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Porous materials

Consider a sample of total volume V. Define the volume of the solid phase to be V_s, and the volume of the pore phase (the holes) to be V_p, with V = V_s + V_p. The volume fraction is a normalized variable that is generally more useful. The volume fraction of the pore phase is commonly called the porosity, and is denoted = V_p / V. The solid volume fraction is then 1 - .

Since a porous material is a two-phase material (at least), a surface separating the pore phase from the solid phase can be defined, with its area denoted S_p. This quantity is often called the pore surface area. A normalized variable common for this quantity is called the specific surface area, s_p = S_p / V. Note that the dimension of 1 / s_p is length, so that sometimes it is thought of as a length that characterizes the length scale of the pores. A simple example would be a collection of N mono-sized non-overlapping spherical pores of radius r. The inverse of the specific surface area, 1 / s_p, would be r / (3 ), which is obviously a length characteristic of the pores. Other ways in which to form a length scale from pore space characteristics will be covered later in this chapter and in other chapters of this book dealing with the transport properties of porous materials.

In thinking about the micro-geometry of porous materials, a common approach is to consider them to be two-phase solid-pore composites, even though the solid phase can be heterogeneous. Properties like elastic moduli are essentially a function of the solid phase, but reduced and modified by the presence of the pores. If there is a fluid that fills the pore space, which can modify the dynamic elastic response, then both solid and pore characteristics must be dealt with in understanding the elastic properties [9]. Elastic moduli decrease as the porosity increases. Properties like diffusivity and permeability are functions of pore size, shape, and connectivity, and increase as the porosity increases.

The topology of the pore space of a porous material is very important in determining the properties of the material, and even in properly formulating ideas about the pore space in the first place. By topology is meant how the pores are connected, if at all. If the pores are completely isolated from each other, then it is clear that one can discuss the shape and size of individual pores. The left side of Figure 1 shows an example of this case, in 2-D, where the pores are random size, non-overlapping circular holes. It is clear in this case how to define the pore size distribution, a quantity which gives the number or volume of pores of a given size.

Figure 2: Schematic picture defining a throat and pore in the pore space of a porous material.

If there is such a throat structure, then a pore throat size distribution, usually but erroneously called the pore size distribution, can be defined. Techniques like nitrogen BET and mercury intrusion porosimetry (see Chapter 3) measure a pore throat size distribution that is convolved with the cross-sectional throat shape and the topology of the pore-throat network [6,10]. These techniques measure an equivalent circular cross-sectional throat diameter [6,10]. In practice, pore-throat combinations can only really be separated in terms of grossly simplified geometrical models of the pore microgeometry.

In most cases, porous materials are random materials, with random pore sizes, shapes, and topology. Because of this fact, most porous materials tend to be isotropic. This is not always the case, however. Many rocks have anisotropy built into them from how they were formed due to deposition of sediment [11]. When looking at a slice of a porous material, one must of course be aware whether the material is isotropic or not. We shall assume isotropy in the remainder of this chapter.