Ajaev Vladimir S., Homsy G. M.
Department of Chemical Engineering, Stanford University, Stanford, CA, 94305
J Colloid Interface Sci. 2001 Aug 1;240(1):259-271. doi: 10.1006/jcis.2001.7562.
We consider vapor bubbles in microchannels in which the vapor is produced by a heater element and condenses in cooler parts of the interface. The free boundary problem is formulated for a long steady-state bubble in a rectangular channel with a heated bottom. Lubrication-type equations are derived for the shape of the liquid-vapor interface in a cross-sectional plane and in the regime for which the vapor phase fills most of the cross section. These equations are then solved numerically over a range of parameter values with given temperature profiles in the walls and subject to a global integral condition requiring evaporation near the heater to balance condensation in colder areas of the interface. Our results show that depending on the temperature, the side walls can be either dry or covered with a liquid film and we identify criteria for these two different regimes. The asymptotic method breaks down in the limit when capillary condensation becomes important near the bubble top and a different approach is used to determine the shape of the bubble in this limit. Solutions here involve localized regions of large mass fluxes, which are asymptotically matched to capillary-statics regions where the heat transfer is negligible. Copyright 2001 Academic Press.
我们考虑微通道中的蒸汽泡，其中蒸汽由加热元件产生并在界面较冷的部分冷凝。针对底部受热的矩形通道中的长稳态气泡，建立了自由边界问题。推导了横截面中液 - 气界面形状的润滑型方程，以及蒸汽相占据大部分横截面的情况。然后在给定壁面温度分布的一系列参数值范围内对这些方程进行数值求解，并满足一个全局积分条件，即要求加热器附近的蒸发量与界面较冷区域的冷凝量平衡。我们的结果表明，根据温度不同，侧壁可能是干燥的，也可能覆盖有液膜，并且我们确定了这两种不同状态的标准。当在气泡顶部附近毛细冷凝变得重要时，渐近方法在该极限情况下失效，此时采用不同的方法来确定气泡在此极限下的形状。这里的解涉及大质量通量的局部区域，这些区域与传热可忽略不计的毛细静力学区域渐近匹配。版权所有2001年学术出版社。
