On the Ostwald ripening of thin liquid films
Shibin Dai · Communications in Mathematical Sciences · 2011
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 V follows a temporal power-logarithmic law: V 4/3 lnV ∼ ct.We propose a mean field model for the Ostwald ripening of 2D thin films and define a structural time scale ts, which is heuristically similar to t.In this mean field model we rigorously prove that V can not grow faster than the power-logarithmic law in ts in the average sense, as long as the droplets are well separated.