Maximum spreading diameter of a water droplet after impact on a hot surface beyond Leidenfrost temperature

The impact of liquid droplets on heated surfaces are relevance across a range of applications. The maximum spreading diameter of water droplet during impact on hot surface was experimentally studied. The surface was made of aluminium. The diameter and height of the aluminium block was 70.0 mm and 30.0 mm, respectively. During experiment, the test surface was heated beyond Leidenfrost temperature. A high-speed video camera was used to capture the droplet images from the first impact until the droplet reached maximum spreading condition. The frame rate was set to be 2,000 fps. Distilled water was used as the test liquid. The impact height was set to be about 65.0 mm. From the high-speed images analysis, the droplet diameter was found to be approximately 4.5 mm. The measured droplet maximum spreading diameters were found to have a good agreement with theoretical calculation.


Introduction
Boiling heat transfer plays a crucial role in various thermal and energy industries, including boiler systems, power plants [1][2][3], spray cooling [4,5], and chillers.Understanding the droplet impact and evaporation mechanisms in boiling heat transfer is of paramount importance for enhancing cooling methods and heat absorption efficiency.High-speed visualization systems, employing high-speed cameras, are commonly used to support experimental investigations.When a water droplet impacts an extremely hot surface, it undergoes a transition from nucleate boiling to transition boiling and finally enters a film boiling regimes [6][7][8].Upon the liquid-solid contact in the film boiling regime, no dispersion occurs on the hot surface, and a vapor blanket forms as the droplet touches the surface [9].This vapor blanket acts as an insulation, preventing heat transfer from the surface to the liquid, leading to the Leidenfrost phenomena [10][11][12].Consequently, the cooling performance significantly decreases compared to nucleate boiling conditions.To address this, further research is required to comprehend this intricate and unique boiling phenomenon.By increasing the Leidenfrost temperature, it is possible to enhance the cooling performance and heat absorption capabilities of materials and liquids.Numerous researchers have conducted detailed studies on droplet behaviour by utilizing high-speed video cameras, investigating critical parameters such as droplet shape, maximum spreading, contact angle, droplet size, wetting behaviour, evaporation time, boundary conditions, and boiling explosion, among others [13][14][15][16][17][18][19][20][21][22][23][24].These studies contribute to the understanding of droplet impact in boiling heat transfer processes.
Illias et al. [13], in their experimental study, have explored droplet impact beyond the Leidenfrost temperature, specifically focusing on the correlation between the residence time of a water droplet and the resulting bouncing phenomena.The experiment involved employing a mirror-polished aluminium surface and degassed, distilled water droplets with an approximate diameter of 4.0 mm and liquid temperature of 16.0°C.The impact velocity of the droplets was 1.129 m/s, and the experiment was recorded at 10,000 fps using a high-speed video camera.The findings indicated a close agreement between the experimentally measured residence time and theoretical calculations.In a related study, Takata et al. [22] conducted experimental investigations to examine the behaviour of small water droplets impacting a hot surface and the subsequent water spray cooling using a micro-jet dispenser.The researchers measured parameters such as solid contact time, maximum spreading ratio on the hot surface, and surface temperature cooling time.Their study demonstrated that the maximum spreading ratio increased with the initial droplet diameter and that the impinging velocity amplified the effect of the initial droplet diameter.
The impact dynamics of liquid droplets on heated surfaces in boiling heat transfer have significant implications for enhancing cooling methods and heat absorption efficiency in thermal and energy industries.The efficiency of heat transfer and cooling performance influenced by factors like the extent of droplet maximum spreading and calls for further research in understanding these phenomena.The present research experimentally investigates the maximum spreading diameter of a distilled water droplet upon impact on a heated aluminium surface beyond Leidenfrost temperature.The measured maximum spreading diameters were then compared with the value from analytical calculation.This research contributes essential insights into the dynamics of droplet impact on hot surfaces beyond Leidenfrost temperature and validates the agreement between experimental and theoretical predictions.

