Systematic analysis of an evaporating wetting meniscus on a smooth surface
The wetting meniscus on a hot isothermal wall consists of a thin flat film controlled by the disjoining pressure and, far from the wall, a static portion controlled by capillarity. These two non-evaporating regions are separated by an evaporating region. In this region capillarity, the disjoining force, hydrodynamics and the kinetics of evaporation interact to determine the meniscus shape, and the evaporation-rate. The existing model of the problem takes the gas phase as passive, and the meniscus slope as small. The model reduces to the dimensionless boundary-value problem (h{sup 3}p{prime}){prime} = {alpha}(1 + p)/(1 + {omega}h), {minus}p = h{double{underscore}prime} + h{sup {minus}3}, with h({minus}{infinity}) = 1 and H{double{underscore}prime}({infinity}) = {epsilon}. The control parameter {alpha} is the ratio of the disjoining and capillary forces. {epsilon} is the ratio of the pressure drop across the static meniscus to that across the meniscus of the wetting film. {omega} controls the ratio of the thermal resistance of the interface to that of the liquid film. This paper summarizes the chief results of the new systematic numerical and asymptotic analysis of this problem. The authors show that in common applications, {epsilon} {much{underscore}lt} {omega} {much{underscore}lt} 1. In the limit {epsilon} {r{underscore}arrow} 0, the model is shown to define an apparent contact angle {Theta}({alpha},{omega}). {Theta}({alpha},{omega}) and the total heat flow q are determined numerically and given graphically. The authors also state and test a formula giving q{Theta}/K{Delta}T = F({alpha},{epsilon},{omega}) as an explicit function of {epsilon} for {epsilon} {r{underscore}arrow} 0. Here K is the liquid conductivity, and {Delta}T the superheat, i.e., the difference between the constant wall temperature, and the saturation temperature. The results are illustrated by an example using microheat pipes which shows a 100-fold reduction in the meniscus radius of curvature roughly halves the total heat flow from the apparent contact region.
- Research Organization:
- Univ. of California, Berkeley, CA (US)
- OSTI ID:
- 20014423
- Resource Relation:
- Conference: 32nd National Heat Transfer Conference, Baltimore, MD (US), 08/08/1997--08/12/1997; Other Information: PBD: 1997; Related Information: In: ASME proceedings of the 32nd national heat transfer conference (HTD-Vol. 349). Volume 11: Interfacial thermal phenomena in thin films; Heat pipes and thermosyphons; Heat and mass transfer in porous media, by Goodson, K.; Chang, W.S.; Charmchi, M.; Hadim, H. [eds.], 211 pages.
- Country of Publication:
- United States
- Language:
- English
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