  We study the shape and growth rate of necks between sintered spheres with
dissolution-precipitation dynamics in the reaction-limited regime. We determine
the critical shape that separates those initial neck shapes that can sinter
from those that necessarily dissolve, as well as the asymptotic evolving shape
of sinters far from the critical shape. We compare our results with past
results for the asymptotic neck shape in closely related but more complicated
models of surface dynamics; in particular we confirm a scaling conjecture,
originally due to Kuczinsky. Finally, we consider the relevance of this problem
to the diagenesis of sedimentary rocks and other applications.
