The Propagation of Wetting Fronts Through Porous Media

这项研究关注的是液体在固体中的流动，这些固体被孔洞网络所渗透；这种材料被称为多孔介质。了解液体如何流过多孔结构也是一系列工业现象的关键因素，例如：-从储油层中回收石油。目前，这是一个效率极低的过程，每口井最多可以回收一半的石油。-将二氧化碳深埋在地下的多孔介质中，试图减少全球变暖。在这里，确保有害气体在数百年内不会逃逸是至关重要的。-液体喷墨液滴渗入纸张中，为了确保图像质量，人们希望知道纸张将以多快的速度吸收墨水。这种流动的全面试验通常是不切实际的、昂贵的和/或危险的。因此，理论建模成为一种工具，可以用来探索这种流动的动态，以确保适当过程的安全性、洞察力和最优化。自19世纪中叶以来，这一领域一直有密集的学术研究，当时亨利·达西出于为第戎市民提供清洁水的需要，提出了一个描述水在沙子中流动的方程式。令人惊讶的是，这个方程仍然适用于大多数多孔介质流动。我们的研究涉及液体进入初始干燥的多孔介质的运动。这通常是自发发生的，例如，你可以观察到一种液体沿着放在一杯茶中的饼干慢慢爬上来。液体在重力的作用下向上爬过多孔介质的原因是，液体的表面与固体的亲和力比液体的其余部分更强，产生了所谓的毛细管力，将液体进一步拖入固体中。毛细效应发生在广泛的现象中，它们导致气泡的球形，小动物在水面上行走的能力，以及葡萄酒在玻璃杯上撕裂的能力。也许观察它们力量的最简单方法是将一个小圆柱形管子垂直放入水浴中，观察管子里的水高于浴缸的水。事实上，流动进入初始干燥的多孔介质的最简单模型是将该介质近似为一束毛细管束。粗略地假设，推动液体前沿进入多孔介质的毛细管力等于其平衡值。这种方法最初是由沃什伯恩在1921年提出的。虽然用这种简化的方法描述多孔介质令人难以置信的复杂结构可以得到令人惊讶的准确结果，但大量的实验证据表明它经常是不准确的。该项目提出了一种知识转移，从邻近的动态润湿领域，它涉及液体在固体上的流动，到我们感兴趣的一类问题，即液体进入固体的流动。最近在动态润湿社区的实验结果表明，有多少工业过程可以以一种以前没有实现的方式进行优化。这最初是在摄影工业中发现的，在那里演示了如何在不破坏胶片质量的情况下尽可能快地将液体层覆盖在固体上，方法是将气泡带入其中。预测这种现象的理论只是在过去几年才在动态润湿领域得到了彻底的探索，从未被应用于多孔介质中的流动。通过将这一理论背后的先进数学模型应用于液体在孔隙网络中的传播，我们希望改进目前描述干燥多孔介质中流动的模型，并弥合这两个群体之间的差距。

This research is concerned with the flow of liquid through solids which are permeated by a network of holes; such materials are known as porous media. Understanding how a liquid will flow through a porous structure is also the key element to a range of industrial phenomena such as:- The recovery of oil from a reservoir. This is currently a highly inefficient process with at most half of the possible oil recovered from each well.- The storage of carbon dioxide deep underground in a porous medium in an attempt to reduce global warming. Here it is vital to ensure that harmful gases will not escape over a period of hundreds of years.- The seeping of a liquid ink-jet droplet into paper where, to ensure quality of the image, it is desirable to know how quickly the paper will absorb the ink.Often a full scale experiment of such a flow is unpractical, expensive and/or dangerous. Consequently theoretical modelling becomes a tool which can be used to probe the dynamics of such flows to ensure safety, insight and optimisation of the appropriate process. There has been intensive academic research in this field from the mid-nineteenth century when Henry Darcy, motivated by the need to provide clean water for the citizens of Dijon, proposed an equation to describe the flow of water through sand. Amazingly this equation is still used for most porous media flows.Our research concerns the motion of a liquid into an initially dry porous medium. This often occurs spontaneously, for example, you can observe a liquid creeping slowly up a biscuit which is placed in a cup of tea. The reason that the liquid climbs up through the porous medium, against the downward pull of gravity, is that the liquid's surface has a stronger affinity for the solid than it does for the rest of the liquid, creating what is known as a capillary force, dragging the liquid further into the solid.Capillary effects occur in a wide range of phenomena, they are responsible for the spherical shape of bubbles, the ability of small animals to walk on water and the tears of wine on a glass. Perhaps the easiest way to observe their power is to place a small cylindrical tube vertically into a bath of water and observe that the water inside the tube is above that of the bath. In fact the simplest model for flow into an initially dry porous medium is obtained by approximating the medium as a bundle of capillary tubes. It is assumed, rather crudely, that the capillary force propelling the front of the liquid into the porous medium is equal to its equilibrium value. This approach was originally proposed by Washburn in 1921. Although describing the incredibly complex structure of a porous medium in this simplified approach leads to surprisingly accurate results, there is a large body of experimental evidence suggesting that it is often inaccurate.The project proposes a transfer of knowledge from the neighbouring field of dynamic wetting, which is concerned with the flow of liquids on solids, to the class of problems we are interested in, namely the flow of liquids into solids. Recent experimental results in the dynamic wetting community have shown how many industrial processes can be optimised in a way which was not previously realised. This was originally discovered in the photographic industry where it was demonstrated how to coat a solid with a liquid layer as fast as possible without ruining the film's quality by entraining air bubbles into it.The theory which predicts this phenomenon has only been thoroughly explored in the field of dynamic wetting in the past few years and has never been applied to flows through porous media. By applying the advanced mathematical model behind this theory to the propagation of a liquid through a network of pores we hope to improve on the current model for describing flow into a dry porous medium and bridge the gap between the two communities.