Examining condensation and freezing behavior on a laser-patterned metallic surface using an AI neural network model

Condensation and freezing of water droplets on solid surfaces occur in a wide range of natural and engineered systems; uncontrolled or unwanted ice formation poses significant challenges to performance and safety. Surface texture greatly influences droplet nucleation, growth, coalescence, and freezing mechanisms by affecting wettability and droplet pinning. In this paper, the effects of a microtextured aluminum surface are visualized at high magnification (e.g., 600×) during condensation from moist air at 20 °C–23 °C and 39%–47% RH. Condensed droplet images are processed with an artificial intelligence (AI) model. Different textures measurably affect droplet condensation dynamics and subsequent freezing behavior. A neural network-based object detection model was developed to quantify droplet population, average diameter, phase state, and surface coverage across entire fields of view. The model was trained on over 1,300 images. The detection model provided statistically robust insights into the relationships of condensation dynamics, surface texture, and freezing behavior. The AI-derived measurements for condensed droplets show that both droplet population decline and diameter growth follow power-law scaling over time. The microtextured surface displayed smaller power-law exponents compared to the smooth control surface. This indicates a shift in condensation behavior caused by increased droplet pinning and decreased mobility on the microtextured surface. These changes are also linked to much faster freezing. The microtextured surfaces achieved full frost coverage at an average time of 139.5 s, which is roughly three times quicker than smooth substrates with an average freezing time of 419.5 s. The findings reveal that surface-induced pinning directly influenced condensation growth and subsequent freezing behavior.

Water droplets condensing and freezing on surfaces is a ubiquitous phenomenon that often must be managed rather than eliminated. From air conditioners freezing over in the summer to icy sidewalks in the winter, the consequences of uncontrolled freezing range from minor inconveniences to serious hazards. Delayed flights, highway pileups, and city-wide power outages during winter storms are just a few examples of how ice formation can disrupt significant infrastructure and endanger lives. On average, severe winter weather costs the U.S. economy approximately $2.5 billion annually (Roth Tran and Wilson, 2024). These events strain resources, disrupt transportation and energy systems, and pose risks to human health and safety (Bloesch and Gourio, 2015). Therefore, understanding the mechanisms of freezing is not only a scientific challenge but also a practical necessity for designing safer, more resilient systems.

Recent research has deepened our understanding of condensation frosting, a multi-stage process involving droplet nucleation from the condensation of moist air, coalescence, initial icing, frost halo formation, ice bridging, and frost densification (Gu et al., 2023; Nath et al., 2017). This has led to the development of engineered surfaces to control the propagation of freezing, such as superhydrophobic and microstructured materials, which delay or suppress ice formation without requiring external energy input. These surfaces reduce droplet residence time and inhibit ice nucleation and offer sustainable solutions for thermal management and environmental control (Gu et al., 2023; Nath et al., 2017).

For condensation from moist air and subsequent freezing, nucleation, propagation, coalescence rates, and droplet dynamics are all affected by the substrate’s texture (Gu et al., 2023). On smooth surfaces, freezing starts through heterogeneous nucleation of ice, often at edges, defects, or rough spots, due to their ability to lower the activation energy for ice formation compared to homogeneous nucleation in the bulk liquid (Stallbaumer-Cyr et al., 2022). Zhao et al. (2021) investigated the effects of ice suppression via passive surface engineering by the introduction of microgroove surfaces with added nucleation sites via “nanoblades” (Zhao et al., 2021). Copper samples were milled to create semicircular peaks and valleys. The secondary step created cactus-like spines on the surface. This secondary surface yielded directionally dependent wetting behavior. The combination of microgrooves and nanoblades effectively controlled the size and distribution of condensed droplets, thereby aiding overall frost reduction. The introduction of hierarchical surfaces to a substrate enabled planned nucleation sites, thereby pinning the droplet in place and controlling access to available water vapor.

