The Propagation of Wetting Fronts Through Porous Media

这项研究关注的是液体通过固体的流动，这些固体被孔网渗透;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：-从储层中回收石油。目前，这是一个非常低效的过程，每口井最多只能回收一半的石油。将二氧化碳储存在地下深处的多孔介质中，以减少全球变暖。在这里，至关重要的是要确保有害气体不会在数百年内逃逸。液体喷墨墨滴渗入纸张的情况。为了确保影像的质素，需要知道纸张吸收墨的速度。这种情况的全尺寸试验通常不切实际、昂贵和/或危险。因此，理论建模成为一种工具，可用于探测这种流动的动态，以确保安全，洞察力和适当过程的优化。从世纪中期开始，亨利·达西（Henry Darcy）出于为第戎戎市民提供清洁用水的需要，提出了一个描述水流过沙子的方程，在这一领域进行了深入的学术研究。令人惊讶的是，这个方程仍然被用于大多数多孔介质的流动。我们的研究关注的是液体进入一个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慢慢地爬上放在一杯茶中的饼干。液体在多孔介质中向上爬的原因是液体表面对固体的亲和力比对其余液体的亲和力更强，产生了所谓的毛细力，将液体进一步拉入固体中。毛细效应发生在广泛的现象中，它们是气泡球形的原因，小动物在水上行走的能力和酒杯里的酒滴。也许观察它们的力量最简单的方法是将一个小圆柱形管垂直放入浴缸中，观察管内的水高于浴缸的水。事实上，最简单的模型流入一个最初干燥的多孔介质是通过近似的介质作为一束毛细管。我们粗略地假定，推动液体前沿进入多孔介质的毛细力等于其平衡值。这种方法最初由沃什伯恩在1921年提出。虽然用这种简化的方法描述多孔介质的复杂结构可以得到令人惊讶的精确结果，但大量的实验证据表明它往往是不准确的。该项目提出了从动态润湿的邻近领域（涉及液体在固体上的流动）到我们感兴趣的问题的知识转移，即液体变成固体的流动。动态润湿社区的最新实验结果表明，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，它被证明了如何用液体层尽可能快地涂覆固体，而不会通过夹带气泡而破坏薄膜的质量。预测这种现象的理论在过去几年中只在动态润湿领域进行了彻底的探索，从未被应用于通过多孔介质的流动。通过将这一理论背后的先进数学模型应用于液体通过孔隙网络的传播，我们希望改进目前描述流入干燥多孔介质的模型，并弥合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.