Surface-tension-driven coarsening in mass-conserved reaction-diffusion systems

TL;DR

This study investigates how surface-tension-like effects influence pattern coarsening in mass-conserved reaction-diffusion systems, revealing mechanisms similar to phase separation and providing new insights into molecular self-assembly.

Contribution

It demonstrates that a surface-tension-like quantity governs coarsening in mass-conserved reaction-diffusion systems, supported by numerical and theoretical analysis in 2D and 3D.

Findings

Spherical droplet patterns obey Young-Laplace law

Coarsening follows evaporation-condensation mechanism

Pattern formation varies with stability regions

Abstract

Mass conservation in chemical species appears in a broad class of reaction-diffusion systems (RDs) and is known to bring about coarsening of the pattern in chemical concentration. Recent theoretical studies on RDs with mass conservation (MCRDs) reported that the interfacial curvature between two states contributes to the coarsening process, reminiscent of phase separation phenomena. However, since MCRDs do not presuppose a variational principle, it is largely unknown whether description of surface tension is operative or not. In this study, we numerically and theoretically explore the coarsening process of patterns in MCRDs in two and three dimensions. We identify the parameter regions where the homogeneous steady state becomes stable, unstable, and metastable. In the unstable region, pattern formation is triggered by usual Turing instability, whereas in the metastable region, nucleation-growth-type pattern formation is observed. In the later stage, spherical droplet patterns are observed in both regions, where they obey a relation similar to the Young-Laplace law and coarsen following the evaporation-condensation mechanism. These results demonstrate that in the presence of a conserved variable, a physical quantity similar to surface tension is relevant to MCRDs, which provides new insight into molecular self-assembly driven by chemical reactions.