Effects of Heat And Mass Transfer of Thin Film Region on the Stability of the Capillary Evaporating Meniscus

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1 Journal of Astronautics Vol. 34 June No 黄晓明 1, 吴江权 1, 刘伟 1 2, 郁伯铭 % TK124 DOI /j. issn A Effects of Heat And Mass Transfer of Thin Film Region on the Stability of the Capillary Evaporating Meniscus HUANG Xiao-ming 1 WU Jiang-quan 1 LIU Wei 1 YU Bo-ming 1. School of Energy and Power Engineering of Huazhong University of Science and Technology Wuhan China 2. School of Physics Huazhong University of Science and Technology Wuhan China Abstract The stability of heated and evaporating capillary meniscus is crucially important for the operation of capillary pumped heat transfer devices. Since more than 50% of the mass transfer by evaporation occurs on a very small region socalled thin film region it is expected that the instability will arise from this region. To explain the stability mechanism of the meniscus effectively a new method that can skillfully combine the linear stability analysis with the numerical analysis of the meniscus is proposed in this paper. Numerical analysis is executed to acquire the characteristic thickness and length of thin film region and a linear stability criteria is calculated by using these two characteristic dimensions. By use of the combination of these two analysis methods the stability mechanism of an evaporating meniscus can be clearly disclosed especially about the effect of the temperature of the meniscus thermophysical properties of the working fluid and the dimensions of the capillary tube on the stability. The effectiveness of this method can be approved by the experimental results of some published references. Key words Capillary evaporating meniscus Linear stability analysis Heat and mass transfer Numerical analysis 0 Heat Pipe LHP 50% - - Microchannel Heat Pipe MHP Loop QN150

2 thin film region W /m 2 1 adsorbed region 2-4 Burelbach 5 long-wave evolution equations S. W. Joo 6 D. Pratt 7 CPL Heat Transfer Loop Buffon 8 PIV 1 Fig. 1 Schematic of evaporation meniscus within a cylindrical capillary pore R 100nm y = h x t h x y t one-sided model 5 lubrication theory intrinsic 9 meniscus region h

3 6 875 ( ) 珘 h τ = - E 珔珘 Π^ 珘 h + K -1 0 h + h - ( ) 1 3 S 珘 h 3 珘 h - 2 E珔 2 D -1 珘 h + K -3 珘 h 3 珘 h 3-1 Ma [ 珘 h + K 2 Pr [ -1 珘 h ] 2 珘 h ] 1 2 珘 h 珘 h = ΔT ΔT cr = 8 珔 Ax c γh 3 0 h /h 0 η x y Hamaker Marangoni Prandtl ΔT cr h 0 x c E 珔 = EX = kδt D = ρνh fg h0 ρ v x c ρ S = σ 0h 3 0 ρν 2 x c Π^ = 珔 A Ma = c pγδth 2 0 P ρν 2 h 0 x c νk r = μc p k k c P ν h fg σ 0 γ 1 σ = σ 0 - γt 珔 A Hamaker Hamaker A 珔 A = A /6π Derjaguin 13 Wayner Young-Laplace Kelvin-Clapeyron 1 d σδ 3σδ'δ 2 dx 1 + δ ' δ ' ΔT < 8 珔 Ax c γh T w ΔT = T w - T v ΔT 2 ΔT cr = x /x c η = y /h 0 h 0 x c x y η τ ΔT cr 2 η τ E珔 E 珔 D S Π^ Ma Pr Marangoni Hamaker /r 2 δ ( [ ] 3 ) - 3Aδ' δ 4 3ν = - m 3 δ δ' δ 2 ΔT m Schrage 15 T v

4 m = 2^σ 2 - ^σ ( ) 珚 M 2πR g ( ) 1/2 P v_equ T lv - P v 4 2 T lv 1/2 T v 1/ ^σ M珚 R g T lv T v P v P v_equ P v_equ T lv = [ ] P sat T lv exp P v_equ T lv - P sat T lv - P d + P c ρ l T lv R g /M [ ( ) ] P sat T lv = P sat_ref T sat_ref exp Mh fg 1 R g T sat_ref - 1 T lv T lv m T lv = - m h fg /k l δ + T w 5 Runge-Kutta 3 ~ 5 2 1nm 2 2 a Pratt 7 2 a 2 Fig. 2 The effect of superheat on the evaporating P d characteristic of the meniscus R = 2500nm T v = 320K 2 b 3 2 c x Pratt 7 x c

