Thin-liquid-film evaporation at contact line

Abstract

When a liquid wets a solid wall, the extended meniscus near the contact line may be divided into three regions: a nonevaporating region, where the liquid is adsorbed on the wall; a transition region or thin-film region, where effects of long-range molecular forces (disjoining pressure) are felt; and an intrinsic meniscus region, where capillary forces dominate. The thin liquid film, with thickness from nanometers up to micrometers, covering the transition region and part of intrinsic meniscus, is gaining interest due to its high heat transfer rates. In this paper, a review was made of the researches on thin-liquid-film evaporation. The major characteristics of thin film, thin-film modeling based on continuum theory, simulations based on molecular dynamics, and thin-film profile and temperature measurements were summarized.

Key words： meniscus; thin film; contact line; disjoining pressure; evaporation

Acknowledgements

The authors acknowledge financial support for this work from the National Natural Science Foundation of China (Grant No. 50706001).

Notation

A	dispersion constant/J
hfg	latent heat of evaporation/(J•kg-1)
K	curvature/(L•m-1)
kl	liquid conductivity/(W•mK-1)
m'	mass flow rate/(kg•ms-1)
m''	interface net mass flux/(kg•m-2•s-1)
\overline{M}	molecular weight/(kg•mol-1)
pc	capillary pressure/( N•m-2)
pd	disjoining pressure/( N•m-2)
pl	liquid pressure/( N•m-2)
Δpl	change of liquid pressure/( N•m-2)
psat	saturation pressure/( N•m-2)
pv	vapor pressure/( N•m-2)
pv_equ	equilibrium pressure/( N•m-2)
q	integrated heat transfer rate/(W•m-1)
R	meniscus radius/m
\overline{R}	universal gas constant (J•mol-1•K-1)
T	temperature/K
V	molar volume/(m3•mol-1)
x	x coordinate/m
y	y coordinate/m
δ	liquid layer thickness/m
ν	kinematic viscosity/(m2•s-1)
μ	dynamic viscosity/(N•s•m-2)
ρl	liquid density/(kg•m-3)
ρv	vapor density/(kg•m-3)
σ	surface tension coefficient (N•m-1)
\hat{\sigma }	accommodation coefficient
subscripts
c	condensation
e	evaporation
l	liquid
lv	liquid-vapor interface
sat	saturated
sum	summation

References

1 Park K, Noh K J, Lee K S. Transport phenomena in the thin-film region of a micro-channel. International Journal of Heat and Mass Transfer, 2003, 46(13): 2381-2388

2 Hallinan K P, Chebaro H C, Kim S J, . Evaporation from an extended meniscus for nonisothermal interfacial conditions. Journal of Thermophysics and Heat. Transfer, 1994, 8(4): 709-716

3 Wang Hao, Garimella S V, Murthy J Y. Characteristics of an evaporating thin film in a microchannel. International Journal of Heat and Mass Transfer, 2007, 50(1,2): 163-172

4 Stephan K. Influence of dispersion forces on phase equilibria between thin liquid films and their vapour. International Journal of Heat and Mass Transfer, 2002, 45(24): 4715-4725

5 Stephan P C, Busse C A. Analysis of the heat-transfer coefficient of grooved heat pipe evaporator walls. International Journal of Heat and Mass Transfer, 1992, 35(2): 383-391

6 Carey V P. Liquid-Vapor Phase-Change Phenomena. New York: Hemisphere Publishing House, 1992

7 Moore F D, Mesler R B. The measurement of rapid surface temperature fluctuations during nucleate boiling of water. AICHE Journal, 1961, 7(4): 620-624

8 Pasamehmetoglu K O, Chappidi P R, Unal C, . Saturated pool nucleate boiling mechanisms at high heat fluxes. International Journal of Heat and Mass Transfer, 1993, 36(15): 3859-3868

9 Lay J H, Dhir V K. Shape of a vapor stem during nucleate boiling of saturated liquids. Trans ASME Journal of Heat Transfer, 1995, 117(2): 394-401

10 Stephan P, Hammer J. A new model for nucleate boiling heat transfer. Heat Mass Transfer, 1994, 30(2): 119-125

11 Derjaguin B V. Modern state of the investigation of long-range surface forces. Langmuir, 1987, 3(5): 601-606

12 Derjaguin B V, Zorin Z M. Optical study of the adsorption and surface condensation of vapours in the vicinity of saturation on a smooth surface. Proceedings of the 2nd International Congress of Surface Activity, London, 1957, 145-152

