  Aqueous foams are an important model system that displays coarsening
dynamics. Coarsening in dispersions and foams is well understood in the dilute
and dry limits, where the gas fraction tends to zero and one, respectively.
However, foams are known to undergo a jamming transition from a fluid-like to a
solid-like state at an intermediate gas fraction,$\phi_c$. Much less is known
about coarsening dynamics in wet foams near jamming, and the link to mechanical
response, if any, remains poorly understood. Here, we probe coarsening and
mechanical response using numerical simulations of a variant of the Durian
bubble model for wet foams. As in other coarsening systems we find a steady
state scaling regime with an associated particle size distribution. We relate
the time-rate of evolution of the coarsening process to the wetness of the foam
and identify a characteristic coarsening time that diverges approaching
jamming. We further probe mechanical response of the system to strain while
undergoing coarsening. There are two competing time scales, namely the
coarsening time and the mechanical relaxation time. We relate these to the
evolution of the elastic response and the mechanical structure.
