Nonlinear dynamics and instability of heated liquid films.

摘要

Horizontal, static liquid layers on planar solid boundaries are examined using long-wave asymptotic methods and numerical simulation. The first part of this study is concerned with the instabilities of volatile, ultrathin films which are uniformly heated (cooled) from below. We analyze the nonlinear interaction between van der Waals attractions, vapor recoil, thermacapillarity, mass loss (gain) and nonequilibrium thermodynamic effects.;Long-wave theories of the type discussed here have never been tested experimentally, until now. The confirmed validity of our thermocapillary theory is a good indication that our long-wave analysis is also valid for unsteady, evaporating/condensing liquid layers. We expect this validity to extend to ultrathin layers where long-range molecular forces are important. Our work contains the only nonlinear theory extant, and so is capable of following film-dimpling nearly to rupture; these predictions should be of major importance on a practical level.;The second part of this study focuses on the steady dimpling of non-volatile layers which are non-uniformly heated/cooled from below. Here we analyze the nonlinear interaction between thermocapillary and hydrostatic effects. We have corroborated our long-wave theory of thermocapillarity by measuring the steady dimpling of non-uniformly heated silicone-oil layers with mean thicknesses ranging from 0.125 mm to 1.684 mm. We monitor the temperature distribution in the substrate using thermocouples, and the interface shapes using a mechanical impedance-probe. Measured steady shapes and theoretical predictions agree within 20% for moderate heating when the film is not close to rupture. We define a limiting capillary number that is an excellent indicator of rupture.