Preprint derives universal relation linking contact-angle asymmetry to external force via free-energy minimization

The authors minimize a forcing-dependent free-energy functional to obtain the asymmetry response, then define its zero-force derivative as a material-independent susceptibility. This yields an explicit linear-to-quadratic relation between asymmetry and force that collapses data from water, oils, and polymer solutions on surfaces spanning 20° to 110° hysteresis. Experiments used sessile-drop tilting and electrowetting, covering Bond numbers 0.1–3.0 and volumes 1–50 µL, confirming the predicted slope within 6 % across 180 trials.

Prior models treated advancing and receding angles as independent constants; the new relation shows they are coupled through a single energy landscape, explaining why retention force scales with hysteresis yet saturates at high forcing. Industrial coating and inkjet processes lose 15–30 % efficiency from uncontrolled pinning; the constitutive curve supplies a predictive design rule rather than empirical calibration.

Medical applications include precise control of liquid-metal droplets in vascular imaging and aerosol deposition in pulmonary drug delivery, where force thresholds determine retention versus mobilization. The main limitation is restriction to quasi-static conditions; dynamic contact-line motion at capillary numbers above 10^-3 remains untested. A follow-up high-speed imaging campaign on 500 droplets would strengthen claims for industrial translation.

Next steps include embedding the relation into lattice-Boltzmann simulations for complex geometries and testing on textured superhydrophobic surfaces to check universality beyond smooth substrates.