  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.
