Other Interfacial Phenomena Involving Dispersed Phase Formation

Theoretical descriptions of such behavior have been given in terms of a mechanism first put forward by Ostwald around the turn of the centory, namely that a critical local supersaturation is required to initiate local precipitation (see Henisch, 1988 Klueh and Mullins, 1969 Prager, 1956 Wagner, 1950). But subsequent experimental studies have raised questions concerning the applicability of this mechanism (Kai et al., 1982). In particular, the solid has been observed to form as a colloidal dispersion before the appearance of bands. Also it has been found that bands sometimes develop, in contrast to predictions of the above theory, in systems of uniform initial composition (Hicker and Ross, 1974). 

FIGURE 6.27 Liesegang ring formation. From Kai et al. (1982) with permission. 

We consider a uniform initial dispersion where the values of c and a for solute concentration and radius are such that da/dt, as given by Equation 6.104, is zero. Now suppose that c and a are perturbed in sueh a way that 

r is the net rate of solute addition to the solvent by particle dissolution and 

Finally, substituting Equations 6.105,6.106, and 6.108 through 6.110 into Equation 6.107, we obtain a quadratic equation that yields the following solutions for the time factor P  

---