Experimental and interfacial model investigation of droplet impact on dual-roughness surfaces

Surfaces with abrupt transitions in roughness are found in patterned coatings and other functional interfaces, but the influence of such junctions on droplet impact spreading remains insufficiently quantified. This study investigates dyed water droplets with an initial diameter of 3.8 mm impacting normally at the junction of chemically etched glass surfaces containing a smooth region and a rough region. The experiments cover Weber numbers from 104 to 416. The nominally smooth region has an areal mean roughness of 0.445 µm, while the rough regions have areal mean roughness values of 3.914, 5.341, and 7.351 µm. Comparisons with the corresponding homogeneous single-roughness surfaces show asymmetric spreading at the junction, and the departure from homogeneous-surface behavior is observed to extend into the nominally smooth region. The maximum spreading response varies non-monotonically with the nominal roughness contrast. Among the tested configurations, the surface combining a rough-side roughness of 5.341 µm with a smooth-side roughness of 0.445 µm gives the highest measured mean response at all four Weber numbers. This behavior is consistent with a competition among inertial spreading, directional suppression associated with the etched surface contrast, and differences in apparent static wettability. The intermediate-roughness configuration shows the largest apparent static-wettability difference. A reduced semi-empirical model is developed to predict the maximum spreading along the junction and the average spreading perpendicular to it. For the twelve dual-roughness condition means used for calibration, the mean absolute percentage errors are 1.42 percent for spreading along the junction and 1.84 percent for spreading perpendicular to it. These results provide a quantitative description of maximum droplet spreading across abrupt surface contrasts within the investigated parameter range and may inform the design of functional surfaces for directional liquid transport.