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

Abstract

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.

Keywords: Laplace pressure; lubricant-impregnated surfaces (LIS); oil depletion; planar laser-induced fluorescence (PLIF); slippery liquid-infused porous surfacers (SLIPS); van der Waals forces, disjoining pressure; wetting ridge; wrapping layer.

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Wrapping layer dynamics. Wrapping layer (red) encapsulates the water droplet (blue) due to the large surface tension of water (≈72.4 dyn/cm). The schematic diagram shows the various interfacial forces (γ_ij) involved in the droplet and wrapping layer dynamics by noting the oil–water (γ_wo), oil–air (γ_oa), and water–air (γ_wa) interfaces with arrows. The balance between the interfacial forces, which is described using the oil-on-water spreading coefficient (S _ow), determines the presence (S _ow > 0) or absence (S _ow < 0) of the wrapping layer that encapsulates the droplet.

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Wrapping layer visualization. (a) Experimental setup for wrapping layer visualization includes a 532 nm laser beam, cylindrical lens, high-reflectance mirror at 45°, long-pass filter, and an sCMOS camera. The laser beam is directed through the cylindrical lens and reflects off a mirror before passing through the transparent substrate. (b) Excitation by 532 nm laser of the Nile Red dye in the oil, causing it to emit light at 636 nm. The emission from the excited Nile Red molecules is passed through a 532 nm long-pass filter to remove scattered laser light before it reaches the sensor/detector in the sCMOS camera. (c) Schematic representation of the excitation (532 nm) and emission (636 nm) signals from a fluorescently labeled silicone oil using Nile Red.

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PLIF visualization. (a) Time-averaged and background-subtracted PLIF image of a water droplet (radius, 1.0 mm) resting on a silicone oil-impregnated glass substrate coated with nanocolloids. The bright strip at the top of the droplet indicates the wrapping layer. The droplet radius was determined by using a circle fit via a MATLAB custom script. (b) PLIF intensity (ξ) image highlighting the wrapping lubricant layer and corrected PLIF image, shifted to align the wrapping oil film for uniform analysis and accurate thickness measurement. (c) Histogram of the film thickness measurement with a Gaussian kernel density estimate (KDE). The analysis shows that the average wrapping layer thickness is ≈50 nm. (d) Intensity profile across the region of interest, showing the contributions from the line-spread function (LSF, shaded red) and the background (BG, shaded blue). The area of the red-shaded region is proportional to the total oil film thickness.

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Wrapping layer thickness. (a) Time-average wrapping layer thickness (δ) as a function of droplet radius (R). The experimental data show that the wrapping layer thickness does not depend on the lubricant viscosity. (b) Wrapping layer thickness as a function of lubricant film thickness. Wrapping layer thickness does not depend on the initial lubricant layer thickness that is used for impregnating the underlying nanocolloid coated glass slide. Error bars represent one standard deviation for repeated experiments.

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Wetting ridge model. (a) Schematic of a droplet residing on a lubricant-infused surface. The shape of the droplet and wetting ridge is approximated by fitting circles along the oil–air and water–air interfaces. The radii of the droplet and wetting ridge are denoted by R and R _w, respectively. The inner radius of the wetting ridge from the droplet side is denoted by R _in, and the horizontal projection distance from the wetting ridge center to the droplet base is denoted by R _Q. The point below the wetting ridge center that lies on the lubricant–air interface is denoted by P. (b) Right triangle that forms when joining the center of the droplet (O) with the center of the wetting ridge (O ₁) and point P. This is used as a basis for estimating the wetting ridge volume (Ω_w).