Beysens and Knobler (1986) determined that dropwise condensation on non-wetting surfaces was characterized by a power-law scaling of droplet growth, unlike filmwise condensation. For these scaling laws, droplet diameter was proportional to t x as determined by investigating the growth rate of single droplets. Coalescence of droplets accelerated the growth rate of a single droplet and affected the total droplet population by re-nucleating droplets in the void created by coalescing droplets (Haque et al., 2018). Importantly, the droplet population was shown to grow by power-law scaling with respect to time (Beysens and Knobler, 1986). Subsequent studies linked observed power law exponents to distinct physical growth mechanisms and environmental conditions (Leach et al., 2006; Castillo et al., 2015). Leach et al. (2006) showed that droplet growth was size-dependent: small droplets grew primarily through surface diffusive transport, while larger droplets grew mainly through direct vapor condensation. Furthering this understanding to realistic atmospheric conditions, Castillo et al. (2015) demonstrated that ambient relative humidity primarily affects the power-law exponent in regimes dominated by direct condensation. However, once coalescence becomes dominant, droplet growth defaulted to a humidity-independent scaling behavior. Dropwise condensation is a coalescence-driven scaling process and is often modeled using power laws (Beysens and Knobler, 1986; Leach et al., 2006; Castillo et al., 2015).

The ability of a surface to pin a droplet in place often plays a significant role in the dropwise condensation behavior exhibited. When a surface exhibits high hysteresis, the three-phase contact line becomes anchored to surface defects, requiring a significant force to advance or recede, thereby immobilizing droplets (Extrand and Kumagai, 1996; Johnson and Dettre, 1964). Micro- and nano-scale roughness can further enhance pinning when droplets adopt a Wenzel state, thereby increasing the effective solid–liquid contact area and increasing resistance to motion (Quéré, 2008; Wenzel, 1936). In condensation, pinning suppresses droplet migration and coalescence-induced shedding, prolonging droplet residence time on the surface and allowing droplets to reach thermal equilibrium with the substrate (Beysens and Knobler, 1986; Rose, 2002).

At temperatures below the freezing and dew point, condensed droplets will freeze. The methods by which a freezing front propagates through a droplet field include cascade, stochastic, or ice-bridging behaviors (Stallbaumer-Cyr et al., 2022). The surface geometry and droplet distribution on the substrate dictate the most likely freezing mechanism (Boreyko and Patrick Collier, 2013). Cascade bridging is dependent on having inter-droplet interactions, typically due to small distances between the droplets but can also be influenced by factors such as substrate thermal conductivity (Chavan et al., 2018). Micropatterned hydrophilic spots on a surface promote uniform droplet spacing and cascade behavior (Boreyko and Patrick Collier, 2013). Stochastic freezing stems from large distances between droplets, as dendrites fail to form successful bridges with close neighbors. Leading droplets to freeze independently, without bridging. Cascade and stochastic freezing are most often observed on grooved or sintered substrates (Stallbaumer-Cyr et al., 2022).

Nath et al. (2020) investigated condensation frosting on chilled surfaces, focusing on inter-droplet ice bridging, in which ice dendrites propagated from the frozen droplets to adjacent supercooled liquid droplets. Ice bridges formed because frozen droplets acted as humidity sinks. For ice bridging, nearby liquid droplets evaporated and deposited vapor. The success of the bridge was entirely dependent on the geometry of droplets, droplet size, and spacing, and was not dependent on humidity, surface, or surface wettability (Nath et al., 2020). For a given pair of droplets, the maximum extent to which an ice bridge could grow was geometrically constrained by the distance from the edge of the frozen droplet to the center of the liquid droplet. In dropwise condensation formation, the amount of water vapor available is a key factor in predicting the size and growth rate of droplets and their subsequent freezing on surfaces (Chattoraj et al., 2024). It has been observed that in plain, smooth surfaces, the predominant freezing mechanism is ice bridging. Creating space between droplets can slow their overall growth (Nath et al., 2026).

