When a fluid-immersed array of supported plates or
pillars is dried, evaporation leads to the formation
of menisci on the tips of the plates or pillars
that bring them together to form complex patterns.
Building on prior experimental observations, we
use a combination of theory and computation to
understand the nature of this instability and its
evolution in both the two- and three-dimensional
setting of the problem. For the case of plates, we
explicitly derive the interaction torques based on the
relevant physical parameters associated with pillar
deformation, contact-line pinning/depinning and
fluid volume changes. A Bloch-wave analysis for our
periodic mechanical system captures the window of
volumes where the two-plate eigenvalue characterizes
the onset of the coalescence instability. We then
study the evolution of these binary clusters and their
eventual elastic arrest using numerical simulations
that account for evaporative dynamics coupled to
capillary coalescence. This explains both the formation
of hierarchical clusters and the sensitive dependence
of the final structures on initial perturbations, as
seen in our experiments. We then generalize our
analysis to treat the problem of pillar collapse
in three dimensions, where the fluid domain is
completely connected and the interface is a minimal
surface with the uniform mean curvature. Our theory and simulations capture the salient
features of experimental observations in a range of different situations and may thus be useful
in controlling the ensuing patterns.