Pattern formation in precipitation processes. II. A postnucleation theory of Liesegang bands

摘要

A theory is presented which explains recurrent precipitation bands (lsquo;lsquo;Liesegang ringsrsquo;rsquo;) as dissolution patterns in a previously produced essentially homogeneous and continuous colloid. This picture is consistent with recent experimental evidence that the formation of Liesegang bands is a postnucleation phenomenon. Mathematically we formulate a model which contains a suitable diffusion equation plus a threshold condition for band formation and repetitive boundary conditions at the location of the previous band. The theory predicts the familiar exponential (spacing) law for the band positions but is sufficiently flexible to account for deviations from this law if additional physico-chemical details are taken into account.