Coarsening in Unstable Thin Liquid Films

摘要

The coarsening dynamics of thermal noise at the free surface ofa thin liquid film sandwiched between a solid and a bounding fluid is investigated based on the numerical solution of the 2-D thin film equation under the influence of various disjoining pressures. These fluctuations spontaneously amplify and coarsen to produce a variety of morphological patterns whenever the disjoining pressure is made up of an attractive long range and repulsive short range component. The appearance of an equilibrium film, termed as pseudo-dewetting of the substrate, is a hallmark of evolution under such antagonistic disjoining pressures. It is seen that coarsening, as denoted by the number of hills and valleys (N) in the pattern, occurs via two distinct stages viz., (1) pre(pseudo-)dewetting and (2) post(pseudo-)dewetting. An obscure intermediate stage, dewetting stage, spanning the duration of time between the first instance of dewetting and complete dewetting at all possible locations is also identified. While the exponent in power law dynamics of the type N (propor. to) t~(alpha), t is time, remains constant (-1/3) for postdewetted stage and varies slightly between -1/10 to -1/20 for the predwetted stage, it changes from a very high value (approx -2) to a very low value (-> 0) for the dewetting stage. The dewetting stage, depending on its exponent, can merge with either of the other two stages and apparently disappear. It is absent in cases where dewetting occurs almost simultaneously at all the locations.