Mesoscopic study of the effects of gel concentration and materials on the formation of precipitation patterns

A mesoscopic model based on the lattice Boltzmann method (LBM) is proposed to simulate the formation of Liesegang precipitation patterns and investigate the effects of gel on the morphology of the precipitates. In this model, nucleation is introduced on the basis of Ostwald's supersaturation theory, and subsequent crystal growth on the precipitate surface is simulated using a crystal growth model by taking into account the heterogeneous reaction on the surface of the precipitate. This model can capture the porous structures of the precipitates and can take into account the effects of the gel concentration and material by adjusting the gel porosity and nucleation threshold. The density of the precipitate nodes in the model is limited. A wide range of precipitation patterns is predicted under different gel concentrations, including regular bands, treelike patterns, and for the first time with numerical models, transition patterns between regular bands and treelike patterns. Both the spacing law and the width law are carefully investigated with different gel concentrations and gel materials, and the obtained α in the width law (w_n≈ xn^α, where x_n and w_n are the position and the width of the nth band, respectively) is in the range of 0.58-0.67, sandwiched by previously predicted ranges.