Two-dimensional Ostwald ripening with irreversible absorption or reaction on boundaries

During Ostwald ripening, the growth of larger patches occurs at the expense of smaller ones via detachment, diffusion, and attachment of monomers. Customarily, the processes belonging to this important class are simulated with periodic boundary conditions. The two-dimensional Monte Carlo simulations presented herein are focused on the situation when diffusing monomers disappear as soon as they reach the lattice boundaries. For the Fickian diffusion (without the driving force for ripening), the shape of the corresponding kinetics and the time scale characterizing the drop of the concentration are independent of the initial concentration of monomers, the shape is independent of the lattice size as well, while the time scale is inversely proportional to the square of the lattice size. With attractive interaction between monomers (this is the driving force for ripening), the time scale characterizing the drop of the concentration remains to be nearly inversely proportional to the square of the lattice size but increases with increasing the initial concentration of monomers. The lattice snapshots show that with increasing time the Ostwald-type patches first rapidly reach appreciable size, but then disappear at the periphery due the loss of monomers at the boundaries. The central area where these patches are observed shrinks, and nevertheless the patches grow there.