Bijeljic B, Markicevic B, Navaz H K
Department of Earth Science and Engineering, Imperial College, London, SW7 2BP, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 May;83(5 Pt 2):056310. doi: 10.1103/PhysRevE.83.056310. Epub 2011 May 9.
The dynamics of capillary climb of a wetting liquid into a porous medium that is opposed by gravity force is studied numerically. We use the capillary network model, in which an actual porous medium is represented as a network of pores and throats, each following a predefined size distribution function. The liquid potential in the pores along the liquid interface within the network is calculated as a result of capillary and gravity forces. The solution is general, and accounts for changes in the climbing height and climbing velocity. The numerical results for the capillary climb reveal that there are at least two distinct flow mechanisms. Initially, the flow is characterized by high climbing velocity, in which the capillary force is higher than the gravity force, and the flow is the viscous force dominated. For this single-phase flow, the Washburn equation can be used to predict the changes of climbing height over time. Later, for longer times and larger climbing height, the capillary and gravity forces become comparable, and one observes a slower increase in the climbing height as a function of time. Due to the two forces being comparable, the gas-liquid sharp interface transforms into flow front, where the multiphase flow develops. The numerical results from this study, expressed as the climbing height as a power law function of time, indicate that the two powers, which correspond to the two distinct mechanisms, differ significantly. The comparison of the powers with experimental data indicates good agreement. Furthermore, the power value from the Washburn solution is also analyzed, where it should be equal to 1/2 for purely viscous force driven flow. This is in contrast to the power value of ∼0.43 that is found experimentally. We show from the numerical solution that this discrepancy is due to the momentum dissipation on the liquid interface.
对受重力作用阻碍的润湿液体在多孔介质中毛细管爬升的动力学进行了数值研究。我们使用毛细管网络模型，其中实际的多孔介质被表示为孔隙和喉道的网络，每个孔隙和喉道都遵循预定义的尺寸分布函数。由于毛细管力和重力的作用，计算了网络内沿液体界面的孔隙中的液体势。该解决方案具有通用性，并考虑了爬升高度和爬升速度的变化。毛细管爬升的数值结果表明，至少存在两种不同的流动机制。最初，流动的特征是爬升速度高，其中毛细管力高于重力，流动以粘性力为主导。对于这种单相流，沃什伯恩方程可用于预测爬升高度随时间的变化。后来，在更长的时间和更大的爬升高度下，毛细管力和重力变得相当，人们观察到爬升高度随时间的增加变得更慢。由于这两种力相当，气液尖锐界面转变为流动前沿，多相流在此处发展。本研究的数值结果以爬升高度作为时间的幂律函数表示，表明对应于两种不同机制的两个幂值有显著差异。将这些幂值与实验数据进行比较，结果吻合良好。此外，还分析了沃什伯恩解的幂值，对于纯粘性力驱动的流动，该值应等于1/2。这与实验发现的约0.43的幂值形成对比。我们从数值解中表明，这种差异是由于液体界面上的动量耗散造成的。
