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In this work, we study a particular system of coagulation equationscharacterized by two values, namely volume $v$ and surface area $a$. Comparedto the standard one-dimensional models, this model incorporates additionalinformation about the geometry of the particles. We describe the coagulationprocess as a combination between collision and fusion of particles. We provethat we are able to recover the standard one-dimensional coagulation model whenfusion happens quickly and that we are able to recover an equation in whichparticles interact and form a ramified-like system in time when fusion happensslowly.

Fast fusion in a two-dimensional coagulation model