Images visualizing condensed and frozen droplets contain a substantial number (i.e., hundreds to thousands) of droplets; thus, this problem is well-suited to an artificial neural network using machine learning (ML). Conventional methods for quantifying droplet size and number from condensation images—such as manual counting or threshold-based segmentation algorithms (e.g., watershed segmentation), are labor-intensive, subjective, and sensitive to variations in illumination, contrast, and droplet overlap (Rutkowski et al., 2021; Leach et al., 2006; Castillo et al., 2015; Stallbaumer-Cyr et al., 2022). These traditional image processing approaches require significant parameter tuning for each new imaging condition and are poorly suited for the large datasets generated in condensation experiments.

Deep convolutional neural networks, by contrast, can generalize across diverse imaging conditions, autonomously detecting and measuring individual droplets in densely populated fields of view, and process large datasets far more efficiently than manual methods (Rutkowski et al., 2021; Suh et al., 2024). A study by Suh et al. demonstrated that deep learning could extract droplet population statistics from condensation surface images significantly faster and more accurately than conventional computer vision methods, enabling quantitative analysis at a scale previously unattainable with manual or threshold-based approaches.

As machine learning techniques become globally accessible, the application of different ML methods is enabling more efficient analysis of key variables in video and image data. Najafian and Mortazavi (2025) conducted a study to predict droplet evaporation and falling rates using machine learning models. After performing 544 numerical simulations with the front-tracking method, they compared the results of five machine learning (ML) algorithms trained on the same data set. The artificial neural network model achieved the highest accuracy, with an R 2 value of approximately 0.999 for both evaporation and fall rate predictions. Showing better performance than the other models. Yee et al. (2024) analyzed the morphological evolution of splashing versus non-splashing drops using explainable artificial intelligence. A feedforward neural network was trained to classify image sequences as splashing or non-splashing, achieving over 96% accuracy (Yee et al., 2024; Najafian and Mortazavi, 2025). The high accuracy rates of Neural Networks helped our team choose this type of ML for our model.

The research objectives of this paper are to understand the impacts of surface texture on the freezing mechanisms of aluminum surfaces using a neural network model. Since droplet pinning and coalescence impact freezing behavior (Stallbaumer-Cyr et al., 2022), the neural network model is developed to continuously determine droplet counts and average sizes which allows the elucidation of power law behavior. The ability to comprehensively count both the droplet population and droplet diameter at any given time allows for the determination of whether condensation is driven by coalescence or direct vapor deposition, which allows the prediction of their subsequent freezing patterns.

The experimental apparatus to observe condensation from moist air and subsequent freezing is shown in Figure 1 (Stallbaumer-Cyr et al., 2022; Bohm et al., 2018; Haque et al., 2018). A Leica DVM2500 microscope is used for all experiments. The sample is placed on a TE Technology Peltier cooler (TE-127-1.0-2.5) and attached using Omega High Temp & Conductive Paste thermal paste (OT-201-16, thermal conductivity of 2.3 W/mK). The Peltier cooler is attached to a custom aluminum water-cooled heat sink, with additional thermal paste, which rests on the microscope stage in a ceramic box. A NESLAB RTE-11 water chiller is set to 10 °C and runs for at least 30 min prior to the experiment.

Two K-type OMEGA thermocouple probes (040G-6) are placed into precision, 1-mm-diameter holes machined in the edge of the sample to obtain a continuous, accurate surface temperature reading. Calibration of thermocouples at three different temperatures demonstrated an accuracy of ±0.5 °C. The 1 mm holes were drilled to a depth of 10 mm. Hole locations were spaced ±5 mm off the vertical centerline and centered on the horizontal centerline, 3.5 mm below the condensing surface, also shown in Figure 1. An Omega data acquisition system (OM-USB-TC-AI) is used to record the surface temperature at the rate of 1 Hz. The Peltier cooler is driven by a separate TE Technology control unit (TC-720) and is managed by the manufacturer’s software on the desktop computer. The microscope operation is managed via Leica’s application suite.

