(518f) Evaporation-Driven Soluto-Capillary Flow of Thin Liquid Films over Curved Substrates

Shaqfeh, E. S. G., Stanford University
Rodriguez-Hakim, M., Stanford University
Barakat, J. M., Stanford University
Shi, X., Stanford University
Fuller, G. G., Stanford University
Soluto-capillary Marangoni flows arise when concentration inhomogeneities of chemical species in solution create gradients in surface tension. These flows are prevalent in foam and emulsion products, biological systems, and coating processes. Understanding how these flows couple to other physical processes, such as evaporation- and pressure-driven flows, has both fundamental and practical value. In the coating application, for instance, evaporation of one or more volatile species in a multicomponent liquid induces spatial variations in both film thickness and species concentration, which can create defects in the final product. Previous theoretical and experimental work has shown the presence and basic mechanism of evaporation-driven solute-capillary flows of binary liquid mixtures in inclined, planar thin films. In this geometry, pressure gradients are suppressed and solute-capillary flows are observed at (non-volatile) solute volume fractions ranging from 2-50%. However, recent experiments with the Dynamic Fluid-Film Interferometer (DFI) have shown the presence of solute-capillary flows in thin films (thicknesses ranging from 50 nm to hundreds of microns) with solute fractions as low as 0.01% over curved (spherical) substrates. In this geometry, additional pressure gradients arise due to spatial variations in film thickness and surface curvature. In particular, conjoining pressure induced by London van der Waals forces can supply a mechanism to stabilize very thin films (tens of nanometers thick), which in turn can sustain solutocapillary flow at low (non-volatile) solute volume fraction. The purpose of our work is to utilize both experiment and theory in order to investigate the synergistic action of evaporation and conjoining pressure in creating and sustaining long-lived solute-capillary flows in thin films over a wide range of conditions — in particular, by varying the solvent volatility and the solute concentration.

The DFI is used to create thin liquid films sandwiched between a spherical solid substrate and an initially planar free surface. Experiments are carried out with binary mixtures of low molecular weight silicone oils and a hemispherical fused-silica substrate. Additional experiments were also performed using bubbles, to show the influence of a slip surface on film dynamics. The apparatus can capture the spatiotemporal evolution of the liquid film at thicknesses ranging from hundreds of nanometers to a few micrometers. We are able to examine the interplay between the rate of evaporation and the initial solute concentration. However, experimental measurements are not able to convey information regarding local surface species concentration and how chemical properties at the solid-fluid interface affect the stability and propagation of flow. Thus, we take advantage of the lubrication approximation to develop a thin-film theory that can simultaneously describe fluid flow and species concentration. The coupled (axisymmetric) transport of fluid and solute is directly correlated to the kinematic and dynamic conditions at the bounding free surface and to the chemical properties at the solid-liquid interface. The nonlinear evolution equations for the film height and species concentration are numerically solved and directly compared to experimental results, yielding a better understanding of the the relative influence of evaporation and Marangoni stresses and of the conditions where conjoining pressure allows for the formation of stable nanoscopic films.

It is shown that at intermediate solute concentration, a viscous mound forms at the apex of the spherical substrate and grows in height over time. The apparent contact line of this mound is stabilized by a conjoining pressure, and flow into the mound is driven by Marangoni stresses. At low solute concentrations, the film thins to a nanoscopic thickness set by the length scale of interaction via London van der Waals forces. At high solute concentrations, the film thickens indiscriminately in space and a very weak flow is induced by capillary pressure gradients and solute concentration gradients. Evaporation (i.e., solvent volatility) drives the rate at which these processes occur in tandem with Marangoni stresses, and it is shown that the rate of film thickening scales linearly with the total evaporative volume flux per unit area of free surface.

If time permits, results pertinent to the bubble system (both experiment and theory) will be presented. It is shown that the slip surface accelerates the competition between Marangoni and pressure-driven effects, resulting in apparent oscillations and symmetry breaking.