Besides being a common natural phenomenon, droplet impingement has been considered a topic of immense interest in numerous industrial and technological applications, including but not limited to spray cooling, fire suppression systems containing sprinklers, cooling of turbine blades, fuel-air interaction in internal combustion engines, and cooling towers [1][2][3][4][5][6][7][8][9]. More recently, with the increase in power density, the microelectronic industries require cooling technologies with high heat removal capacity, where spray cooling has emerged as an effective technique with its outstanding capability of retaining uniform cooling temperature distribution throughout the heat flux surface [3,10]. Studying hydrodynamics and local heat transfer for a single droplet impingement on a heated solid wall is essential to enhance a deeper understanding of the spray cooling technique and maximize overall effectiveness [2,6,9,11]. Despite its ubiquity across natural and manmade events as outlined above, studying droplet impingement on a heated wall is not trivial as it is a complex phenomenon involving mass, momentum, and heat transfer interactions [1,2]. The characteristics of the droplet and heated surface interactions mainly depend on the physical properties of liquid, substrate properties, impact velocity, impact diameter, and surface temperature [2,5,6]. Droplet impact on a heated surface and subsequent evaporation comprises several physical phenomena that requires researchers to investigate from both heat transfer and hydrodynamic perspectives. Preceding studies have identified five distinct characteristic behaviors: completely wet, wet film boiling, transition, dry rebound, and satellite dry rebound [2,12]. When the surface temperature is lower than the saturation temperature of the liquid or insufficient to nucleate bubbles, the droplet spreads on the surface after impact and adheres to the surface throughout the evaporation process; this behavior is referred to as the completely wet/deposition impact behavior [2,12]. The expansion of the droplet upon impact on a solid wall refers to the spreading regime, with droplet impact velocity and surface wettability playing the most crucial role [13,14]. After reaching the maximum spreading diameter, the liquid's surface tension initiates retraction, known as the receding regime. The liquid surface tension, surface shape, and wall temperature greatly influence the receding regime of an impacting droplet [15]. From a heat transfer perspective, surface temperature plays the most crucial role in influencing the hydrodynamics and heat transfer phenomena involved with the impingement and subsequent evaporation [6,11]. Four distinct behaviors have been identified depending on the surface temperature and duration of evaporation of a single droplet on a heated surface: film evaporation, nucleate boiling, transition boiling, and film boiling [2,16]. Film evaporation occurs when a droplet impacts a solid wall having a surface temperature below the saturation temperature of the liquid or even if the surface temperature exceeds the saturation point but is still inadequate to nucleate vapor bubbles [2,15,17]. A comprehensive review by Liang et al. [2] of heat transfer mechanisms and hydrodynamics during droplet impingement on heated walls denoted that the overall heat transfer during the process strongly depends on the magnitude of surface temperature relative to the saturation temperature of the liquid. Other key factors that influence the droplet/surface interactions are impact velocity, impact diameter, and the physical properties of the liquid [2]. A seminal experimental work on droplet impingement heat transfer by Bernardin et al. [18] revealed Applied Thermal Engineering 248 (2024) 123152 that the surface temperature and spreading characteristics of the droplet are the two most significant parameters that influence the overall heat transfer mechanisms, again highlighting the need to study impacting droplet phenomena from a multi-physics approach. Experimental and numerical studies by Gholijani et al., [6,9], have demonstrated that the impact velocity of a droplet also significantly influences the heat transfer that occurs during the impingement. These studies have revealed that the higher impact velocities enable higher heat transfer due to the higher maximum spreading diameter, which causes higher temperature differences at the solid-liquid interface.
In recent studies, researchers have employed modern techniques such as high-speed imaging, interferometry, and total internal reflection schemes to thoroughly investigate the hydrodynamics of the impinged droplet, including the impact and spreading characteristics, to establish a correlation with the local heat transfer mechanism [12,[19][20][21]. Experimental investigations and numerical simulations on spreading behavior [8,22] have demonstrated that the overall heat transfer process due to droplet impingement comprised three subsequent segments: droplet spreading, receding, and sessile droplet evaporation. It is worth mentioning that experimental investigations [23,24] have deduced the three-phase contact line or moving contact line (MCL) as the region with the highest heat transfer during droplet impact and evaporation on a heated surface. Our recent work on sessile droplet evaporation [25] conclusively proved this via independent microscale measurements of surface temperature and contact line movement. An experimental work by Lee et al. [26] combining MEMS device and high-speed imaging denoted that the maximum heat transfer occurs at the droplet spreading phase right after the impact, which occurs because of the maximum temperature difference between the cold liquid and the solid heated substrate.