Sample creation and characterization

A bar of 6061 aircraft-grade aluminum with a mirror finish was used as the substrate. A smooth surface was used as a control, and microtextured surfaces were created with a Pharos Laser and a 125 mm focal lens. The laser parameters were as follows: fluence of 0.62 J/cm 2, wavelength 800–1,056 nm, pulse duration 184 fs, repetition rate 50 kHz (kiloHertz), scanning speed 10 mm/sec. The microtextured surface was generated using 15% of the total laser power. The laser created a pattern of parallel lines of a width of 100 ± 5 μm spaced 150 ± 5 μm apart (Figure 2). A Hitachi S 3000 N VP-SEM was used for inspection. The SEM accelerating voltage was 15,000 V, working distance 45,900 μm, and a backscattered electron detector type was used.

On the microtextured sample, the laser redeposited the material onto the surface, making a positive ridgeline (Figure 3). These topographical features will be referred to as peaks and plains (Figure 3). The peaks are not a uniform height. The stage of a scanning electron microscope was tilted at 70° to enable a clear side view of the microtextured sample. After imaging ten separate lines, sampled 5 mm apart, an average of 100 of the tallest peaks was found to be 6.8 µm ± 0.98 µm. The measured peak range was 3.3–9.5 µm.

The wetting characteristics were determined using a goniometer. It was found that the control surface is hydrophobic with an average contact angle 94° ± 3.71°. The microtextured surface displayed an interesting directional wetting behavior. Although hydrophobic, when the line pattern was aligned with the goniometer lens, the contact angle was 129° ± 3.08°. However, when lines were perpendicular to the goniometer lens, the contact angle was 96.7° ± 5.29°.

Operational procedures

Testing was held in an environmental chamber within the Institute for Environmental Research at Kansas State University. The experiment was conducted in the fall; air temperatures were 20 °C–23 °C and relative humidities were 39%–47% RH, ambient air conditions were maintained. The sample was prepared for observation by first inserting two thermocouples into the holes with thermal paste. Surface temperatures were measured at a rate of 1 Hz during the experiments. The sample was adhered with additional thermal paste applied to the top of the Peltier cooler to minimize trapped air and maximize thermal contact.

The Peltier controller was set to −10 °C. Once the Peltier cooler was turned on, the surface temperature (as measured by the embedded thermocouples) reached −8 °C ± 1 °C within 20–30 s. Condensation from the moist air and subsequent freezing was observed. The experiment was considered complete when the entire field of view was fully frozen. A video of each experiment was recorded at 600× magnification, yielding a field of view of 0.51 x 0.38 mm; high magnification was required to observe initial nucleation. Each microscope image had 1.92 × 10 6 total pixels with an area of 318 × 316 nm/pixel. Air temperature, surface temperature, relative humidity, and the total time until freezing were recorded.

After initial data collection, the video was reduced to a rate of 1 frame per second (1 fps). This frame rate was chosen to create a manageable file size of the dataset for processing via the purpose-built AI model. The model measured the number of droplets, the average droplet diameter, the droplet phase (i.e., liquid water or ice), and the water or ice area as a percentage of the total area.

The droplet detection model was implemented using a YOLOv11 architecture. Training images were resized to a fixed input resolution of 640 × 640 pixels prior to model training. The dataset consisted of manually annotated droplets used to generate bounding boxes for the water class. Figure 4 shows pre- and post-annotations on droplet fields or liquid water, a mix of liquid water and ice, and ice images. Standard preprocessing steps included image normalization and resizing, while data augmentation techniques such as random horizontal and vertical flips, scaling, rotation, and brightness/contrast adjustments were applied to improve model robustness. The model was trained using a batch size of 16 with the Adam optimizer and an initial learning rate of 0.001.

