Solute reaction mediated precipitate patterns in cross gradient free systems

Abstract

Recent studies on the spontaneous formation of undulatory patterns of precipitate concentration, such as Liesegang and related phenomena, have shown that these effects can be explained on the basis of a competitive particle growth mechanism as underlies Ostwald ripening. However these effects require an overall gradient or boundary perturbation to induce regular patterning on a scale greater than the interparticle spacing to override the single crystal-so called “greedy giant” instability. Here we show that by allowing for precipitate particle mediated reactions involving the solute species (from which the precipitate is constructed) a fastest growing mode of wave vectorkd, 0<kd<∞, exists and thus pattern formation can occur completely autonomously at a well defined wave length without the need of cross gradients. These processes may be much more widely realized in physical and biological self organization processes than the familiar reaction diffusion (Turing) model due to the rather nonspecific nature of the present phenomenon.