Front Propagation in Patterned Precipitation. 1. Simulation of a Migrating Co(OH)2 Liesegang Pattern

Abstract

The model of Müller and Polezhaev for periodic precipitation is applied to a salt system that can dissolve in excess diffusing electrolyte due to complex formation. A typical example is the Co(OH)2 Liesegang pattern from Co2+ and NH4OH, which propagates due to band formation ahead and band dissolution at the tail of the stratum (Co(OH)2 dissolves in excess ammonium hydroxide forming Co(NH3)62+). Diffusion profiles are constructed by plotting the computed distance of the last band (dlb) and that of the first band (dfb) versus time. The propagation is investigated under two main conditions: at fixed concentration of the inner electrolyte (X0) while varying that of the outer electrolyte (Y0), and the reverse (i.e., at fixed Y0 while varying X0). While in the first case, the propagation is faster at higher Y0, the opposite trend is obtained when X0 is varied, exactly reproducing the experimental observations in the literature on Co(OH)2. A correlation close to linear is found between the dissolution and precipitation events. The advancing banded patterns are also displayed in a special map representation combining the diffusion profiles with the band contours. A special criterion is developed, delineating the situations where either a single pulse or a stratum of bands propagates.