Preamble

Here we are concerned with fluid flow through a body which is accordingly ‘porous’ in some sense. In order that such flow be possible it is necessary that

1. (i) there is vacant space available ‘within’ the body to accommodate fluid, and

2. (ii) the space in which fluid can reside must be connected in order that the fluid can move through the body.

Vacant space within a body is termed pore space, a measure of which is porosity. Of course, not all pore space may be accessible to fluid: there may be isolated space inaccessible to fluid penetration. Such penetration, associated with connectivity, gives rise to the notion of permeability. Consider an insect attempting to crawl through a rectangular block of porous material from the centre of one face to exit through another particular face. This may or may not be possible. It could be that no connected route between the point of entry and the destination face exists, or that the insect is unable to squeeze through available ‘gaps’ en route. The former snag indicates that permeability is in some sense direction-dependent, while the latter draws attention to the scale dependence of both porosity and permeability.

Before addressing technicalities, it is worthwhile to note that the effects of porosity are crucial to our very existence: semipermeable membranes help to govern vital processes throughout our bodies, and the porous nature of bone provides structural strength without undue mass. Further, plant life and soil properties depend in part on relevant porosities, while the presence of subterranean water sources (aquifers) and oil-bearing shale derives from porosity within the surface of the Earth. More mundanely, we utilise sponges for cleaning and filtration systems in our water supplies but can be inconvenienced by dampness in the fabric of buildings and swelling of kitchen worktops due to water ingress. The foregoing serves to illustrate the diversity of porous system effects and the range of associated length scales.