13 Derjaguin B V. Definition of the concept of the magnitude of the disjoining pressure and its role in the statics and kinetics of thin liquid layers. Colloid Journal of the USSR, 1955, 17(2): 191-197

14 Derjaguin B V, Starov V M, Churaev N V. Profile of the transition zone between a wetting film and the meniscus of the bulk liquid. Colloid Journal of the USSR, 1976, 38(5): 786-789

15 Israelachvili J. Intermolecular Forces. Washington: Academic Press, 1992

16 Hamaker H C. The london-van der waals interaction between spherical particles. Physica IV, 1937, 4(10): 1058-1072

17 Wee S K. Microscale observables for heat and mass transport. Dissertation for the Doctoral Degree. College Station: Texas A&M University, 2004

18 Wayner P C, Kao Y K, Lacroix L V. Interline heat-transfer coefficient of an evaporating wetting film. International Journal of Heat and Mass Transfer, 1976, 19(5): 487-492

19 Schonberg J A, Wayner Jr P C. Analytical solution for the integral contact line evaporative heat sink. Journal of Thermophysics and Heat Transfer, 1992, 6(1): 128-134

20 Schonberg J A, Dasgupta S, Wayner P C. An augmented young-laplace model of an evaporating meniscus in a microchannel with high heat-flux. Experimental Thermal and Fluid Science, 1995, 10(2): 163-170

21 Panchamgam S S, Gokhale S J, Plawsky J L, . Experimental determination of the effect of disjoining pressure on shear in the contact line region of a moving evaporating thin film. ASME Journal of Heat Transfer, 2005, 127(3): 231-243

22 DasGupta S, Plawsky J L, Wayner Jr P C. Interfacial force field characterization in a constrained vapor bubble thermosyphon. AIChE Journal, 1995, 41(9): 2140-2149

23 Potash M, Wayner P C. Evaporation from a 2-dimensional extended meniscus. International Journal of Heat and Mass Transfer, 1972, 15(10): 1851-1863

24 Holm F W, Goplen S P. Heat-transfer in the meniscus thin-film transition region. ASME Journal of Heat Transfer, 1979, 101(3): 543-547

25 Deryagin B V, Nerpin S V, Churayev N V. Effect of film heat transfer upon evaporation of liquids from capillaries. RILEM Bull, 1965, 29(1): 93-98

26 Wang Hao, Garimella S V, Murthy J Y. An analytical solution for the total heat transfer in the thin-film region of an evaporating meniscus. International Journal of Heat and Mass Transfer, 2008, 51(25,26): 6317-6322

27 Dasgupta S, Schonberg J A, Wayner P C. Investigation of an evaporating extended meniscus based on the augmented young-laplace equation. ASME Journal of Heat Transfer, 1993, 115(1): 201-208

28 Chakraborty C, Som S K. Heat transfer in an evaporating thin liquid film moving slowly along the walls of an inclined microchannel. International Journal of Heat and Mass Transfer, 2005, 48(13): 2801-2805

29 Ma H B, Peterson G P. Temperature variation and heat transfer in triangular grooves with an evaporating film. Journal of Thermophysics Heat Transfer, 1997, 11(1): 90-97

30 Schrage R W. A Theoretical Study of Interface Mass Transfer. New York: Columbia University Press, 1953

31 Marek R, Straub J. Analysis of the evaporation coefficient and the condensation coefficient of water. International Journal of Heat and Mass Transfer, 2001, 44(1): 39-53

32 Paul B. Complication of evaporation coefficients. ARS Journal, 1962, 32(9): 1321-1328

33 Xu X, Carey V P. Film evaporation from a micro-grooved surface-an approximate heat transfer model and its comparison with experimental data. Journal of Thermophysics Heat Transfer, 1990, 4(4): 512-520

34 Morris S J S. The evaporating meniscus in a channel. Journal of Fluid Mechanics, 2003, 494: 2801-2805

35 Wee S K,Kihm K D, Pratt D M, . Microscale heat and mass transport of evaporating thin film of binary mixture. Journal of Thermophysics Heat Transfer, 2006, 20(2): 320-326

36 Pearson J R A. On convection cells induced by surface tension. Journal of Fluid Mechanics, 1958, 4: 489-500

37 Sternling C V, Scriven L E. Interfacial turbulence: Hydrodynamic instability and the marangoni effect. AIChE Journal, 1959, 5: 514-523

