Control of Evaporatively Driven Instabilities of Thin Liquid Films

Evaporating liquid layers are found in many areas of science and technology, so their practical significance is rather high. Examples include evaporative cooling and numerous coating applications. In the latter a substrate is coated with a layer of solution which, upon the evaporation of solvent, leaves a layer of solute on the surface of the substrate. The main difference between various coating techniques is in the way the initial liquid coating is produced. For instance, dip-coating technique is used for optical fiber coating [1], and (anti)reflective optical coatings of lenses and mirrors. Similar techniques are used to produce hydrophobic [2] and hydrophilic coatings. Spray coating is used to produce sol-gel coatings of TV screens [3] and, more routinely, for painting. Spin coating [4] which was originally developed for microelectronics applications has also found numerous applications in the optical industry. One of the critical issues related to the quality of produced coatings is stability of the liquid layer during evaporation. For instance in spin-coating applications, striations (radially oriented lines of thickness variation) arise due to the thermal and solutal effects induced by evaporation [5]. These effects are also responsible for the rupturing instability [6] which results in the formation of a pattern of dry spots [7], a phenomenon often referred to as reticulation. The ultimate fate of the linearly unstable liquid film, with or without evaporation, is eventually determined by the properties of the substrate: if it is nonwetting, the film will generally rupture [8], otherwise it may remain continuous and nonuniform. In most circumstances dewetting is a highly undesirable effect, so understanding its mechanisms and learning to control it is very important. The process of dewetting is intrinsically nonlinear, so it cannot be adequately described by the linear theory. This means that either numerical [8,9] or approximate analytical [10] solutions have to be obtained. However, neither approach is suitable for control purposes. The more practical approach is to prevent the instability from forming at the linear stage, rather than suppress the rupturing itself. This approach has an additional advantage that, if the liquid layer is uniform at all times during the evaporation, the produced coating will be uniform as well. Several different approaches have been suggested to enforce control of evaporating liquid films. All of them are properly classified as passive. The examples include the use of surfactants [11] and internal (volumetric) heating of the liquid layer [12,13]. Albeit the passive approaches are relatively simple, their applicability is very restricted (e.g., surfactants may contaminate the coating). Active, or feedback, control schemes are generally significantly more flexible and efficient. Although none currently exist, several approaches designed to suppress MarangoniBénard convection in thin nonvolatile films can be generalized for the case with evaporation. The underlying idea of the latter approaches is to exploit the same physical mechanism that leads to instability, in this case the thermocapillary effect: a spatially distributed thermal perturbation is applied to either the bottom [14] or the top [15] interface, which opposes the spontaneously produced disturbances, an approach sometimes referred to as noise-cancellation. When evaporation is present, thermocapillarity represents only one of several destabilizing mechanisms: vapor recoil (normal pressure on the liquid-gas interface due to non-equilibrium evaporation), differential evaporation (dependence of the evaporation rate on the thickness of the film) and, sometimes, solutocapillarity all contribute to the development of the interfacial instability. There might also be additional destabilizing mechanisms not related to evaporation, e.g., van der Waals interactions, gravity, and curvature effects. Since all mechanisms in the former group are evaporatively driven, it should come as no surprise that all of them can be al-