Training was conducted for 110 epochs, where an epoch can be defined as one complete pass through the entire training dataset by the model. The dataset was divided into 92% training, 4% validation, and 4% test images. A larger proportion was allocated to the training set due to the limited size of the annotated dataset, ensuring sufficient examples for model learning while retaining independent subsets for validation and final evaluation.

Training and validation losses (box, classification, and objectness) were monitored at each epoch, along with standard performance metrics including precision, recall, and mean average precision (mAP) (Figure 5). The model exhibited rapid convergence during the early epochs, with performance saturating after approximately 50–60 epochs, after which mild overfitting in classification loss was observed. The best-performing model checkpoint was selected based on validation mAP.

Model uncertainties

In YOLOv11 (Jocher et al., 2024), the confidence value assigned to each detected object is directly linked to how mean average precision (mAP) is computed for the model (Lin et al., 2015). The model first produces a confidence score for every predicted box–class pair, reflecting how sure it is that a given box tightly matches a real object and that the chosen class label is correct (Redmon et al., 2016). During evaluation, these raw confidences are swept over a wide range of thresholds (from very low to high values), and for each threshold the predictions with confidence above that value are kept while the rest are discarded. At each threshold, the resulting set of detections is compared with the ground-truth annotations to compute precision (how many predicted objects are correct) and recall (how many real objects are successfully found), using an overlap criterion such as intersection over union (IoU). These pairs of precision and recall values form a precision–recall curve for each class (Padilla et al., 2020), and the area under this curve is called the average precision (AP) of that class (Everingham et al., 2010). Finally, mAP is obtained by averaging these AP values over all object classes, giving a single summary score of how well YOLOv11’s confidence scores, bounding boxes, and class labels work together across different confidence thresholds and IoU settings (Dalal et al., 2026).

Following training, the model achieved a Mean Average Precision at an Intersection over Union (IOU) threshold of 0.50 of 78%, along with a precision of 75% and a recall of 76.5%. Mean Average Precision at an IoU threshold of 0.50 is used to assess the model’s object localization capability by quantifying the degree of overlap between predicted bounding boxes and corresponding ground truth annotations. Under this criterion, a detection is considered correct when the IoU meets or exceeds 50%. A relatively high mAP@0.50 value, approaching unity, suggests that the model is generally able to produce bounding boxes with substantial spatial agreement relative to the ground truth for a considerable fraction of the evaluated instances, although this metric alone does not fully capture performance under more stringent localization thresholds.

Four trials were conducted for each surface. For all eight trials, the same general behavior was observed. Once the surface cooled below the dew point, small droplets rapidly nucleated on the surfaces. These droplets grew both through coalescence and direct growth. The detailed differences between the droplet growth behavior on the surfaces is explained below. As droplet growth slowed, droplets began to freeze from the edge of the frame as observed previously (Bohm et al., 2018; Haque et al., 2018). The time at which the first droplet freezes in the field of view is denoted as the initial icing time. The freezing front then propagated across the frame, primarily through ice bridging. Once all the drops in the frame are frozen the test is concluded and the time recorded as the final freezing time.

Figure 6 shows the video of test 1 for the control surface with the results of the model overlaid on the video at three different times. The image on the far left (Figure 6A) shows the initial nucleation at t = 34s. The red overlay indicates that the model has detected a water droplet. During the initial nucleation, the model is less successful at recognizing all the droplets in the field of view. It is partially due to the lack of training data for initial nucleation. In the images used in our training data set, there are often over 1800 drops in a frame during the first few seconds of nucleation. During late coalescence, droplet counts range from 450 to 600 drops. The images with all ice typically have 220–250 distinct drops. Therefore, the images of initial nucleation are significantly more time-consuming to annotate.

