Inclination-Induced Interfacial Asymmetry and Tangential Force Balance of Bubbles Pinned at Wetting-Step Boundaries

Bubble growth on inclined surfaces is governed by the coupling among buoyancy, interfacial deformation, and three-phase contact-line constraint. Here, we experimentally investigate quasi-static bubble growth and detachment on superhydrophobic substrates patterned with a circular wetting-step line, which pins the three-phase contact line throughout the prenecking stage. Increasing substrate inclination shortens the detachment period while maintaining cycle-to-cycle coefficients of variation below 2%. Because lateral contact-line motion is suppressed, the substrate-parallel component of buoyancy produces both inclination-dependent global shape deformation and progressively stronger lateral asymmetry, characterized by a higher aspect ratio at a given normalized growth stage and a larger lateral offset of the projected bubble centroid, respectively. The apparent contact-angle distribution also becomes asymmetric: the upslope advancing-side angle decreases during growth, whereas the downslope receding-side angle remains comparatively high, causing the apparent contact-angle difference to increase throughout the prenecking stage. A quasi-static tangential force balance, formulated using the resultant capillary traction along the pinned circular boundary, quantitatively relates the dimensionless tangential load to the measured contact-angle asymmetry. A zero-intercept regression yields an effective retention coefficient of 0.8683 with R2 = 0.9989, while the coefficients evaluated separately at each nonzero inclination differ from the global regression value by less than 4% and exhibit no monotonic dependence on inclination. These results establish a reduced interfacial-mechanics description of the critical prenecking state under geometric contact-line constraint and clarify how inclination-induced tangential buoyancy is accommodated through coupled interfacial and apparent-contact-angle asymmetry, providing a mechanistic basis for regulating bubble growth and release on wettability-patterned surfaces.