Although there have been numerous experimental and numerical studies conducted in literature to explore hydrodynamics and heat transfer mechanisms during droplet impingement, the number of studies focused on measuring the microscopic thermo-fluid phenomena near the three-phase contact line is limited, specifically correlating the heat transfer data to the interfacial behavior of the impacted droplets. Due to its complex nature, when it comes to investigating phase-change heat transfer at the microscale, it is essential to correlate the interdependence of heat transfer mechanisms with dynamic phase interface behavior, requiring more sophisticated and multifaceted sensing schemes. Moreover, there are only a few comprehensive studies in the literature that focus on studying the influence of significant parameters such as surface temperature and impact velocity as well as denoting the specific contribution of the heat transfer regimes like conduction, convection, and surface evaporation during droplet impingement and subsequent evaporation. Quantifying and differentiating the distinct heat transfer regimes, their transition, overall magnitude, and dependence on the surface temperature and impact velocity is another pressing need for improving heat transfer models, optimizing droplet surface interactions, and enhancing overall effectiveness. Previous studies have mainly focused on measuring heat transfer dynamics and often used external equipment such as high-speed cameras and optical image processing to evaluate interfacial behavior. These techniques' macroscopic spatial resolution and visibility, i.e., line of sight and viewing angle, often hamper precise detection of the location and temperature gradient in the MCL region. Our current study addresses these research needs by employing a custom-designed MEMS device for independent, real-time, minimally invasive temperature measurements and simultaneous microscale tracking of the MCL during droplet impingement and subsequent evaporation.
To the best of the authors' knowledge, there has been no investigation so far that combines the exploration of various heat transfer regimes occurring during droplet impingement and subsequent evaporation, along with examining the impact of influential parameters such as impact velocity and surface temperature for subcooled impinging droplets. In this study, the impinging droplets have been experimentally investigated via a custom-designed MEMS device to explore the interdependence of underlying heat transfer mechanisms at the three-phase contact line region with the simultaneous tracking of the phase interface behavior. Apart from investigating the effect of impact velocity and surface temperature for subcooled impinging droplets, this work mainly focused on discerning the specific contribution of conduction, convection, and surface evaporation throughout the process. The findings of this study regarding the transition from initial heat conduction to quasisteady surface evaporation and effective heat transfer rates associated with these can lead to more accurate models for phase-change heat transfer processes and maximize overall effectiveness. Additionally, the capability to track the MCL behavior and temperature measurements simultaneously at the microscale in real-time with a minimally invasive Applied Thermal Engineering 248 (2024) 123152 device used in this work can pave the way for new possibilities in thermal management and process control in high-precision manufacturing and electronics cooling.
To date, most of the research in this field has employed infrared thermography or macroscopic temperature sensing probes to measure the temperature distribution due to the impact and the subsequent spreading and receding of the impacted droplet on a heated wall. Although infrared thermography is a widely used technique in literature, it is only applicable for measuring temperature distribution in places where optical access to the surface is available. The limitation of resolution of other macroscopic temperature sensing probes and wavelength diffraction limit of infrared thermography often restricts their applicability in microscale temperature measurement. However, all these methods' knowledge of temperature distribution alone does not provide critical insights into the interdependence of phase-interface dynamics and heat transfer mechanism on a microscale. Thus, it requires a sensing scheme for microscale tracking of the MCL to unlock a meaningful correlation between the phase interface and the heat transfer mechanisms involved in dynamic phase-change heat transfer processes. When it comes to tracking the location of the MCL, most of the previous works employed high-speed optical imaging and postprocessing of infrared images. These techniques usually infer the MCL as the region coinciding with local temperature minimum and high heat flux values. However, these methods have limited accuracy due to their macroscopic spatial resolution and visibility, which is restricted by the line of sight and viewing angle, making it difficult to detect the exact location and temperature gradient in the MCL region. In order to overcome these barriers and reveal new insights, a composite MEMS device was utilized in this work to measure the temperature changes and monitor the location of the MCL of the droplet throughout the heat transfer process simultaneously on the microscale. This microdevice also contains a thin-film resistance heater to provide desired surface temperature, which makes it an independent experimental setup for investigating phase-change heat transfer processes.
Fig. 1 shows the laser microscopic images of the composite microdevice employed for investigating the heat transfer process due to droplet impingement. As the cross-sectional diagram in Fig. 1(d) shows, this microdevice consists of three metal layers, where a thin polyimide layer provides electrical insulation between each two consecutive metal layers. This microdevice adopted a commercially available silicon wafer with a PECVD grown 2 µm thick silicon nitride on top as the starting substrate. The initial metal layer deposited on the starting substrate acts as a thin film resistance heater to achieve the desired surface temperature. A series of resistance temperature detectors (RTD) was deposited as the second metal layer on top of the first insulation layer of polyimide. The RTDs provided temperature distributions underneath the impacted droplet, where the minimum spatial separation between two consecutive RTDs is 20 µm. A 1.2 µm deposited thin polyimide film served as the second insulation layer that separated the RTDs from the capacitance sensors and provided electrical insulation between the top two metal layers of the microdevice.
