Trapezoidal Microstructure-Mediated Antagonistic Regulation of Liquid-Bridge Capillary Force and Wetting Stability

Precise control of liquid-bridge mechanical behavior and rupture is foundational to microdroplet manipulation in microfluidics and MEMS. However, the quantitative mechanism by which solid-surface microstructures regulate liquid-bridge wetting states, liquid-bridge capillary forces, and post-rupture adhesion has not been clarified. Based on the Gibbs free energy minimization principle, we derive a unified analytical model of the liquid-bridge capillary force that incorporates three typical wetting states (Young, Cassie, and Wenzel), which is evaluated through comparison with VOF simulations implemented in ANSYS Fluent. The results reveal that the geometric parameters of trapezoidal microstructures (top width, bottom width, height, and spacing) exert antagonistic regulation on liquid-bridge wetting stability and liquid-bridge capillary force: increasing the top width and height of microstructures or decreasing the bottom width and representative unit size enhances Cassie-state stability while modulating the liquid-bridge capillary force in an opposite trend. Cassie-state liquid bridges rupture at the solid-liquid interface without residual droplets, whereas Wenzel-state bridges undergo central rupture with significant liquid retention. Asymmetric pinning of the liquid-gas interface on microstructured surfaces is identified as the primary factor causing minor discrepancies between theoretical predictions and simulation results. This work establishes a unified framework for liquid-bridge behavior on textured surfaces and offers preliminary design insights for droplet manipulation, transport, and breakup control in microfluidic and interfacial engineering systems.