Dropwise Condensation in Ambient on a Depleted Lubricant-Infused Surface

Durability of a lubricant-infused surface (LIS) is critical for heat transfer, especially in condensation-based applications. Although LIS promotes dropwise condensation, each departing droplet condensate acts as a lubricant-depleting agent due to the formation of wetting ridge and cloaking layer around the condensate, thus gradually leading to drop pinning on the underlying rough topography. Condensation heat transfer further deteriorates in the presence of non-condensable gases (NCGs) requiring special experimental arrangements to eliminate NCGs due to a decrease in the availability of nucleation sites. To address these issues while simultaneously improving heat-transfer performance of LIS in condensation-based systems, we report fabrication of both fresh LIS and a lubricant-depleted LIS using silicon porous nanochannel wicks as an underlying substrate. Strong capillarity in the nanochannels helps retain silicone oil (polydimethylsiloxane) on the surface even after it is severely depleted under tap water. The effect of oil viscosity was investigated for drop mobility and condensation heat transfer under ambient conditions, i.e., in the presence of NCGs. While fresh LIS prepared using 5 cSt silicone oil exhibited a low roll-off angle (∼1°) and excellent water drop (5 μL) sliding velocity ∼66 mm s–1, it underwent rapid depletion as compared to higher viscosity oils. Condensation performed on depleted nanochannel LIS with higher viscosity oil (50 cSt) resulted in a heat-transfer coefficient (HTC) of ∼2.33 kW m–2 K–1, which is a ∼162% improvement over flat Si-LIS (50 cSt). Such LIS promote fast drop shedding as is evident from the little change in the fraction of drops with diameter <500 μm from ∼98% to only ∼93% after 4 h of condensation. Improvement in HTC was also seen in condensation experiments conducted for 3 days where a steady HTC of ∼1.46 kW m–2 K–1 was achieved over the last 2 days. The ability of reported LIS to maintain long-term hydrophobicity and dropwise condensation will aid in designing condensation-based systems with improved heat-transfer performance.

immersed in acetone for 6 hours. This lift-off process created orthogonally connected ridges of sacrificial Cr & Cu. Then, 300 nm thick SiO2 film was deposited over patterned Cr & Cu layer by plasma enhanced chemical vapor deposition (PECVD). After depositing 300 nm thick SiO2, SPR 220-3 photo resist was used to obtain a ~ 3 µm coating on the wafer. After baking, GCA stepper was used to expose the sample using custom made reticle (~ 2 µm diameter holes at 10 µm pitch, exposure time 0.5 s) and executing required job file. It is important to note that alignment of reticle is very important while executing exposure such holes are exposed at the intersection of the ridges.
After hard bake and development wafer with exposed SiO2 (at ~ 2 µm diameter holes) undergoes dry etching followed by photoresist removal in hot bath and plasma strip resist. The wafer was immersed in Cr & Cu etchant to remove sacrificial Cr & Cu to form the nanochannels which are interconnected orthogonally and open to environment via pores (~ 2 µm holes). Wafer is cut in to required dimension of sample using dicing saw.

Note S2
In the FT-IR spectrum of nc-dep LIS ( Figure S2), the absorption peaks located at 2962 cm -1 and 2904 cm -1 are due to the asymmetric and symmetric stretching vibration of C-H in methyl and methylene groups present in silicone oil, respectively 1 and the peaks appeared at 1413 cm -1 and 666 cm -1 can be attributed to the bending vibration of C-H bonds 2 due to the remaining nonreacted precursors or the presence of adsorbed fats or contaminants on the surface of the material.
The peaks centered at 1259 cm -1 , 1085 cm -1 , and 1016 cm -1 can be related to the stretching vibration of Si-OH 3 and asymmetric and symmetric stretching vibration of Si-O-Si, respectively 4,5 . The absorption peak centered at 794 cm -1 is due to the bending vibration of the Si-O-Si bonds 6 .

Note S3
The velocity measurement was performed by analyzing the drop sliding frames recorded by the high-speed camera. To visualize the drop, a solution of sodium fluorescein was prepared (0.1 gm in 1 liter of deionized water) 7 and a custom written MATLAB algorithm was used to track the motion of water drop as shown in Figure S3. The images obtained from the high-speed camera were counter rotated by same angle as that of inclination of sample to make the drop motion appear horizontal during image processing. Then, after cropping out the required area in the image, it is converted into binary i.e., black & white image. This enabled easy tracking of the contour front of the drop as the white pixels on the drop would always have value 1. In Figure S3, P1 (point on drop front at the beginning of drop sliding) and P2 (point on drop front after time "t" of drop sliding) shows the location of front being tracked. The difference between pixel location along with calibrated pixel length (i.e., number of pixels in 1 mm denoted as "p") would give the distance travelled by the drop. Elapsed time (t) between frames was obtained from number of frames (nf) and captured frame rate (fps) of video. Velocity was obtained as, S3

Note S4
To capture the temperature variation at the outlet we conducted an experiment with 4 thermocouples instead of 1 thermocouple. Figure S6a shows the 4 thermocouples (T1-T4) inserted (1.5 cm from the cold plate) at different depths, and two more thermocouples (T5-T6, Figure S6b Figure S5. The tube inside cold plate is shown as dashed line in Figure S5. Condensation experiment was carried out with primary interest being the temperature readings at the outlet. Figure S6d-e show the variation of temperature recorded by all six thermocouples. The maximum difference between any two thermocouples among T1-T4 is < 2ºC. The temperature readings of T5 and T6 which would see some mixing due to sharp contraction show maximum difference < 2ºC. This maximum temperature difference of less than 2 o C is within the maximum error listed in the experiments (Table S2). Moreover, for all our experimental data and analysis (as in the manuscript), we used data from one thermocouple which was placed near the center of the outlet tube, which would underestimate (that too only by < 2ºC) the outlet temperature rather than overestimating it; thus, the results in our work are conservatively presented. Hence, we can conclude that temperature variation within the thermal boundary layer is insignificant for our experiments and analysis. In fact, similar arrangements of thermocouples has been reported in literature to measure the temperature [8][9][10] .

Note S5
Uncertainty related with temperature and humidity was taken as the standard deviation in data recorded during the condensation experiment. Condensation heat transfer coefficient (HTC) was calculated at each data point in temporal domain and related standard deviation in HTC is due to fluctuations in temperatures during experiments. The uncertainty calculation for condensation heat flux (q " ) is obtained using following equations:
Temperature collection rate during condensation on fresh porous nanochannel sample is given below:

Note S6
Drop size distribution for flat silicon surface is shown in Figure S7. It was found that percentage of drops having diameter < 250 µm at the start and towards the end of condensation experiment was ~ 41% and ~ 28% respectively. For drops having diameter < 500 µm, it was ~ 80% and ~ 60% respectively.

SUPPORTING FIGURES
Supporting Figure S1

Supporting Movie Captions
Movie S1 Description: Water jet shear depletion of nanochannels LIS.