Nucleation and colloidal growth in concentration gradients (Liesegang rings)

Abstract

We analyze nucleation and colloidal growth in the presence of concentration gradients of electrolytic reactants by means of a postulated set of reaction–diffusion equations, which contain a sink (or reaction) term to account for nucleation and subsequent growth. These equations are more realistic than previous ones used in formulations of the Ostwald hypothesis of Liesegang ring formation, in which that formation is supposed to be a prenucleation process, but in limits contain the previous formulations. We calculate length and time scales of our equations and estimate values of the physical quantities involved. Numerical solutions of our equations predict nucleation to occur as a spatially continuous process, in agreement with experiments. In previous formulations spatial discontinuties in nucleation were obtained by unwarranted approximations or ad hoc assumptions (boundary conditions).