Experimental apparatus and procedure
Figure 1 depicts the experimental setup employed in this study.It comprises of a heating & lighting systems, manual droplet dispenser, and high-speed visualization arrangement.The high-speed camera utilized had a frame rate of approximately 2,000 fps.Four type K thermocouples were strategically placed to measure surface temperature, Tw (CH1 and CH2), water temperature (CH3), and room temperature (CH4).These thermocouples were directly connected to a thermal sensor (Brand: Oakton, Model: WD-69200-00) with a temperature range spanning from -250°C up to 1800°C.A hot plate (Labmart HT-1003) served as the heat source for the test material.The test material is an aluminium cylinder with a diameter and height of 70.0 mm and 30.0 mm, respectively.Two 2.0 mm diameter and 10.0 mm depth holes were drilled on the top surface of the cylinder in order to insert thermocouples (CH1 and CH2) for surface temperature measurement.These holes were carefully prepared using CNC milling techniques.An approximately 4.5 mm diameter droplet was released at approximately 65.0 mm above a solid surface.This height was chosen to ensure that the droplet remains intact during impact without breaking up.The impact velocity of the droplet can be estimated from drop height ( = 2( −  )).However, the actual impact velocity determined through high-speed images analysis was found to be only about 80% of theoretical value.This is due to the droplet size in the experiment was relatively large which cause the droplet shape to deform.This deformation gives rise to a notable augmentation in the drag coefficient, subsequently inducing a reduction in the terminal velocity exhibited by the droplet [25].The droplet dispenser was attached to a retort stand with an adjustable arm, enabling precise positioning at the centre of the impact point during droplet dispersion.In order to avoid radiation effect from the heated surface, the droplet dispenser was positioned above the heated surface only during the dispensing process, otherwise it will be kept away from the heated surface by adjusting the arm.For clarity, the experimental procedure closely resembles the setups reported elsewhere [14,15].

Results and discussion
The first manifestation of Leidenfrost effect was observed at aluminium surface temperature of 178°C.Figure 2 shows the representative water droplet images (at different times) during impact until the droplet attained the maximum spreading state on a hot aluminium surface beyond Leidenfrost temperature.The number under the images is the elapsed time after the droplet collision.It can be seen that, the droplet was spread radially to a maximum spreading diameter.
The temporal evolution of droplet spreading diameter is presented in Figure 3 for various aluminium surface temperatures beyond Leidenfrost temperature.It can be seen that, the droplet experienced a rapid diameter growth immediately after the impact (0 < t < 5ms).This phenomenon was visually ascertainable through the sequence of images presented in Figure 2, spanning from (a) to (f).The initial spreading exhibited by the droplets is primarily governed by the inertia and kinetic energy of the falling droplet.As the droplet make contacts with the solid surface, its momentum causes it to rapidly deform and spread radially outward.As time progresses, the spreading rate gradually decreases (5ms < t < 10ms).This phenomenon can be observed in Figure 2 (g) to (i).The reduction in spreading velocity can be attributed to the effect of viscosity, which resist the water movement, and surface tension forces, which strive to minimize the droplet's diameter.The interplay between these forces leading to a relatively constant spreading rate during this intermediate stage.
Finally, at t = 10ms, regardless of a surface temperature, all the droplet reaches its maximum spreading diameter.It shows that the maximum spreading time is independent to the aluminium surface temperature.At this point, the spreading forces (inertia, viscous, and surface tension) have reached a delicate balance.The droplet fully spreads out and forms a thin film over the solid surface, signifying the completion of the spreading process.The maximum spreading diameter was measured as 14.62 mm, 14.38 mm and 14.33 mm for aluminium surface temperature of 179°C, 183°C and 185°C, respectively.These maximum spreading diameters agreed well with theorical value calculated from Eq. ( 1) by Akao et al. [26] with maximum discrepancy of 5.28%.
where  is Weber number and  is the droplet diameter just before the impact.

Conclusions
This experimental study aimed to investigate the maximum spreading diameter of a water droplet upon impact on a hot aluminium surface.The primary focus was to compare the results obtained from experimental work with theoretical calculations.Data analysis was conducted using the high-speed images captured during the experimental procedure.The maximum spreading diameters were found to be approximately 14.62 mm, 14.38 mm, and 14.33 mm for aluminium surface temperature of 179.0°C, 183.0°C and 185.0°C, respectively.Overall, the results revealed a good agreement between the maximum spreading diameter obtained from theoretical calculations and the experimental measurements.On top of that, it also can be concluded that the effect of surface temperature on the maximum spreading diameter of a droplet upon impact on a heated aluminium surface in film boiling regime is miniscule.

Figure 1 :
Figure 1: Schematic diagram of the experimental setup.

Figure 2 :
Figure 2: Sequential images of droplet impacting on aluminium surface at Tw = 179°C.