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Besides using digital images of real materials to compute their various physical properties, it is often useful to construct artifical models to elucidate the essential physics. There are three broad classes of 3-D models for porous materials.
The first kind of model is called a percolation-type model. Here, one builds up a structure using randomly or regularly deposited shapes of various kinds within a finite imaging field, e.g., overlapping ellipsoids, lattices of overlapping spheres, or a random or regular lattice of tubes. The result is a 3-D structure that bears some similarities to real materials, and is easy to generate on a computer. They can give real insight into parameters like percolation thresholds, transport properties, and their interrelationships. However, the values of parameters in the models are not to be compared with real materials.
The second type of model is usually based on smoothing of a random noise image. A random noise image is first created, and then be mathematical operations are carried out to transform it into something that resembles a real material. There is no attempt to simulate the actual physical and chemical processes that create the porous material. Cellular automaton methods can also be used to generate images that look like the "real thing", without attempting to duplicate the actual physics and chemistry [95].
The third kind of model is a microstructure development model that tries to simulate the actual processes by which the material is made. Examples, to be discussed further below, include models for the formation of cement-based materials, sintered ceramic materials, and sedimentary rocks. These kinds of models are usually harder to create than the first two kinds, requiring insights into the physical and chemical processes, and the algorithms are more complicated. However, their output can be compared directly to images of the real materials and their measured properties. An image of the actual starting materials, as we shall see, can often be used as the starting point for these kinds of models. The outcome of a microstructure development model can be visually compared to images of the real material. At the crudest level, this is the "duck" test: if it looks like a duck, then it is a duck. However, using the tools developed in Section 2, more quantitative tests can be conducted, e.g., various correlation functions can be compared and other properties can be computed and compared against experimental data. Good agreement validates the assumed physical and chemical processes contained in the model.