. B. Leão, J. McQuillen, and J. C. Hermanson, Examining liquid hydrogen wettability using neutron imaging, J. Heat Transf. 138, 080901 (2016).
  65. K. Bellur, D. Hussey, D. Jacobson, J. Lamana, E. Medici, J. Hermanson, Dr. Jeffrey S. Allen, and Chang Kyoung Choi, Neutron attenuation analysis of cryogenic propellants, J. Heat Transf. 140, 030904 (2018).
  66. K. Bellur, E. F. Médici, J. C. Hermanson, C. K. Choi, and J. S. Allen, Determining solid-fluid interface temperature distribution during phase change of cryogenic propellants using transient thermal modeling, Cryogenics 91, 103 (2018).

Outline

Information

Phys. Rev. Fluids 5, 024001– Published 10 February, 2020
  • Received 5 September 2019
  • Accepted 8 January 2020
Article part of CHORUS
Crossmark - Check for updates button

©2020 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation