Transient Solidification Dynamics of Molten Droplets: Impacts of Substrate Properties and Thermal Conditions

The way liquid droplets spread and behave after hitting solid surfaces is a complex process that has intrigued scientists for a long time. While it might seem straightforward at first glance, this phenomenon is anything but simple. It plays a vital role in many industrial fields, from thermal spraying and inkjet printing to advanced manufacturing techniques and even preventing ice formation on airplane surfaces. What makes it even more fascinating is how many factors come into play—fluid motion, heat transfer, material characteristics, and phase changes all work together in ways that can significantly affect the final result. When it comes to molten droplets, like paraffin wax, the picture gets even more complicated because solidification happens in real-time, adding another layer of complexity that researchers are still trying to fully grasp. One of the biggest challenges in studying how droplets behave is capturing what happens in those critical moments right after impact. The process of solidification starts almost instantly at the interface between the droplet and the surface, where there is a sharp temperature difference. This early-stage transformation has a huge impact on how the droplet spreads, recoils, and eventually settles into its final form. To make sense of it, researchers need to consider many variables—like how thermally conductive the surface is, how smooth it is, and what temperature the droplet starts at. While these aspects are key to understanding the behavior, much of the research so far has focused more on what the droplets look like after they solidify, leaving the initial, fleeting moments of transformation largely unexplored. Another limitation is the lack of tools to directly observe what happens where the droplet meets the surface. Many experiments rely on opaque surfaces, which block the view of the critical interface where solidification kicks off. On top of that, simulating these events using numerical models has proven difficult because of how tricky it is to capture the nuances of heat transfer, fluid dynamics, and phase change all happening at once.

New research paper published in International Journal of Heat and Mass Transfer  and conducted by Dr. Chao Kang, Mr. Ikki Ikeda and led by Professor Motoki Sakaguchi from the Department of Mechanical Engineering at the Tokyo Institute of Technology (currently Institute of Science Tokyo) tried to answer these questions. The researchers investigated how paraffin droplets behave when they hit solid surfaces and go through the rapid process of transient solidification. Using high-speed cameras, they captured the entire action from horizontal and bottom angles, giving them a detailed view of how the droplets spread, recoil, and solidify in real-time. They worked with three types of transparent substrates—polycarbonate, quartz glass, and sapphire glass—each selected for its unique thermal conductivity. These materials gave the team a way to explore how differences in heat transfer influence the behavior of the droplets upon impact.

One key part of the study involved testing how the temperatures of both the substrate and the droplets affected the outcomes. The droplets were heated to either 95°C or 123°C and dropped from the same height onto surfaces that were either kept at room temperature or heated to match the droplet’s temperature. The authors’ results showed a clear distinction between what happened under isothermal and non-isothermal conditions. According to the authors, when the temperatures of the droplet and the substrate were the same (isothermal conditions), the droplets spread evenly and eventually stabilized without much recoil. However, under non-isothermal conditions, where the substrate was cooler than the droplet, rapid solidification occurred at the interface. This caused the droplet’s spreading to be more limited and led to a noticeable recoil effect, especially on high-conductivity materials like sapphire glass.

One of the standout discoveries came from observing how solidification patterns changed depending on the substrate material and its temperature. On polycarbonate, which has low thermal conductivity, solidification began at the edges of the droplet and moved inward gradually. This gave the droplet more time to spread before solidification took over. On the other hand, sapphire glass, with its high thermal conductivity, triggered almost instant solidification across the entire bottom surface, resulting in less spreading and thicker, denser splats. The team also noticed that the droplet’s initial temperature played a big role, with hotter droplets forming wider, thinner splats due to their lower viscosity. Addiitoally, the researchers Used transparent substrates and were able to directly observe and measure solidification at the droplet’s base—something rarely done in previous studies. By tracking changes in grayscale values, they linked these shifts to the thickness of the solid layer. Their findings showed that solidification happened in just milliseconds and was heavily influenced by the heat transfer properties of the substrate and the temperature gap between the droplet and the surface. To top it off, numerical simulations backed up these results, accurately replicating the observed spreading and solidification dynamics.

In conclusion, Professor Motoki Sakaguchi and his colleagues have taken a complex topic—how molten paraffin droplets behave when they hit solid surfaces—and brought it to life with clarity and purpose. By focusing on the earliest, most fleeting moments of impact and solidification, they’ve shed light on processes that had previously gone unexplored. Their work doesn’t just answer questions; it opens new doors to understanding. What really makes this research stand out is its potential to change how industries approach droplet behavior. For fields like thermal spraying or additive manufacturing, where precision isn’t just important—it’s everything—this study has huge implications. Being able to predict and control how droplets spread and solidify could lead to stronger, more reliable coatings, better adhesion, and improved product quality. The insights about how material properties and temperature affect these dynamics offer something practical—real tools that engineers and designers can use to fine-tune their processes. And it’s not just about manufacturing. This research reaches into areas like surface engineering and even anti-icing technologies. The authors showed that high-thermal-conductivity materials can dramatically speed up solidification, creating thicker, more compact splats, while low-conductivity materials allow droplets to spread further before solidifying. These findings could inspire designs for surfaces tailored to specific needs. Imagine a coating that solidifies quickly for durability or a surface that resists ice formation in freezing conditions—this study lays the groundwork for both. What’s we really impressive is how the team combined experimental observation with advanced simulations. They didn’t just observe these processes; they measured and modeled them, creating a level of precision and depth that’s hard to achieve. The high-speed cameras captured the visible changes, while the simulations filled in the details that couldn’t be seen, like the exact thickness of the solidified layer. Together, this approach doesn’t just confirm what’s happening—it explains why and how it happens.