  We study the Becker-D\"oring bubblelator, a variant of the Becker-D\"oring
coagulation-fragmentation system that models the growth of clusters by gain or
loss of monomers. Motivated by models of gas evolution oscillators from
physical chemistry, we incorporate injection of monomers and depletion of large
clusters. For a wide range of physical rates, the Becker-D\"oring system itself
exhibits a dynamic phase transition as mass density increases past a critical
value. By formal asymptotics in the near-critical regime, we connect the
Becker-D\"oring bubblelator to a transport equation coupled with an
integrodifferential equation for excess monomer density. For suitable
injection/depletion rates, we argue that time-periodic solutions appear via a
Hopf bifurcation. Numerics confirm that the generation and removal of large
clusters can become desynchronized, leading to temporal oscillations associated
with bursts of large-cluster nucleation.
