Direct Measurement and Modeling of Wrapping Layer on Lubricant-Infused Surfaces

By enabling an atomically smooth and chemically homogeneous interface, state-of-the-art lubricant-infused surfaces minimize contact line pinning, which directly translates to remarkable droplet mobility and ultralow drop friction. A unique feature of these surfaces is the formation of a wrapping layer─a nanometric lubricant film that encapsulates droplets. However, the mechanism that governs the formation of the wrapping oil layer and its thickness remains poorly understood to date. In this study, we develop and experimentally validate a theoretical modeling framework for the wrapping layer thickness by balancing two competing forces: curvature-induced Laplace pressure and van der Waals interaction-induced disjoining pressure. Using planar laser-induced fluorescence microscopy, we directly visualized and measured the wrapping layer thickness across a range of droplet radii, lubricant viscosities, and lubricant thicknesses used to impregnate the underlying textured substrate. Our results show that the wrapping layer thickness, which is insensitive to lubricant viscosity and initial thickness, scales with the droplet radius to the 1/3rd power. After lending credence to our analytical approach by validating model predictions with experiment, we estimated the volume of the wrapping layer using a simple, yet important, scaling argument. Moreover, we estimated the wetting ridge volume by capturing the steady-state shape of the oil meniscus that forms near the droplet base. Our analysis and theretical treatment show that the volume of oil in the wrapping layer is four orders of magnitude smaller than that of the wetting ridge, a result that points to the annular wetting ridge as the major source of lubricant depletion by moving droplets. The insights gained from this work improve the current understanding of wrapping layer dynamics and its impact on lubricant depletion.