5 6 877 P d P d P d = 1 /2000P d0 3 x c 2 Fig. 4 4 h 0 Critical superheat variation with temperature of meniscus based on different h 0 Pentane R = 2500nm ΔT = 1K Fig. 3 3 Length of the thin film region with different super heat h 0 h 0_m h 0_T h 0_a T v 4 4 h 0_m 5 5 Fig. 5 The effect of meniscus temperature on the a evaporating characteristic of the thin film region Pentane R = 2500nm ΔT = 1K 4 h 0_T 5 b

6 nm ΔT = 5K h 0_a ΔT = 10K Pratt 7 Buffone 8 4 1K h 0_a 7 Fig. 7 Critical superheat variation with tube radius 0. 1 ~ 0. 2KPratt at different evaporating condition Pentane T v = 300K K /m 8 Pentane R = 2500nm ΔT = 1K h 0_a ΔT = 1K ΔT = 5K ΔT = 10K Buffone Buffone h 0_a 9 a Fig. 6 Critical superheat variant with temperature of meniscus basing on average film thickness 9 b

7 evaporating /condensing liquid films J. J. Fluid Mech 1988 Fig. 9 Evaporating characteristic of the thin film region for different working fluid T v = 300K ΔT = 1K Fig. 8 Critical superheat at variant superheat for different working fluid R = 2500nm T v = 300K Holm F W Goplen S P. Heat transfer in the meniscus thin-film transition region J. ASME. Heat Transfer Maroo S C Chung J N. Heat transfer charac-teristics and pressure variation in a nanoscale evaporating meniscus J. Int. J. Heat and Mass Transfer Dhavaleswarapu H K Murthy J Y Garimella S V. Numerical investigation of an evaporating meniscus in a channel J. Int. J. Heat and Mass Transfer Harmand S Sefiane K. Experimental and theoretical investigation of the evaporation and stability of a meniscus in a flat micro-channel J. Int. J. Thermal Sciences Burelbach J P Bankoff S G Davis S H. Nonlinear stability of Joo S W Daivs S H Bankoff S G. Long-wave instabilities of heated falling films two dimensional theory of uniform layers J. Journal of Fluid Mech the stability of a heated curved meniscus J ASME an evaporating liquid-vapor interface J 7 Pratt D M Brown J R Hallinan K P. Thermocapillary effects on. J. Heat Transfer 8 Buffone C Sefiane K Easson W. Marangoni-driven instability of Phys. Rev. E Kaya T. J

8 Huang Xiao-ming Kaya T. A linear stability analysis based explicit stability criterion of capillary evaporating meniscus J. J. Astronautics Dasgupta S Kim I Y Wayner P C. Use of the Kelvin-Clapeyron equation to model an evaporateing curved microfilm J. Journal of Heat Transfer Wang H Garimella S V. Characteristics of an evaporating thin film in a microchannel J. Int. J Heat Mass Transfer Kaya T. J Huang Xiao-ming Kaya T. Heat and mass transfer characteristics and stability of capillary evaporating meniscus J. Journal of Xi an Jiaotong University Derjaguin B V. Definition of the concept of andrnagnitude of the disjoining pressure and its role in the statics and kinetics of thin layers of liquids J. Colloid J. USSR Potash M Wayner P C. Evaporation from a two-dimensional extended meniscus J. Int. J. Heat Mass Transfer Schrage R W. A theoretical study of interface mass transfer M. Columbia University Press New York Hallinan K P Chebaro H C Kim S J et al. Evaporation from an extended meniscus for non-isothermal interfacial conditions J. J. Thermo-physics and Heat Transfer xmhuang@ hust. edu. cn

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