Further Extensions

The purpose of this chapter is to give attention to three directions along which more ideas could be attached, building on the preceding chapters as base. Labels or titles for the three directions are: unsteady behavior and elastic effects; the factor f; anisotropy. Throughout the preceding chapters, a highly artificial practice has been followed: attention has been focused on states where processes are occurring in the steadiest possible manner. The purpose of this chapter is to consider the question: if processes are less steady, can we still describe them concisely and predict their evolution? If we can, presumably it is by adding some terms to the descriptive equations, and we consider briefly what kinds of terms might be needed. As with turning from a single cylindrical inclusion to a granular aggregate, there is an immediate change to a vast field of complexities. The purpose of the chapter is to give just a preliminary view of how one might begin to identify possibilities. The purpose is to enquire how unsteady or transient effects might occur in a system that is capable of steady behavior. For this purpose, something simpler than a chemical nonhydrostatic system can be used, as shown in Figure 20.1. The simpler of the systems illustrated, Figure 20.1a, consists of a weight that is supported by two elements P and Q. The elements are known as dashpots; each is imagined to consist of a cylinder and piston; each cylinder is full of oil both above and below the piston and each piston has a hole. In consequence, when the element is pulled it can change length as fast as oil can slip through the piston's hole, and ideally the rate of elongation is proportional to the force pulling on the element. The fact that ultimately the piston comes to the end of the cylinder is ignored; we imagine P and Q to have as much length as we need. In Figure 20.1a, the system is such that the two elements have to elongate at equal rates; but they are dissimilar and we imagine a system where, to achieve equal rates, the force pulling P needs to be three times the force pulling Q.