Modeling of Multicomponent Coatings

Abstract

Thin liquid films play a central role in coating processes and other industrial and natural applications. Efficient optimization of these processes requires an understanding of capillary leveling, Marangoni flow, evaporation, and related phenomena. Although mathematical models are useful for gaining such understanding, it can be difficult to extract physical insight as the number of phenomena considered increases, so simplifying assumptions such as the vertical-averaging (VA) approximation for solute concentration are often employed. In the first part of this work, we examine the performance of the VA approximation for three common evaporation models: constant, one-sided, and diffusion-limited. We find that the formal regime of validity of the VA approximation is inaccurate and strongly depends on the evaporation rate. Furthermore, applying the VA approximation outside of its regime of validity results in drastically different film-height and solute-distribution predictions depending on the evaporation model. Many applications often demand multilayer films where each layer has distinct properties, and this gives rise to additional challenges. It has been experimentally demonstrated that two-layer films in which the layers are miscible can undergo dewetting, but theoretical understanding of this phenomenon is lacking. The second part of this work addresses the mechanisms that may initiate dewetting in miscible two-layer two-component films. It is found that a disparity in initial solute concentration between the film layers drives flows that lead to significant film-height nonuniformities. The third part of this talk focuses on evaporating sessile droplets which are critical to many industrial applications and are also ubiquitous in nature. Two predominant evaporation models have emerged in the literature, one-sided and diffusion-limited, with differing assumptions on the evaporation process. While both models are widely used and their predictions can differ greatly from each other, the physical mechanisms underlying these differences are not yet well understood. For the one-sided model, we derive expressions for the droplet lifetime, show that the evaporation rate is proportional to the droplet surface area, and demonstrate that the contact line is always warmer than the bulk of the droplet. Furthermore, we show that differences in the structure of the evaporation models near the contact line lead to qualitatively different behavior of the apparent contact angles and interface temperature profiles.