38 Smith M K, Davis S H. Instabilities of dynamic thermocapillary liquid layers. Part 1: Convective instabilities. Journal of Fluid Mechanics, 1983, 132: 119-144

39 Smith M K, Davis S H. Instabilities of dynamic thermocapillary liquid layers. Part 2: Surface-wave instabilities. Journal of Fluid Mechanics, 1983, 132: 145-162

40 Goussis D A, Kelly R E. On the thermocapillary instabilities in a liquid layer heated from below. International Journal of Heat and Mass Transfer, 1990, 33(10): 2237-2245

41 Miladinova S, Slavtchev S, Lebon G, . Long-wave instabilities of non-uniformly heated falling films. Journal of Fluid Mechanics, 2002, 453: 153-175

42 Joo S,Davis S, Bankoff S. Long-wave instabilities of heated falling films: Two-dimensional theory of uniform layers. Journal of Fluid Mechanics, 1991, 230: 117-146

43 Kabov O A, Marchuk I V, Muzykantov A V, . Regular structures in locally heated falling liquid films. In: Proc. 2nd Intl Symp on Two-phases Flow Modelling and Experimentation, Pisa, 1999, 5: 1225-1233

44 Kabov O A, Marchuk I V, Chupin V M. Thermal imaging study of the liquid film flowing on a vertical surface with local heat source. Russian Journal of Engineering Thermophysics, 1996, 6: 105-138

45 Kabov O. Formation of regular structures in a falling liquid film upon local heating. Thermophys Aeromech, 1998, 5: 547-551

46 Scheid B, Kabov O, Minetti C, . Measurement of free surface deformation by reflectance-schlieren method. 3rd European Thermal Sciences Conference, Heidelberg, 2000, 651-657

47 Kalliadasis S, Kiyashko A, Demekhin E A. Marangoni instability of a thin liquid film heated from below by a local heat source. Journal of Fluid Mechanics, 2003, 475: 377-408

48 Oron A, Davis S H, Bankoff S G. Long-scale evolution of thin liquid films. Rev Mod Phys, 1997. 69(3): 931-980

49 Oron A, Bankoff S G. Dewetting of a heated surface by an evaporating liquid film under conjoining/disjoining pressures. Journal of Colloid and Interface Science, 1999, 218(1): 152-166

50 Münch A, Wagner B. Contact-line instability of dewetting thin films. Physics D: Nonlinear Phenomena, 2005, 209(1-4): 178-190

51 Lyushnin A V, Golovin A A, Pismen L M. Fingering instability of thin evaporating liquid films. Phys Rev E, 2002, 65(2): 021602

52 Fujita T, Ueda T. Heat transfer to falling liquid films and film breakdown-I: Subcooled liquid films. International Journal of Heat and Mass Transfer, 1978, 21(2): 97-108

53 Hoke J B C, Chen J C. Thermocapillary breakdown of subcooled falling liquid films. Ind Eng Chem Res, 1992, 31: 688-694

54 Pautsch A G, Shedd T A. Adiabatic and diabatic measurements of the liquid film thickness during spray cooling with fc-72. International Journal of Heat and Mass Transfer, 2006, 49(15,16): 2610-2618

55 Yang T H, Pan C. Molecular dynamics simulation of a thin water layer evaporation and evaporation coefficient. International Journal of Heat and Mass Transfer, 2005, 48(17): 3516-3526

56 Kikugawa G,Takagi S, Matsumoto Y. A molecular dynamics study on liquid-vapor interface adsorbed by impurities. Computers & Fluids, 2007, 36: 69-76

57 Wolde P R T, Frenkel D. Computer simulation study of gas-liquid nucleation in a lennard-jones system. J Chem Phys, 1998, 109: 9901-9918

58 Wang Jinzhao, Chen Min, Guo Zengyuan. A two-dimensional molecular dynamics simulation of liquid-vapor nucleation. Chinese Sci Bul, 2003, 48(7): 623-626

59 Maruyama S, Kimura T. A molecular dynamics simulation of a bubble nucleation on solid surface. Proceedings of the 5th ASME/JSME Joint Thermal Engineering Conference, 1999

60 Yi Pan, Poulikakos D, Walther J, . Molecular dynamics simulation of vaporization of an ultra-thin liquid argon layer on a surface. International Journal of Heat and Mass Transfer, 2002, 45(10): 2087-2100

