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Holes in objects may be desirable or undesirable. For instance, when we unwrap a piece of clothing that was ordered from an expensive mail-order catalogue, and find that there are unwanted holes in it, we usually send it right back, with a more or less polite demand for a refund or an exchange. And everyone knows the effect of holes in bicycle or automobile tires. However, holes in the middle of records (remember records?) allow them to be played on a phonograph, and holes in the middle of bagels and doughnuts not only eliminate the hard-to-cook part, but also allow ease of handling by clumsy fingers. So holes can indeed sometimes be useful.
A porous material is simply some kind of solid material that has holes in it. The holes are also called pores. However, most people, if asked, would make a distinction between a pair of socks with three holes in the toes, an empty closed cardboard box, and a household sponge. The socks and the box would not generally be considered to be porous materials, while the sponge would be. In order to call a material a porous material, there is usually some kind of implicit assumption of homogenization and length scale.
Attempting to state this intuitive feeling more quantitatively is difficult. We might in general say that the holes must be small enough, compared to the typical size of the piece of material that is considered, so that it is reasonable to consider the material as a mixture of solid framework and pores. Also, the holes must be distributed fairly evenly throughout the material. Therefore, if the length scale of the sample is large compared to the typical pore size, and the pores are distributed reasonably uniformly throughout the material, then the material is a porous material. We will use these qualitative ideas as a working definition of most porous materials in this and later chapters.
Common porous materials, some of which will be considered in the chapters of this book, include concrete [1], paper, ceramics (with natural [2] or artificially-created pores [3]), clays [4], porous semiconductors [5], chromotography materials, and natural materials like coral, bone, sponges, rocks, and shells. Porous materials can also be reactive, such as in charcoal gasification, acid rock dissolution, catalyst deactivation [7], and concrete [1].
The purpose of this chapter is to describe a "tool kit" of mathematical and computational tools that are available for use on digital images in general, and digital images of porous materials, in particular. These include tools for measuring geometrical and morphological quantities, tools for computing physical properties of various kinds, and tools for generating 3-D images, either from 2-D images or using models of various kinds. There are many standard review papers and monographs in this area. Sahimi's book, in particular, is a good overall reference that covers some of the same material as this chapter [8].