Interfacial-curvature-driven coarsening in mass-conserved reaction-diffusion systems

Abstract

Mass conservation in chemical species appears in a broad class of reaction-diffusion systems (RDSs) and is known to cause coarsening of the pattern in chemical concentration. Recent theoretical studies on RDSs with mass conservation (MCRDSs) have reported that the interfacial curvature between two states contributes to the coarsening process, which is reminiscent of phase separation phenomena. However, since MCRDSs do not presuppose a variational principle, it is largely unknown whether description of surface tension is operative. In this paper, we numerically and theoretically explore the coarsening process of patterns in MCRDSs 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 (type-II_{s}) 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 RDSs, which provides insight into molecular self-assembly driven by chemical reactions.