Additionally, the tiny nature of the droplets makes it difficult to crisply capture in videos, which compounds the difficulty of accurately measuring in the annotation and for the model to recognize. However, the current model’s lower identification threshold is currently 4.5 μm. The middle image (Figure 6B) shows the model overlay at t = 160s. Here, the model is much more robust, and it captures nearly every droplet. A few of the smaller droplets (which nucleated in the void between coalesced droplets) were not identified by the model. The blue shaded areas represent water-water overlap where droplets are actively merging. The figure on the far right (Figure 6C) shows the test as droplets are beginning to freeze. The green represents ice and the yellow represents areas of ice-water overlap. When water freezes, its index of refraction changes. Therefore, the ice is more opaque than the liquid water droplets. There are two frozen droplets that were not detected by the model. The image shows that both the droplets have ice bridging from the droplet, which is a clear indication that the drops are frozen. It may also be part of the reason that the ice may not have been detected by the model; additional training images with distinct ice bridging are also needed.

The microtextured surfaces presented challenges to imaging. The ridgeline is significantly taller, 3.3–9.5 µm, than the “smooth” portion, and consequently was out of the focal plane of the microscope when attempting to image droplets in both regions. Experiments were conducted focusing predominantly on the plain region. The condensation started as dropwise in both regions. As time progresses, the microtextured region appears to become filmwise, while the plain region remains dropwise.

Figure 7 shows frames extracted from the video of test 2 for the microtextured surface at three distinct times. The figure on the far left (Figure 7A) is during the initial nucleation phase. While the model correctly identifies several droplets, in the first ∼20 s, it struggles to identify small and tightly packed droplets. As the droplets grow, the model significantly improves droplet identification. Figure 8 (on the left) shows a zoomed in view on the microtextured surface of droplet identification for test 2 at 62 s into the test. The model correctly identifies most of the water droplets which are red. It also correctly identifies several areas where droplets are actively merging in blue. A few small and irregularly shaped droplets are missed by the model. Also shown in Figure 8 (on the right) is an image where the model incorrectly identified a region of the surface texture as a drop; this incorrect identification also significantly reduces after the initial nucleation phase.

Figure 9 shows the total droplet count in the total field of view (droplet population) over time for 4 different trials of the control surface. The droplet population rapidly increases due to nucleation on the surface. This initial nucleation is difficult to capture by the model because fewer training images were used in early nucleation. This is due to the significant number of drops and the small droplet size, which is more difficult to annotate. Once the surface becomes saturated with droplets, they grow through direct growth by condensing moisture from the air. As the droplets grow, they begin to coalesce and the total droplet population decreases. The relationship of droplet population with respect to time followed a power-law relationship, which has been previously reported in the literature (Leach et al., 2006; Castillo et al., 2015; Haque et al., 2018). Using best-fit functions, the power-law equation was found for each test. The data collected prior to the model reaching a confidence of ≥50% was omitted from this analysis. R values were found to be 0.95 or greater for the control surface. An average exponent of each relationship was found (Table 1). The decrease in droplet population during this phase follows the power law with an exponent of −1.5, as shown in Table 1.

Figure 10 shows the droplet population over time for four trials on the microtextured surface. The overall behavior of growth and decline of the droplet population is seen in the overall shape of the graph. The increase and decrease of the microtextured surface are different from the control. However, there is no period of stable population size for either surface. The decrease of the droplet population, which begins around 50 s, also follows a power law but the exponent is −1.2, which shows a slower population decline due to less coalescence of droplets.

For the droplet diameter over time, shown in Figures 11, 12, the presence of large droplets in the first few seconds is a model error. It is most likely due to the model being trained on smooth surfaces as well as the lack of training data for the initial nucleation of droplets. Once the model reaches higher confidence levels, the growth of the droplet size matches visual inspection of the videos. Figure 11 shows that the droplet diameter also follows a power law curve with an exponent of 0.6, shown in Table 1. Figure 12 shows the droplet diameter growth over time on the microtextured surface. The microtextured surface has an average exponent of 0.57. Previous work has shown that an exponent of 0.5 is expected for diffusion-dominant growth (Leach et al., 2006).

