  An important strategy to stabilize emulsions is to arrest coalescence of the
constituent droplets with an opposing rheological force. Colloidal particles
adsorbed on the surface of emulsion droplets in a Pickering emulsion become
increasingly crowded during successive coalescence events because the combined
surface area of coalescing droplets is less than that of the constituent
droplets. Beyond a critical density, the particles form a rigid shell around
the droplet and inhibit both relaxation of the droplet shape and further
coalescence. The resulting droplets have a nonuniform distribution of curvature
and, depending on the initial coverage, may incorporate a region with negative
Gaussian curvature around the neck that bridges the two droplets. Here, we
resolve the relative influence of the curvature and the kinetic process of
arrest on the microstructure of the final state. Identifying the dimensionless
ratio of the rate of area change \dot{A} to the diffusion constant D as a
measure of the importance of kinetics in this system, we show that this depends
on the extrinsic geometry of the surface as opposed to the static packings that
depend solely on intrinsic geometry.