An array of capacitance microsensors based on interdigitated electrodes (IDEs) was the microdevice's third and final metal layer. These IDE-based microsensors detected droplets and kept track of the moving contact line throughout the experiment, as described in more detail within our previous works [27,28]. Finally, a 500 nm thin polyimide layer was deposited as the topmost protective coating, acting as the solid heated wall during droplet impingement. The sensing zone of the microdevice spans over a region of 1500 µm.
We followed a naming convention for the RTDs, and IDE-based capacitance sensors of the microdevice. According to Fig. 1, the RTDs and IDEs located on the right and left side of the microdevice's center are labeled with "R" and "L," respectively, after their corresponding number, where "1″ refers to the one nearest to the center and "14″ indicates the farthest from the center. To illustrate, RTD-1L is the closest temperature detector to the center of the device on the left side, whereas RTD-14R is the most distant from the device's center on the right side. The IDE-based capacitance sensors are named with the short form of "CS" and follow the same naming convention as the RTDs. To learn more about this composite microdevice, refer to our previous work [25], where we employed this microdevice to investigate heat transfer mechanisms and phase-interface behavior during the evaporation of sessile droplets from a heated polyimide surface.
Applied Thermal Engineering 248 (2024) 123152
The experimental setup for investigating droplet impact and subsequent heat transfer mechanisms consists of a sample stage underneath a syringe controlled by a drop shape analyzer equipment (DSA 25E, KRÜSS Scientific). The DSA provided controlled dosing of water droplets during each experiment. An optical camera attached to the DSA recorded the droplet changes throughout the evaporation process after the impact. The volume of water droplets was 6.0 µL for all the experimental results shown in this article. The droplet's volume was chosen in a way so that it entirely covered the sensing zone of the microdevice upon impact. To dose such small-scale droplets, we utilized a working fluid comprised of 90 % deionized water and 10 % isopropanol by volume. Adding isopropanol aided in decreasing the surface tension and made it possible to dispense small-scale droplets capable of gravity-induced detachment while minimally changing the fluid properties of deionized water.
Since the capacitance change with the passage of the droplet can be relatively small, a supporting circuit was employed to ensure a detectable capacitance change. The supporting circuit consists of an operational amplifier, an RC oscillator circuit, and a reference capacitor connected in parallel with the capacitance sensor employed for tracking the moving contact line of the impacted droplet. Please refer to our previous work [25] for more details on this capacitance sensing and calibration of the RTDs.
A high-speed B/W camera (VEO 410L, Phantom) was employed to observe the impact of droplets and subsequent changes in hydrodynamics during the experiments. The recorded video/images were postprocessed via Phantom post-processing software to evaluate the impact velocity, diameter, and duration of spreading and receding phases of the impacted droplets. The resolution and framerate of the captured images were 1280 ´ 800 pixels and 1000 frames per second, respectively.
The temperature sensing uncertainty was analyzed by measuring the standard deviation of initial temperature readings from each RTD. Results showed a precision of ±0.2 C and an absolute accuracy of ±1.2 C when combined with calibration against thermocouples or an IR camera. The primary source of uncertainty is bias error rather than random error, allowing for smaller uncertainty of ±0.5 C in temperature difference measurements. A sampling at 100 Hz provided adequate data for precise measurement, and repeating experiments three times on each surface temperature enabled accurate precision estimation. The Supplementary Materials section contains a chart summarizing this microdevice's measurement uncertainty and lower limit of spatial resolution. For more details on measurement uncertainty, please refer to our previous work [25].
While the RTDs of the microdevice allow for higher sampling rates when working independently, for optimal accuracy and in cases of combined data acquisition with IDE-based capacitance sensors, we used a sampling rate of 100 Hz for all experiments reported in this work. This sampling rate was optimal given that all experiments involved subcooled impinging droplets and the overall length of the evaporation process was in tens of seconds.
We investigated the influence of air currents or large-scale convective flows on the sensitivity of the RTDs or IDEs of the microdevice since all the experiments reported in this work took place in an open environment. The measured capacitance and temperature data from the RTDs and IDEs did not exhibit any fluctuations above the signal noise levels before the impingement of the droplets that abrupt air currents or larger-scale convective flows can cause. The changes in signals occurred solely due to the droplet impact and subsequent evaporation, and the change in magnitude was sufficiently greater than signal noise levels, indicating the effect of air currents or large-scale convective flow was negligible in comparison.
Fig. 2 shows time-elapsed images of 6.0 µL impacting droplets on the top polyimide surface of the microdevice at varying impact velocities. A high-speed B/W camera (VEO 410L, Phantom) captured the moment of impact and subsequent changes in the spreading diameter and shape of the impacted droplets. Figs. 2 and3 show that a period up to 6 ms refers to the droplet spreading regime as the impacted droplet reached its maximum spreading diameter regardless of the impact velocity or associated Weber (We) number. As the droplet visualization depicts, the droplet spreading regime involves the radially outward movement of the impacted droplet.
Impact velocity and We number (a dimensionless parameter that denotes a ratio of inertial to surface tension forces) are the two significant parameters that influence the impact characteristic patterns [13,14]. According to the experiments reported in this work, the higher Weber number or impact velocity led to the maximum spreading diameter of the impacted droplets. To illustrate, at 6 ms an impact velocity of 0.58 m/s (We = 11.2) exhibited the lowest value of 5.16 mm as the maximum spreading, whereas an impact velocity of 1.35 m/s (We = 60.7) facilitated the highest spreading diameter of 7.15 mm.
As shown in the time-elapsed images, after reaching the maximum spreading, the surface area of the droplet started to shrink because of the dominant surface tension forces of the liquid. As shown in Fig. 3, the spreading diameter of the impacting droplets gradually decreased until it reached its equilibrium state. This phase is known as the dropletreceding regime, leading to the subsequent sessile droplet evaporation phase.
As stated in the experimental setup, a drop shape analyzer (DSA) equipment facilitated the dosing of the consistent volume of impacting droplets and recorded the evaporation process. DSA also kept track of the contact diameter and changes in contact angle throughout the evaporation process via its image analysis software. Experiments involving droplet impingement and subsequent evaporation at varied surface temperatures demonstrated a consistent trend regarding changes in contact angle and diameter. Fig. 4 illustrates a representative plot depicting the evolution of diameter and contact angle over time of the impinging droplet at a surface temperature of 80.9 C. As shown in Fig. 4, at the beginning of the evaporation process, there is a brief period where the contact angle increased to its maximum value of 49.5 from its initial value of 39.6 . Approximately 57 % of the total duration of the evaporation maintained a constant contact angle (CCA) phase, followed by a phase with a sharp reduction in contact angle. During this phase, the evaporating droplet held a nearly constant contact diameter, known as the constant contact diameter (CCD) phase. This CCD phase constituted about 27 % of the total duration of the evaporation process.
Fig. 5 illustrates the temperature change and vertical heat fluxes upon droplet impact on the heated top polyimide surface of the microdevice at four different impact velocities ranging from 0.58 to 1.35 m/s. Analyzing the time-elapsed images captured by the high-speed camera while the droplet was in flight just before impact made it possible to calculate the accurate impact velocities. As shown in Fig. 2, for all experiments reported in this work, water droplets completely covered the sensing zone of the microdevice upon impact. As a result of droplets impinging onto the heated surface of the microdevice, the measured temperature change by the RTDs demonstrated a sudden and simultaneous decline. Since all the RTDs of the microdevice employed during experiments showed the same temperature change within our experimental uncertainty of ±0.5 C during and initially after impact, for the clarity of presentation, we chose RTD-2L located in the center of the device to demonstrate the temperature changes due to the impingement of a 6.0 µL water droplet at varying impact velocities while maintaining the surface temperature at 72.9 C. As Fig. 2 demonstrates, the higher impact velocities resulted in a greater spreading diameter of the droplet, facilitating a larger contact area between the heated polyimide surface and the impacted droplets. The larger contact area allowed higher heat Applied Thermal Engineering 248 (2024) 123152 transfer from the heated surface to the liquid droplet. Consequently, the highest impact velocity resulted in the highest temperature drop and contained the maximum magnitude of vertical heat flux, as shown in Fig. 5. Please refer to the Supplementary Materials for more details on the vertical heat flux calculations.
The surface temperature of the solid wall also significantly influences the amount of heat transferred upon droplet impact. All the experiments reported in this work were in the film evaporation regime, where we investigated the effects of varying surface temperature for 6.0 µL water droplets by keeping the impact velocity constant. Fig. 6 shows the temperature changes and heat flux values due to droplet impact on the heated polyimide surface of the microdevice at four different surface temperatures ranging from 53.3 C to 74.5 C. The impact velocity of the droplet impingement was 1.05 m/s for all four experiments, and these results were merged in a single plot by arbitrarily shifting along the time axis to aid in visibility. Fig. 6 exhibits experimental results in ascending order of the surface temperature, where "1″ and "4" dictate the lowest and highest surface temperatures, respectively, out of the four. When the surface temperature was higher, it facilitated a more significant temperature difference between the impacting droplet and the heated surface; as a result, temperature drop and vertical heat flux values due to droplet impingement were greater in magnitude for experiments with higher surface temperatures.
To investigate the interdependence of phase interface and heat transfer dynamics, we conducted additional experiments for impacting droplets having a volume of 6.0 µL and impact velocity of 1.05 m/s at shows the temperature drop upon droplet impact and temperature change during the evaporation process of droplet impacting the heated polyimide surface of the microdevice. The capacitance and temperature data presented were recorded simultaneously and time-aligned with one another for each experiment reported in this work. Additional figures for the droplet impact and succeeding sessile droplet evaporation processes at 80.9 C and 89.5 C can be found in the Supplementary Materials. In these plots, time "0" second denotes the impingement of the droplet, demonstrated by the capacitance sensors with a sharp and sudden rise in their signals as the droplet covered these sensors upon impact. Near the end of the evaporation process, when the droplet evaporated away, the change in capacitance signals was more gradual and lower in magnitude, differing from the moment of impact. These capacitance sensors can thus precisely detect the key events, such as droplet impact and the moment at which droplets evaporated away via the pattern and magnitude of the signals.
As these temperature distribution plots show, the RTDs also reported a sharp decrease in temperature at "0″ second with the impingement of the droplet, followed by a gradual increase in temperature and another sharp change at the near end of the experiment when the droplet completed its evaporation. The temperature distribution underneath the evaporating droplet measured by the RTDs is in excellent agreement with the capacitance signals denoting the location of the MCL of the impacting droplets. The duration of the evaporation process measured by the RTDs, and IDE-based capacitance sensors is the same. The absolute capacitance changes and temperature distribution data reported in Fig. 7 combine to validate the dual functionality of this composite microdevice, where the capacitance sensing scheme enabled precise tracking of the MCL rather than inferring. As the surface temperature increased, the duration of the evaporation process decreased because of the high evaporation rates. The duration of the evaporation process at 68.8 C was 125.8 sec, which was reduced by 42.7 % and 60.5 % when the surface temperature increased to 80.9 C and 89.5 C, respectively. These temperature change plots also revealed that the whole process can be divided into two distinct parts: the first part consists of a sharp temperature drop due to droplet impact followed by a gradual increase in temperature as heat is conducted into the droplet from the heated surface. On the other hand, the second part corresponds to a nearly constant temperature until a sharp change in temperature occurs at the end of the evaporation process. The length of each segment significantly depends on the surface temperature. The duration of the first part increases with increasing surface temperature, while the second segment's length decreases. The later section of this manuscript describes the underlying heat transfer mechanisms behind this in detail.
As shown in Fig. 2, the time-elapsed images captured by the highspeed camera exhibited the initial droplet impact, spreading and receding on the millisecond timescale. However, the temperature drop observed over the first few milliseconds after the droplet impingement did not reveal any additional insights beyond what could be obtained from the longer timescale data. Specifically, the temperature distribution during these initial milliseconds showed a decrease followed by the droplet impingement (see Fig. 7(b)), consistent with the longer timescale data. As the millisecond data did not provide any further elucidation of the physics governing the evaporation process, we have chosen to emphasize the analysis of the temperature distribution over the whole evaporation process, which is on the timescale of seconds.
We utilized the measured temperature data from the evaporation processes reported above to quantify the heat flux values. Fig. 8 illustrates the change in vertical heat flux from the resistance heater of the microdevice to the evaporating droplet for evaporation studies performed at 68.8 C. Please refer to the Supplementary Materials for more details on the vertical heat flux calculations and additional figures for evaporation studies conducted at 80.9 C and 89.5 C.
For these experiments, the local heat flux has the maximum values immediately upon the droplet impact resulting from the significant temperature change because of the deformation of the thermal boundary layer between the heated polyimide surface and the impacting droplets. Another sharp change was observed at the near end of the evaporation process when the droplets evaporated away. These changes denoted the passage of the MCL and the advancing and receding movement due to impingement and evaporation, respectively. As summarized in Table 1, the local heat flux values due to droplet impact are, on average, more than 12 times higher than the initial dry state when no water droplet was present on the sensing zone of the microdevice. When the droplets impinged on the heated surface, it facilitated a higher heat flux than the heat flux caused by the receding MCL due to evaporation. The heat fluxes caused by droplet impact are, on average, more than 4.5 times higher than those associated with the receding MCL movement. These data also suggest that higher surface temperatures increase the evaporation rate and the MCL speed, resulting in higher local heat flux values during the receding MCL passage. Our previous research found that the 1, the average heat flux caused by droplet impact (times initial dry state) increased only by 1.74 % from its corresponding value of 12.09 when the surface temperature increased from 68.8 C to 89.5 C. In contrast, the average heat flux caused by receding MCL (times the initial dry state) exhibited a significant increase of 30.77 % with the same increase in surface temperature. These results suggest that heat flux caused by droplet impact has a weak dependence on surface temperature; conversely, the receding MCL heat transfer is significantly surface temperature dependent due to its influence on MCL speed as shown in our previous work [25].
An energy balance equation can be employed to fully understand the contribution of different heat transfer mechanisms on the evaporation of a droplet from a heated surface. After droplet impact/deposition, heat is transferred from the heated surface to the droplet via conduction. The overall heat transfer rate from the heated surface to the droplet can be estimated by:
In this equation, T is the temperature of the heated surface, determined through surface temperature calibration at known power inputs to the microdevice's resistance heater. On the other hand, T represents the temperature change caused by the droplet throughout the experiment, measured using the RTD. Heat transfer also includes the sensible heat required for the temperature increase within the droplet bulk Q , the external convective heat transfer from the evaporating droplet to the ambient Qconv/ext, radiation heat transfer Qrad, and heat transfer associated with vapor transport during evaporation Qliq/vap. The energy balance of an evaporating droplet from a heated surface can be estimated as:
In the initial period when the droplet impacts on the heated surface, sensible heat is significant, and the time scale for heat conduction into the droplet can be estimated by [29]:
w According to this equation, the thermophysical properties of the working fluid were considered constant and r was measured from timelapsed images after the droplet reached its equilibrium state, following the initial spreading and receding upon impact. The estimated time scale for heat conduction is 16.86 s, similar to the period that exhibits the gradual decrease in heat transfer rate values, as shown in Fig. 9, showed as the sensible heat regime. During the initial evaporation phase, the sharp increase in heat transfer rate upon droplet impact denotes the highest temperature difference between the droplet and the heated surface. After that, the gradual decrease in heat transfer rate indicates an increase in the temperature of the droplet as heat is being conducted to the droplet from the heated surface until surface evaporation dominates the process and causes relatively constant heat transfer rate. After this initial heating, the conductive heat transfer process achieves a quasisteady state, and the heat transfer associated with mass transfer due to vapor removal becomes dominant. Due to the high efficiency of phasechange heat transfer, the heat transfer associated with vapor removal or evaporation accounts for more than 95 % of the overall heat transfer,
. Heat transfer rate distribution with time at the solid-liquid interface due to droplet impact and subsequent evaporation of a 6.0 µL water droplet on a heated polyimide surface at 80.9 C as measured by the microscale RTDs.
making other modes of heat transfer negligible [29,30]. Therefore, we can approximate the energy balance of an evaporating droplet as:
The variation in heat transfer rate at the liquid-vapor interface can be calculated by employing the equation below that expresses Qliq/vap in terms of the change in volume with time. Fig. 10 shows the change in volume with time recorded by the DSA for the experiment conducted at 80.9 C. These recorded values facilitated the calculation of the heat transfer rate values at the liquid-vapor interface throughout the evaporation process, also displayed in Fig. 10.
Qliq/vap = ρ w hfg dt (5) For the experiment conducted at 80.9 C (see Fig. 9), the average heat transfer rate Q was 1.99 W during the sessile droplet evaporation phase. This calculation was based on the RTD-measured temperature distributions during the evaporation study. The average heat transfer rate for vapor removal Qliq/vap was calculated as 1.84 W (see Fig. 10) using the DSA-recorded change in volume of the evaporating droplet from the same experiment. The percentage difference between these values is 7.54 %, within the range of estimated propagated error of 11 % resulting from the temperature difference measurement uncertainty of ± 0.5 C [25].
A thermal resistance model can also be employed to determine an evaporating droplet's overall heat transfer mechanism. The total thermal resistance can be estimated by:
w c liq/vap s Since small-scale evaporating droplets experience minor heat loss via radiation and external natural convection to the surroundings, R and Rconv/ext contribute negligibly [29,30]. As the droplet evaporates, the thickness of the droplet decreases, as does the resistance within the liquid. So, after the initial heat-up period, the resistance associated with vapor removal dominates over the resistance within the liquid [26]; hence the total thermal resistance can be approximated as:
During the experiment at 80.9 C, the total thermal resistance was calculated to be 28.6 C/W. This calculation was based on the average heat transfer rate at the solid-liquid interface obtained from the RTDmeasured temperature distributions during the evaporation study. The resistance associated with vapor removal was calculated as 30.9 C/W. The percentage difference between these was 7.54 %, which falls within the range of estimated propagated error.
