Condensation of Satellite Droplets on Lubricant-Cloaked Droplets

Condensation on lubricant-infused micro- or nanotextured superhydrophobic surfaces exhibits remarkable heat transfer performance owing to the high condensation nucleation density and efficient condensate droplet removal. When a low surface tension lubricant is used, it can spread on the condensed droplet and “cloak” it. Here, we describe a previously unobserved condensation phenomenon of satellite droplet formation on lubricant-cloaked water droplets using environmental scanning electron microscopy. The presence of satellite droplets confirms the cloaking behavior of common lubricants on water such as Krytox oils. More interestingly, we have observed satellite droplets on BMIm ionic liquid-infused surfaces, which is unexpected because BMIm was used in previous reports as a lubricant to eliminate cloaking during water condensation. Our studies reveal that the cloaking of BMIm on water droplets is theoretically favorable due to the fast timescale spreading during initial condensation when compared to the long timescale required for dissolution of the lubricant in water. We utilize a novel characterization approach based on Raman spectroscopy to confirm the existence of cloaking lubricant films on water droplets residing on lubricant-infused surfaces. The selected lubricants include Krytox oil, ionic liquid, and dodecane, which have drastically different surface tensions and polarities. In addition, spreading dynamics of cloaking and noncloaking lubricants on water droplets show that ionic liquid has the capability to mobilize water droplets spontaneously owing to cloaking and its relatively high surface tension. Our studies not only elucidate the physics governing cloaking and satellite droplet condensation phenomena at micro- and macroscales but also reveal a subset of previously unobserved lubricant–water interfacial interactions for a large variety of applications.


S1 Condensation of satellite droplets captured with optical microscopy
To ensure the observed satellite droplet formation in ESEM is not due to interaction between the electron beam and lubricant, we conducted optical microscopy experiments using a customized top-view optical light microscopy setup 1,2 . Top view imaging was performed with a 10X (TU Plan Fluor EPI, Nikon) objective, capturing images at 5 s intervals. 1" x 1" flat coupon samples were horizontally mounted to a cold stage (TP104SC-mK2000A, Instec) and cooled to the test temperature of Tw = 2 ± 0.5 °C, in a laboratory environment having air temperature Tair = 22 ± 0.5 °C and relative humidity ϕ = 40 ± 1% (Roscid Technologies, RO120). Illumination was supplied by an LED light source (SOLA SM II Light Engine, Lumencor). The LED light source was specifically chosen for its high-intensity, low-power consumption (2.5 W) and narrow spectral range (380−680 nm) in order to minimize heat generation at the surface due to light absorption. Furthermore, by manually reducing the condenser aperture diaphragm opening size and increasing the camera exposure time, we were able to minimize the amount of light energy needed for S-2 illumination and hence minimize local heating effects during condensation experiments. Figure S1   Solubility. As BMIm is slightly soluble in water, it is possible that the interfacial tension between BMIm and water would change over time due to the dissolution. This may result in non-cloaking of water droplet on BMIm-infused surfaces. Here, to confirm that time scale of dissolution is much larger than that of lubricant spreading, we measured the BMIm-water interfacial tension over time. By using the same pendent droplet method described before, one BMIm droplet is dispensed in a water reservoir and kept undisturbed.
The interfacial tension is measured every 2 mins for a period of 40 mins, as shown in Figure     To evaluate the thickness of cloaking films, we first measure the thickness of the focal plane corresponding to the depth resolution of Raman spectrometer. The focal depth is measured by z-scanning the characteristic intensity of ultra clean silicon wafer around 520 cm -1 . Figure S6 shows the signal intensity profile collected by using a 0.55 NA, 50× objective. The full width at half-height is around 5 μm, which provides us information about the focal depth or depth resolution of Raman system 10 . S-7

S4 Prediction of Surface Temperature
In order to characterize the nucleation processes for satellite droplets and mother droplets, the temperature at different interfaces should be predicted, especially for the infusing lubricant-vapor and cloaking lubricant-vapor interfaces. Growth dynamics of condensate droplets on flat and micro/nano-textured superhydrophobic surfaces has been studied with a thermal resistance model previously 11,12 . This model considers thermal resistances of all contributing components from saturated vapor through the droplets to the cold condensing surface. In this work, the droplets are cloaked with a thin lubricant oil layer, which will alter the total thermal resistance and thus affect growth rate of the droplets. The original thermal resistance model is extended with additional terms to take into account of the cloaking lubricant layer. Figure S7 shows a schematic of one single cloaked water droplet on lubricant-infused surface with regular pillars and the respective thermal resistance diagram. The water droplet has a radius of , which is dependent on time S-8 t. The solid condensing surface is textured with pillars of dimensions: diameter d, height h, spacing l and coated with hydrophobic coating with thickness of . Thickness of the infusing layer on the solid surface is , , while the cloaking lubricant layer thickness is represented by , . The radius of cloaked water droplet , = + , , which is approximated to as the thickness cloaking layer is much smaller than radius of the droplet. Temperatures at the saturated vapor , vapor-cloaking lubricant interface ,1 , cloaking lubricant-water interface ,2 , droplet base , coated pillar top ,1 , pillar top below the coating , coated spacing between pillars ,2 , and the cold surface are all as illustrated in Figure S7  Given surface temperature , saturation temperature and apparent contact angle measured in condensation experiment, the heat transfer rate is predicted with Eq. (S3) for various droplet size. Then, by using the definition of thermal resistances in Eq. (S5-S8), we can calculate the temperature at different interfaces, including ,1 , ,2 , and . The predicted results are presented in Fig. 6d in the main manuscript.

S5 Prediction of Nucleation Energy Barrier
To analytically understand the nucleation process of the satellite droplets, the classical nucleation theory  Figure 6e of the main manuscript. Apparently, nucleation energy barrier on BMIm-infused surface is lower that on the Krytox-infused surface. Moreover, the energy barrier increases with condensing surface temperature. As temperature at infusing lubricant-vapor interface is always lower than that at S-10 cloaking lubricant-vapor interface, droplet nucleation happens preferentially at the infusing lubricant-vapor interface and nucleation of satellite droplets starts after the infusing lubricant-vapor interface is fully occupied by mother condensates.

S6 Spreading dynamics of cloaking and non-cloaking lubricants on water droplets
Spreading dynamics of Krytox, BMIm and Dodecane lubricants on water droplets are shown in Fig. S8.