Growth of a thin film as a result of mass transfer from a limited fluid pocket has been modeled. The numerical solution of the moving-boundary problem has been obtained by freezing the time-dependent boundary through Landau transformation. Effects of various physicochemical parameters on the growth of film with time have been I,resented. Although originally developed for liquid films, the model successfully predicts the experimentally observed qualitative features of the growth of a solid him. This success takes us a step closer to the larger goal of developing a unified model for growth of all kinds of thin films, involving diffusion as the principal mechanism of transport.