see Section 17.2.3. To prevent leakage of liquid from the gel, its permeability
as appearing in the Darcy equation (5.24) should be small. This is discussed
in Section 5.3.1. A significant value of the yield stress may also be needed,
since otherwise liquid may be pressed from the gel under its own weight (cf.
the Question at the end of Section 5.3.1). Hindered diffusion is discussed in
Section 5.3.2.
Finally, the gel network itself should be stable, implying that it should
not show some undesirable change in structure. Since the kind of changes
that can occur and the variables involved greatly depend on gel type, these
aspects will be discussed further on.
17.2.2 Polymer Gels
Basic aspects of polymers are discussed in Chapter 6; see especially Section
6.2.1.
The Rubber Theory of Elasticity. The simplest structure that a
polymer gel can have is depicted in Figure 17.10a: long linear polymer
molecules that are cross-linked at various places along the chains. We will
denote the part of a molecular chain from one cross-link to the next one a
cord. A similar structure occurs in vulcanized rubbers. The rheological
properties of such a system are supposed to be determined by the
conformational entropy of the cords. It is assumed that the distribution of
the monomers—or, more precisely, of statistical chain elements—in each
cord is Gaussian (‘‘normal’’), which will be true if their numbern^0 is large
enough. Any change in the end-to-end distance of the cords due to
deformation of the gel will lead to adecrease in entropy, hence to an increase
TABLE17.2 Gel Properties Needed to Provide Physical Stability
Prevent or impede Gel property neededMotion of particles
Sedimentation Significant yield stressþshort restoration time
Aggregation Significant yield stress
Local volume changes
Ostwald ripening Very high yield stress
Motion of liquid
Leakage Small permeabilityþsignificant yield stress
Convection Significant yield stress
Motion of solute
Diffusion Very small pores, high viscosity of continuous liquid