(250j) Instability and Symmetry Breaking in Binary Evaporating Thin Films over a Curved Substrate

Marangoni flows are surface tension gradient driven flows that are commonly found in thin liquid films. Specifically, solutal Marangoni flows are flows driven by surface tension gradients generated via composition changes at the interface. Such systems can be found in a wide range of applications such as paint drying, tear film breakup,and the formation of wine legs.

We examine evaporating binary silicone oil films over a glass sphere – perhaps the simplest system driven by solutal Marangoni flows. The liquid film consists of two miscible silicone oils with different surface tension, evaporation rate, and kinematic viscosity (1cSt and 5cSt). To further simplify the system, we focus on silicone oil mixtures where the higher surface tension species with a negligible evaporation rate is present in the system at a low volume fraction (5cSt ≤ 2%). With the aid of a dynamic fluid film interferometer, we experimentally observe thin film evolution at different concentrations [1]. At the start of each experiment, the glass dome is submerged in the binary liquid and the dome is subsequently raised till the apex of the dome has penetrated the initially flat oil-air interface. Throughout this process, a thin film is formed by the squeezing motion and evaporation drives the formation of concentration gradients across the curved thin film. Due to the established concentration gradient and the resulting solutal Marangoni flow, liquid is drawn from the bulk region towards the apex of the dome. We find, at concentrations lower than 0.15% (5cSt), the thin film benefits from the stabilizing effect of a nanoscopically thin barrier ring and the film apparently thickens axisymmetrically. At higher concentrations (5cSt > 0.3%), a mound forms in the apex region and at later times the mound discharges asymmetrically, thus picking a particular direction for discharge. The film develops thereafter in a complex, asymmetric fashion.

To further understand the mechanisms behind this instability, we have developed a 2D (i.e. non-axisymmetric) lubrication model that captures and explains the trends observed in the experiments. As the mound grows, the opposing forces of capillarity and Marangoni flow are both growing in magnitude, but the difference in their magnitudes is diminishing. When the system is subjected to an ambient disturbance, the disturbance grows till its magnitude can compete with the difference in the driving forces, leading to the mound discharge observed in the experiments. Further analysis of the problem shows that the system is linearly unstable, even at early times, to the lowest order non-axisymmetric mode. However, the instability growth rate is such that mound discharge appears only at later times.

[1] Rodríguez-Hakim, M., Barakat, J. M., Shi, X., Shaqfeh, E. S., & Fuller, G. G. (2019). Evaporation-driven solutocapillary flow of thin liquid films over curved substrates. Physical Review Fluids, 4(3), 034002.