We quantified the contribution of convection within the droplet to the overall heat transfer by considering the effects of buoyancy and thermocapillary flows inside the impacted droplets. Grahshoff (Gr) and Marangoni (Ma) numbers are the two dimensionless numbers widely used to characterize the buoyancy and thermocapillary-driven convections within droplets. A higher Gr number indicates that buoyancy-driven convection is the more dominant mode of heat transfer, whereas a lower Gr suggests weaker buoyancy and conduction-dominated heat transfer [31]. The range of Gr number values for our experiment is 3.63-5.31, much lower than the reference value (Gr is < 2400) [32], indicating the contribution of buoyancy-driven convection is negligible. Ma number characterizes thermocapillary-driven convection in evaporating droplets by comparing the surface tension gradient caused by temperature gradient to viscous force. The contribution of thermocapillary flows, known as the Marangoni convection, increases with increasing Ma number. The effect of Marangoni convection is negligible for horizontal liquid films if the Ma number is less than 80-100 [32]. With a characteristic length of 0.318 mm, our experiments yield Ma values in the range of 16500-24250, higher than the reference value (80-100), denoting the contribution of thermo-capillary convection within the droplet. Another dimensionless number, the Bond (Bo) number, characterizes the relative contribution between buoyancy convection and Ma convection in an evaporating droplet. The calculated value of Bo is 0.00138 for the experiments reported in this work, and when Bo 1 [32], internal flow is dominated by Ma convection. During the process, when evaporation is in constant contact diameter (CCD) mode, the evaporative mass loss near the contact line must be balanced by new liquid flowing from the droplet's bulk [31]. Therefore, a capillary flow can exist within an evaporating sessile droplet, although it is not significant due to the high efficiency of the phase-change heat transfer. Heat transfer associated with the surface evaporation of an evaporating droplet accounts for more than 95 % of the overall heat transfer [29,30], making other modes of heat transfer negligible. Moreover, in our experiments, the CCD mode constituted only about 27 % of the total duration of the evaporation process, as demonstrated in Fig. 4. Therefore, the contribution of internal convection in small-scale evaporating droplets is often neglected in the literature. Gholijani et al. [6] and Lee et al. [26] found that the total heat is mainly transferred through diffusion or surface evaporation during the sessile droplet evaporation phase of impacting droplets onto a heated solid wall. Chandramohan et al. [33] also reported that the contribution of convection within the evaporating droplets can be neglected in wetting droplets because of their low height-to-contact diameter ratio. Please refer to the Supplementary Materials for a comprehensive explanation and calculation process of all the dimensionless parameters used in this study.
In terms of investigating the influence of impact velocity and surface temperature during droplet impingement heat transfer, our current study is qualitatively comparable to Gholijani et al. [6] and Herbert et al. [8], despite the difference in the sensing scheme, interacting surface, and working fluids. Although these studies solely relied on infrared thermography, they likewise reported that increasing impact velocity increases the maximum spreading diameter and heat flux at the solid-liquid interface. Additionally, they found that an increase in wall temperature increases the heat flux at the solid-liquid interface for an impacting droplet.
Findings from our current study also align well with experimental and theoretical investigations of sessile droplet evaporation reported by Huang et al. [29] and Hays et al. [30]. These works have similarly shown that during droplet evaporation, the overall heat transfer rate from the heated surface to the droplet can be approximated as equal to the heat transfer associated with vapor removal or evaporation, making other modes of heat transfer negligible. Additionally, we found that the Gr numbers were much lower for the experiments reported in this work, indicating weaker buoyancy-driven convections within the droplets; hence, conduction and diffusion dominate the overall heat transfer. Other relevant research works on evaporating droplets [6,26,29,30] in the literature have likewise reported conduction and diffusion-based heat transfer while neglecting the internal convection of the droplet.
Applied Thermal Engineering 248 (2024) 123152
When a droplet impacts a heated surface and evaporates, the process can be divided into two segments based on the effective heat transfer rate, as shown in Fig. 9. The first segment, "sensible heat regime," corresponds to the sharp increase in heat transfer rate upon droplet impact resulting from the highest temperature difference between the droplet and the heated surface. After that, the gradual decrease in heat transfer rate indicates an increase in the temperature of the droplet as heat is being conducted to the droplet from the heated surface. After this initial heating, in the second segment, the conductive heat transfer process achieves a quasi-steady state, and the heat transfer associated with mass transfer due to vapor removal becomes dominant and causes a nearly constant heat transfer rate. Microscopically, the previous research closest to ours is the microscale heaters array-based investigation of heat transfer characteristics of a single isolated impacting droplet on a heated surface by Lee et al. [26]. They likewise reported two distinct segments throughout the droplet vaporization process regarding effective heat transfer rate at the solid-liquid interface. According to them, for superheated impacting droplets, the first segment is mainly caused by the oscillatory motion of the droplet after impact and initial heat conduction into the droplet. An important distinction for subcooled impacting droplets observed in our current study is that the initial oscillations into the droplets lasted only a few tens of milliseconds, whereas the duration of the first segment was a few seconds, denoting the effect of oscillatory motion is negligible; hence, heat conduction into the droplet from the heated surface entirely dominated this segment.
