Far-field asymptotic behavior of the meniscus and generalized Archimedean buoyancy of a superhydrophobic spherical surface

Most small water-walking arthropods rely on surface tension to maintain flotation, and for those supported by superhydrophobic leg tips piercing the water surface, each contact region can be mechanically approximated as a spherical surface. The resulting meniscus deformation encodes the forces, thereby enabling inference from the liquid surface shape. However, existing methods rely on full-field three-dimensional reconstruction or precise measurement of the contact angle and contact line. This study reveals that the far-field meniscus profile induced by a superhydrophobic spherical surface exhibits an asymptotic behavior: it is dominated by the generalized Archimedean buoyancy and the liquid properties but insensitive to local geometric details and the contact angle. Accordingly, on the basis of this structure and numerical fitting, a practical asymptotic relationship is established that links the far-field meniscus depth to the generalized Archimedean buoyancy. In light of these findings, a method is proposed to infer the buoyancy using the far-field meniscus profile. Furthermore, validation experiments on three superhydrophobic spheres confirm that the method achieves a relative error below 1% within the applicable parameter range.