Spontaneous discrete precipitation pattern formation directed by the coupling of solution permeation and solvent evaporation

Hypothesis: Permeation of liquids into porous media associated with evaporation has attracted attention due to its industrial importance. During evaporation-coupled permeation process, where a solution is continuously supplied into a porous medium, the solute concentration increases over time and a concentration gradient develops. Furthermore, evaporative cooling can induce condensation of water vapor from the air, which generate steep compositional gradients. Under such conditions, steep supersaturation gradients can develop, which are expected to give rise to unique precipitation behavior. Experiments: A saturated ethanol solution of a hydrophobic dye was continuously injected into filter paper under various humidity conditions. The resulting precipitation patterns were analyzed, and theoretical studies were conducted to elucidate the pattern formation mechanisms. Findings: Spontaneous formation of discrete precipitation patterns similar to the Liesegang ring were observed on the filter paper in any humidity condition. Experiments for monitoring the surface temperature of filter paper revealed that the pattern configuration was significantly influenced by the humidity of the surrounding atmosphere. Progressively advancing supersaturation front of the dye was considered to be formed by the combination of solvent evaporation and condensation. Based on these findings, a theoretical model incorporating the supersaturation theory was developed and successfully reproduced the pattern formation and its dependence on humidity. The spatial regularity of the observed patterns followed a logarithmic spacing law reflecting a new regime of precipitation pattern formation in this evaporation-coupled system, where evaporation, condensation, and advection play the leading roles instead of diffusion.