61 Freund J B. The atomic detail of an evaporating meniscus. Phys Fluid, 2005, 17(2): 022104

62 Jawurek H H. Simultaneous determination of microlayer geometry and bubble growth in nucleate boiling. International Journal of Heat and Mass Transfer, 1969, 12(8): 843-848

63 Voutsinos C M, Judd R L. Laser interferometetric investigation of the microlayer evaporation phenomena. Journal of Heat Transfer, 1975, 97: 88-93

64 Chen J D, Wada N. Edge profiles and dynamic contact angles of a spreading drop. Journal of Colloid and Interface Science, 1992, 148: 207-222

65 DasGupta S, Plawsky J L, Wayner Jr P C . Interfacial force field characterization in a constrained vapor bubble thermosyphon. AIChE Journal, 1995, 41: 2140-2149

66 Renk F J,Wayner Jr P C. An evaporating ethanol menicus, part I: Experimental studies. Journal of Heat Transfer, 1979, 101: 55-58

67 Zheng L, Wang Y X, Plawsky J L, . Accuracy of measurements of curvature and apparent contact angle in a constrained vapor bubble heat exchanger. International Journal of Heat and Mass Transfer, 2002, 45(10): 2021-2030

68 Plawsky J L, Panchamgam S S, Gokhale S J, . A study of the oscillating corner meniscus in a vertical constrained vapor bubble system. Superlattice Microst, 2004, 35(3-6): 559-572

69 Panchamgam S S, Plawsky J L, Wayner P C. Spreading characteristics and microscale evaporative heat transfer in an ultrathin film containing a binary mixture. Trans ASME Journal of Heat Transfer, 2006, 128(12): 1266-1275

70 Gokhale S J, Plawsky J L, Wayner P C, . Inferred pressure gradient and fluid flow in a condensing sessile droplet based on the measured thickness profile. Physics of Fluids, 2004, 16(6): 1942-1955

71 Argade R, Ghosh S, De S, . Experimental investigation of evaporation and condensation in the contact line region of a thin liquid film experiencing small thermal perturbations. Langmuir, 2007, 23(3): 1234-1241

72 Deng L, Plawsky J L, Wayner P C, . Stability and oscillations in an evaporating corner meniscus. Trans ASME Journal of Heat Transfer, 2004, 126(2): 169-178

73 Churaev N V, Esipova N E, Hill R M, .The superspreading effect of trisiloxane surfactant solutions. Langmuir, 2001, 17(5): 1338-1348

74 Liu A H, Wayner P C, Plawsky J L. Image scanning ellipsometry for measuring nonuniform film thickness profiles. Applied Optics, 1994, 33(7): 1223-1229

75 Liu A H, Wayner P C, Plawsky J L. Image scanning ellipsometry for measuring the transient, film thickness profiles of draining liquids. Physics of Fluids, 1994, 6(6): 1963-1971

76 Liu A H, Wayner P C, Plawsky J L. Drainage of a partially wetting film: Dodecane on silicon. Ind Eng Chem Res, 1996, 35(9): 2955-2963

77 Hohmann C, Stephan P. Microscale temperature measurement at an evaporating liquid meniscus. Experimental Thermal and Fluid Science, 2002, 26(2-4): 157-162

78 Buffone C, Sefiane K. Temperature measurement near the triple line during phase change using thermochromic liquid crystal thermography. Exp Fluids, 2005, 39: 99-110

79 Buffone C,Sefiane K, Christy J R E. Experimental investigation of the hydrodynamics and stability of an evaporating wetting film placed in a temperature gradient. Applied Thermal Engineering, 2004, 24(8,9): 1157-1170

80 Buffone C, Sefiane K. Ir measurements of interfacial temperature during phase change in a confined environment. Experimental Thermal and Fluid Science, 2004, 29(1): 65-74

81 Buffone C, Sefiane K. Controlling evaporative thermocapillary convection using external heating: An experimental investigation. Experimental Thermal and Fluid Science, 2008, 32(6): 1287-1300

82 Buffone C, Sefiane K. Investigation of thermocapillary convective patterns and their role in the enhancement of evaporation from pores. International Journal of Multiphase Flow, 2004, 30(9): 1071-1091

83 Buffone C, Sefiane K, Christy J R E. Experimental investigation of self-induced thermocapillary convection for an evaporating meniscus in capillary tubes using micro-particle image velocimetry. Physics of Fluids, 2005, 17(5): 052104