Smoluchowski's equation for cluster exogenous growth
Résumé
We consider an extended Smoluchowski equation describing coagulation processes for which clusters of mass s grow between collisions with dot s = Asβ. A physical example, dropwise condensation, is provided, and its collision kernel K is derived. In the general case, the gelation criterion is determined. Exact solutions are found and scaling solutions are investigated. Finally, we show how these results apply to nucleation of discs on a plane.