Porous-medium flow

This is a special case of multiphase flow, in which one or more fluid phase flows through a permeable matrix. In many cases, the matrix itself is deformable, for example when water is squeezed out of a sponge. This leads to mathematically interesting problems, in which the motions of the fluid and solid phases are coupled through the mutual drag force that each exerts on the other. We are involved with many applications of these ideas, including the following.

Environmental applications

The rock that constitutes the Earth's crust is essentially a porous medium that deforms over geological timescales. The flow through, and erosion of, this medium by magma leads to such phenomena as layered magma chambers and volcanic eruptions. The flow of groundwater through soil and/or rock has important applications in agriculture and in pollution control. Other topics of interest include compaction of sedimentary basins and the phenomenon of frost heave, which occurs when groundwater freezes. As well as damaging roads and pavements, frost heave is responsible for geological formations like the stone garland shown opposite.

Oil recovery

One of the original motivations for studying porous-medium flow was the extraction of oil from porous rock. It was found that suction of viscous fluid from a porous medium is often unstable, tending to leave behind a sizeable proportion of the oil in small isolated packets, and increasing the extracted fraction is a constant challenge. Sometimes solvents are used to enhance recovery. Another important issue for the oil industry is upscaling from locally measured properties (e.g. permeability) and laboratory experiments, so that useful predictions can be made over the much longer scales (hundreds of metres) relevant to an oil well.

Medical applications

Most of the tissues in the body (e.g. bone, cartilage, muscle) are deformable porous media. The proper functioning of such materials depends crucially on the flow of blood, nutrients and so forth through them. Porous-medium models are used to understand various medical conditions (such as tumour growth) and treatments (such as injections).

People working in this area within OCIAM are