Markicevic B, Bijeljic B, Navaz H K
Department of Mechanical Engineering, Kettering University, Flint, Michigan, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Nov;84(5 Pt 2):056324. doi: 10.1103/PhysRevE.84.056324. Epub 2011 Nov 28.
The experimental and numerical results of the capillary-force-driven climb of wetting liquid in porous media, which is opposed by the gravity force, are analyzed with respect to the emergence of a multiphase flow front and flow stability of the climbing liquid. Two dynamic characteristics are used: (i) the multiphase flow front thickness as a function of time, and (ii) the capillary number as a function of Bond number, where both numbers are calculated from the harmonic average of pores radii. Throughout the climb, the influence of capillary, gravity, and viscous force variations on the flow behavior is investigated for different porous media. For a specific porous medium, a unique flow front power law function of time is observed for the capillary flow climbs with or without gravity force. Distinct dynamic flow front power law functions are found for different porous media. However, for capillary climb in different porous media, one is able to predict a unique behavior for the wetting height (the interface between wetted and dry regions of porous medium) using the capillary and Bond number. It is found that these two numbers correlate as a unique exponential function, even for porous media whose permeabilities vary for two orders of magnitude. For climbs without the gravity force (capillary spreads), the initial climb dynamics follows this exponential law, but for later flow times and when a significant flow front is developed, one observes a constant value of the capillary number. Using this approach to describe the capillary climb, only the capillary versus Bond number correlation is needed, which is completely measureable from the experiments.
分析了在重力作用下，多孔介质中润湿液体受毛细力驱动爬升的实验和数值结果，涉及多相流前沿的出现和爬升液体的流动稳定性。使用了两个动态特性：(i) 多相流前沿厚度随时间的变化，以及 (ii) 毛细数随邦德数的变化，其中这两个数均根据孔隙半径的调和平均值计算得出。在整个爬升过程中，针对不同的多孔介质，研究了毛细力、重力和粘性力变化对流动行为的影响。对于特定的多孔介质，在有或没有重力作用的毛细流爬升中，观察到了随时间变化的独特的流前沿幂律函数。不同的多孔介质有不同的动态流前沿幂律函数。然而，对于不同多孔介质中的毛细爬升，利用毛细数和邦德数能够预测润湿高度（多孔介质润湿区和干燥区之间的界面）的独特行为。研究发现，即使对于渗透率相差两个数量级的多孔介质，这两个数也以独特的指数函数相关联。对于没有重力作用的爬升（毛细铺展），初始爬升动力学遵循该指数规律，但在较长流动时间且形成显著的流前沿时，会观察到毛细数为恒定值。使用这种方法描述毛细爬升，仅需要毛细数与邦德数的相关性，而这完全可以从实验中测量得到。
