ON THE OSTWALD RIPENING OF THIN LIQUID FILMS

Dewetting instabilities cause a thin liquid film coating a solid substrate to rupture and finally form complex patterns, which are quasiequilibrium parabolic droplets connected by an ultra thin residual film. During the Ostwald ripening process, droplets exchange mass through the residual thin film without touching each other. Bigger ones grow while smaller ones shrink and disappear. As a result the total number of droplets N(t) decreases while the average size increases. For the physically realistic case when the underlying substrate is two dimensional, it is predicted that the average volume of droplets nu follows a temporal power-logarithmic law: nu(4/3) ln nu similar to ct. We propose a mean field model for the Ostwald ripening of 2D thin films and define a structural time scale t(s), which is heuristically similar to t. In this mean field model we rigorously prove that nu can not grow faster than the power-logarithmic law in t(s) in the average sense, as long as the droplets are well separated.