The Propagation of Wetting Fronts Through Porous Media

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.