The modification of the substrate resulted in a measurable change in droplet growth dynamics. Exhibited as a shift in the power-law exponent governing droplet radius evolution and population, R ∼ t α (Leach et al., 2006; Castillo et al., 2015). On the unmodified control surface, droplet growth follows a scaling consistent with coalescence-dominated growth, where population grows n α t -1.5 and droplet diameter grows d α t 0.63 (Beysens and Knobler, 1986; Leach et al., 2006). In contrast, the modified substrate exhibits a smaller exponent for population growth n α t -1.3 and droplet diameter growth d α t 0.57, indicating an earlier transition to direct condensation. The change in exponents is characteristic of systems where enhanced droplet pinning and reduced mobility prevent coalescence (Beysens and Knobler, 1986; Castillo et al., 2015). These results suggest that surface modification alters the balance between vapor deposition and coalescence, thereby shifting condensation dynamics toward faster droplet growth.

We measured freezing time by recording the total time from nucleation to a frozen field of view. Total frosting occurred on the control in approximately 7 min, while the microtextured surface froze completely in 2 min and 20 s on average. Thus, the microtextured surface froze three times faster than the control (Table 2). Increasing surface area and greater surface roughness provided by the ridge lines increased droplet pinning and solid–liquid contact area, which stifled their growth and accelerated freezing rates (Gu et al., 2023; Bohm et al., 2018). Solid-liquid contact area and pinning both lowered the energy barrier for heterogeneous nucleation and improved heat transfer from the droplet to the substrate (Extrand and Kumagai, 1996; Johnson and Dettre, 1964). Faster freezing was not due to an intrinsic change in ice growth rate; it was a result of altered condensation dynamics driven by surface properties. The machine learning model helped establish a direct link between changes in power-law relationships and accelerated icing on the microtextured surface. The change in surface characteristics shifted the condensation behavior from coalescence-dominated growth on the control surface to direct growth on the microstructured surface.

Neural network evaluation

The resulting confidence graphs from the model are shown in Figures 13, 14. The experimental timeline starts at nucleation and ends at complete freezing. The model’s confidence is reflected by the total number of images annotated at each stage of the process. Due to the large number of hours required to annotate these images, annotation efforts focused on images that show the greatest variety in droplet growth mechanisms (typically in the middle section of the experiments). The model exhibits higher confidence for smooth surfaces when the average droplet size is approximately 15 µm or greater. Confidence continues to increase and hovers around 70% for the microtextured surface or the control until freezing is complete. This trend is due to the greatest number of annotated images being completed for this portion of the experiment. We expect confidence to increase across all parts of the timeline as the data set grows.

Droplet pinning and coalescence play a significant role in governing freezing behavior. Using the AI neural network model, we observed that condensation exhibits power-law behavior in both droplet population and size, regardless of whether the process is dominated by coalescence or dropwise condensation. For the control surface, coalescence was more prevalent, because the higher exponent in droplet growth and the decrease in exponent for the droplet population. This matches prior literature that shows structures pinning droplets prevent coalescence. structures pinning droplets and preventing coalescence. Results from the microtextured sample indicate that increased surface topography enhances droplet pinning, thereby decreasing freezing time even though ice bridging dominated the freezing front propagation on both surfaces.

Rather than tracking a single droplet, we analyzed the full observed droplet field, capturing both population dynamics and the evolution of droplet diameters over time. This field-level perspective yields stronger statistical confidence and a more comprehensive characterization of droplet behavior during condensation and freezing. These results motivate further investigation of pinning effects across a broader range of engineered surfaces and substrate materials to evaluate the generality of the observed trends. Beyond condensation, the YOLO model and AI workflow can be adapted to related multiphase phenomena by adjusting the observation and event definitions to the underlying physics. Promising extensions include spray-pattern characterization and bubble-nucleation analysis during the boiling phase. Further progress is also expected by integrating neuro-symbolic AI approaches to improve the explainability of results for surface types, enhance the interpretability of inferred mechanisms, and better support generalizations.