Heat conduction is vital for droplet dynamics


For driving in the rain, it’s preferable that the raindrops roll or bounce off the windshield instead of coating it or even freezing. A team of engineers in the McKelvey School of Engineering at Washington University in St. Louis has found that conduction of heat plays a larger role than previously thought in the dynamics of droplets on smooth surfaces that repel water.

Patricia Weisensee, assistant professor of mechanical engineering & materials science, and Junhui Li, a doctoral student in her lab, made the finding after using high-speed imaging methods to study a microscopic entrapped bubble that forms when droplets of water hit a heated, smooth, water-repellant surface. Results of the research are published in the Experimental Thermal and Fluid Science. The bubble only a few hundred microns in size forms inside a water droplet from absorbing the air underneath it as it begins to lift off from the surface.

The investigators successfully created capillary waves on the droplet, because as the droplet impacts, it compresses, and that sends a shockwave through the droplet and creates a doughnut-shaped droplet with the air bubble entrapped in the middle. Weisensee and Li tested water droplets on three heated surfaces: Teflon and two materials that have similar surface chemistry PDMS, a biocompatible material; and HTMS, a hydrophobic silane-based monolayer coating. Using synchronized high-speed optical and high-speed infrared imaging, they found that the amount of heat transferred from the smooth surface to the water droplet increased with increased spreading velocity. In addition, they found that the bubble changed in size and shape as the temperature of the surface increased. Interestingly, during the retraction of the droplet, the total heat transfer was reduced by 5.6% and 7.1% at surface temperatures of 50˚C and 65˚C, respectively, as the bubble reduced the total liquid-solid interface area. Overall, this entire process lasts only a few milliseconds, but can have a profound influence on the cooling efficiency and droplet dynamics of these systems. They found that thermal conduction was the most prominent form of heat transfer during droplet impact over convection or evaporation.

In addition, they tested the droplets on a rough surface. The droplets showed a smaller spreading area due to enhanced friction, a smaller heat transfer area, and consequently, a lower rate of heat transfer, which would ultimately lower the efficiency of for example spray cooling processes.

Though they used heated surfaces for this particular study, our findings also have implications for other systems where you have droplets impacting a surface, such as a windshield, an airplane wing or a wind turbine blade. For example, in cold conditions, you don’t want the droplets to stay there and freeze. Lifting off is important so that you don’t flood a surface or accumulate a lot of liquid on the surface. So you need know the interplay of droplet dynamics and heat transfer.

The authors investigated low Weber number droplet impact on heated hydrophobic surfaces. Using synchronized high-speed optical and infrared (IR) imaging, they correlated the droplet dynamics to the spatial distribution of the solid-liquid interfacial temperature, heat flux, and the total heat transfer to the droplet. The total transferred heat of a completely rebounding droplet was also modeled analytically. Denoting the drop diameter and impact velocity as D and v, they also found that the total transferred heat Q scales as D1.25v, which is validated using experiments.

A unique feature of low-We droplet impact on non-wetting surfaces is the formation of a sub-millimetric entrapped bubble that forms during receding. The substrate temperature in the bubble region is significantly higher than the surrounding area due to the low thermal conductivity of air. Right after the bubble forms, the local heat flux remains stable at the inner contact line (bubble contact line), but decreases at the retracting primary outer contact line. As a result, the local heat flux at the inner contact line becomes increasingly important as the droplet recedes. Nonetheless, the overall heat transfer is reduced by 5.6% and 7.1% at surface temperatures of 50 ˚C and 65 ˚C, respectively, as the entrapped bubble reduces the total liquid-solid interface area. The influence of surface roughness on the heat transfer is also quantified. Droplets on the rough surface have a smaller maximum spreading diameter, leading to a smaller heat transfer area and lower heat transfer rate. Moreover, the average heat flux on the rough surface is also lower compared to the smooth surface, indicating a larger interfacial thermal resistance of the rough surface. Overall, the findings by Dr. Li and Professor Weisensee highlight the dominance of thermal conduction (as compared to convection or evaporation) as the prominent mode of heat transfer during droplet impact.

Heat conduction is vital for droplet dynamics - Advances in Engineering

About the author

Dr. Weisensee joined the faculty of Mechanical Engineering & Materials Science at WashU in January of 2017. She earned her PhD in Mechanical Engineering from University of Illinois at Urbana-Champaign in 2016. She received a Diplom-Ingenieur in Mechanical Engineering from TU Munich in 2013 and also holds a M.S. in Materials Sciences from University of Illinois, Urbana-Champaign (2011). For her work on condensing steam bubbles in sub-cooled flow, Patty received the Siemens Energy Award 2014. Patty is an alumna of the German National Academic Foundation.


Junhui Li, Patricia, B .Weisensee. Low Weber number droplet impact on heated hydrophobic surfaces. Experimental Thermal and Fluid Science. Volume 130, 1 January 2022, 110503.

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