Condensed water on vertical surfaces ultimately leaves the substrate at the lower edge, where accumulated liquid detaches as drops. While droplet growth and surface transport have been extensively studied, this final release step remains poorly understood and largely uncontrolled. Yet this boundary event determines how and when condensed water is removed. We ask whether geometry can replace randomness as the governing mechanism of edge dripping. By engraving vertical grooves upstream, we redirect water from surface flow into groove-guided drainage toward the boundary. This switch in transport mode changes how liquid accumulates and detaches at the edge. Using rapid forced condensation and high-resolution imaging, we systematically vary groove spacing s, aspect ratio d/w, and orientation. We then analyse how these geometric parameters influence the formation, stability, and spatial organization of droplets hanging below the edge. Smooth substrates exhibit irregular, impact-driven detachment. Grooved substrates produce localized and steady dripping points. When grooves converge, dripping occurs at fixed, geometry-defined locations. For convergent designs, a simple condensation-capillarity model captures the dependence of the dripping period on the area of the drainage basin. Together, these results demonstrate that geometry alone can transform stochastic edge dripping into spatially organized and temporally regular release, with implications for dew harvesting, passive cooling, and millifluidic transport.
Water flowing down vertical surfaces is a familiar sight in rainy climates, yet beneath this simplicity lies a remarkable diversity of morphologies. Depending on surface affinity and flow rate, water can appear as isolated droplets [1,2], narrow rivulets [3,4], or continuous films [5][6][7]. These behaviors have been widely explored on different surfaces, from wide flat panes [3,8] to cones [9,10] and fibers [11][12][13][14][15][16], revealing how geometry and wetting properties shape drainage.
However, one region of these vertical surfaces has received far less attention: the lower edge, where the downward flow meets an abrupt discontinuity [17,18]. At this boundary, water release depends on both the shape of the incoming liquid and the surface geometry [19][20][21][22]. A droplet may stick to the edge, a rivulet may cling and drip, and a film may shatter [23]. Despite its prevalence in both natural and engineered systems, the transition from surface transport to detachment at an edge remains poorly studied [24]. This question becomes critical under condensation, where water forms continuously and must be removed efficiently [25][26][27]. In dew collectors and heat exchangers, the fate of condensed water at the lower edge influences both retention and efficiency. Surface structuring offers a way to influence this process. Grooves are known to influence liquids in both static and dynamic ways. Statically, they pin contact lines [28,29], elongate droplets [30,31], and absorb liquid through capillary suction [32][33][34][35]; dynamically, they speed up transport along their length [36], guiding droplets [37,38] or even stretching rivulets into thin films [39]. During condensation, grooves suppress gravitational shedding and draws the liquid into the grooves, allowing drainage within the texture rather than on the surface [40,41].
While grooves reorganize water transport along the vertical face, it remains unknown how this confined flow ultimately transitions into detachment at the lower edge. In particular, it is unclear how groove geometry shapes the moment and location at which condensed water leaves the substrate. Answering this question requires examining the lower edge directly, where groove-fed drainage meets gravity-driven detachment.
The traditional method of forced condensation involves cooling a surface by bringing it into contact with a thermal exchanger. Like condensation forming on a cold water bottle out of the fridge, water condenses when a surface is cooled below the dew point. While reliable, this technique is slow, typically yielding condensation rates around 6 g/m 2 h [41][42][43]. As a result, experiments often require several hours to complete.
Our approach takes the opposite route: instead of cooling the surface, we blow warm, humid air onto a room-temperature substrate, just like breathing on a cold window. Using this method, we achieve rates up to 900 g/m 2 h, 150 times faster, thereby reducing experiment time and enabling multiple tests across a wide range of parameters. Experiments are performed in a climate-controlled chamber at T = 20.0 ± 0.5 • C and relative humidity RH = 65 ± 2%. To generate the humid airflow, we heat a water reservoir to 75 ± 2 • C. Compressed air is injected through a diffuser at the bottom of the reservoir. As it rises, the air warms up through thermal exchange and becomes saturated with water vapor. This warm, moist air exits through four nozzles located on the reservoir lid and flows perpendicularly toward the vertically suspended substrate at a velocity v < 1 m/s (see Figure 1). These velocities are comparable to those occurring in natural dew formation environments [25,44].
The substrate reaches a temperature of T = 45.0 ± 1. Surface structuring is done with a laser cutter (Trotec Speedy 100), producing grooves with spacing s ranging from 0.30 to 10.00 mm, with depth d and width w (specified when appropriate and measured using optical microscopy (Keyence VHX), see inset of Figure 1). A smooth surface (s = 80.00 mm) serves as the reference. Each experiment lasts 50 minutes (3000s) and is repeated three times to ensure reproducibility.
Condensation on a smooth vertical surface proceeds in a well-known sequence. Nucleation begins at material imperfections, which act as preferential sites for droplet formation [46]. Droplets grow first by vapor adsorption and then by coalescence with neighbors. Once a droplet reaches the critical radius R c ≈ 1 mm [40], its weight exceeds the surface retention force, and it starts sliding downward [47,48]. These sliding droplets collect smaller ones along their path [26], rapidly increasing in size. For this reason, we call these drops sweep drops. As they descend, droplets may become unstable and break up into smaller ones due to the Rayleigh-Plateau instability [2,49], limiting their volume and leaving behind a narrow, nearly dry trail of width approximately 2λ wide. This dry wake provides a clean region for renewed nu
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