Our current study shows that the surface temperature significantly affects the length of these two segments. In the case of subcooled impinging droplets, the duration of the sensible heat regime increases with increasing surface temperature. However, the duration of the constant heat transfer segment decreases with the rise in surface temperature. The duration of the conduction-dominated first segment increased from 16 % to 20 % of the total time of the process when the surface temperature increased from 68.8 C to 89.5 C. Meanwhile, the duration of the evaporation-dominated second segment decreased from 81 % to 75 %. This study also facilitates a comparison of the magnitude of the heat transfer rate of both segments, where the sensible heat segment has higher heat transfer rates than the segment dominated by vapor removal/surface evaporation.
Experimental results of this work based on the distinct heat transfer regimes during droplet impingement and subsequent evaporation can reveal essential insights into the underlying physics. Understanding the transition from initial heat conduction to quasi-steady surface evaporation and associated effective heat transfer rate can facilitate more accurate models for phase-change heat transfer processes.
Capability of microscale temperature measurements and phase interface sensing facilitated unlocking the dominant heat transfer mechanisms underneath the evaporating droplet both on the onset of droplet impact and subsequent evaporation. In terms of detecting the MCL's location, most previous works relied on a combination of highspeed optical imaging and post-processing of the IR images; these works often inferred MCL as the coinciding region with the local temperature minimum and high heat flux values. These techniques' macroscopic spatial resolution and visibility, i.e., line of sight and viewing angle, often hinder precise detection of the location and temperature gradient in the MCL region. In our work, the IDE sensors facilitated independent and microscale tracking of the MCL validated by the temperature measurement of the RTDs, facilitating an important distinction and utility. The resistance and capacitance-based operating principles of this microdevice offer a significant utility in detecting temperature changes and tracking MCL at the microscale in real-time, even for applications with limited or no visibility. Eliminating the need for an external heater or optical image processing scheme makes it an independent experimental setup for investigating phase-change heat transfer processes and usable within thermal management hardware or processing equipment.
Droplet impact and subsequent evaporation of subcooled impinging droplets have been investigated on a heated polyimide surface at varying impact velocities and surface temperatures utilizing a custom MEMS device to determine the underlying physics behind the phase-change heat transfer process. This microdevice facilitated an independent experimental setup, ensuring microscale tracking of the MCL validated by the temperature measurement of the RTDs. Experimental results have shown that when a droplet impacts a heated surface and evaporates, the process can be divided into two segments based on the effective heat transfer rate: an initial conduction-dominated segment followed by another segment dominated by surface evaporation. The experimental investigations have also led to the following conclusions:
• The first segment, "sensible heat regime," corresponds to a sharp increase in heat transfer rate upon droplet impact, followed by a gradual decrease as heat is being conducted to the droplet from the heated surface. In the second segment, the heat transfer associated with mass transfer due to vapor removal becomes dominant and causes a nearly constant heat transfer rate. Higher surface temperatures lengthen the sensible heat regime but shorten the constant heat transfer segment. The sensible heat regime exhibits higher heat transfer rates between these two segments. • The effect of oscillatory motion is negligible for subcooled impacting droplets, unlike in a superheated regime; hence, heat conduction into the droplet from the heated surface entirely dominates the first segment. • Heat flux caused by droplet impact has a weaker dependence on surface temperature; conversely, the receding MCL heat transfer is significantly surface temperature dependent. • The heat flux at the solid-liquid interface of an impacting droplet increases with the rise of either impact velocity or surface temperature. The local heat flux values due to droplet impact are, on average, more than 12 times higher than the initial dry state and more than 4.5 times higher than those associated with the receding MCL movement. In the film evaporation regime, droplets impacting a heated surface have approximately 1.6 times higher vertical heat flux values than gently deposited droplets. • Buoyancy and thermocapillary convection within evaporating droplets contribute negligibly to overall heat transfer, which is dominated by heat conduction into the droplet and surface evaporation.
To summarize, the experimental results of this work from studying the heat transfer regimes and comprehending the transition from conductive heat transfer to surface evaporation during droplet impingement and following evaporation can provide essential insights into underlying physics to improve heat transfer models, surface engineering, and overall effectiveness. Moreover, real-time, minimally invasive temperature measurements and simultaneous tracking of MCL at the microscale by a composite microdevice utilized in this work can aid in thermal management and process control for electronics cooling.
The authors declare that they have no known competing financial Applied Thermal Engineering 248 (2024) 123152 interests or personal relationships that could have appeared to influence the work reported in this paper.