Geometrical-Optical Determination of the Apparent Contact Angle of Sessile Water Drops: A Multiscale Perspective on Hydrogen-Bond Cooperativity

Water exhibits unique interfacial properties that arise from the collective organization of its hydrogen-bond network. Establishing clear links between molecular-scale interactions and macroscopic observables remains a central challenge in understanding the behavior of liquid water. In this work, we combine experimental measurements of the contact angle of sessile water drops with quantum-chemical modeling of small water clusters (H2O)n (n = 2–6) to explore multiscale effects of hydrogen-bond cooperativity. The cluster calculations reveal a nonlinear, saturating evolution of hydrogen-bond geometries with increasing cluster size, reflecting the onset of cooperative many-body effects. Experimentally, the evolution of the apparent contact angle during evaporation is quantified using both conventional geometry and a non-invasive geometrical-optical method based on analysis of the dark refractive ring, which provides independent validation against conventional goniometric measurements. The evaporation dynamics are further interpreted within the diffusion-limited framework of the Popov model, indicating that the temporal evolution of the apparent contact angle is primarily consistent with geometry-controlled mass loss under diffusion-limited conditions, rather than requiring variations in intrinsic surface energy. By combining macroscopic contact-angle measurements with molecular-level cluster analysis, this study offers a qualitative multiscale perspective in which minimal cooperative hydrogen-bond motifs provide molecular context for interpreting interfacial behavior, without implying direct quantitative prediction of macroscopic interfacial observables.