Universal and scaling behavior at the proximity of the solid to the deformable air-water interface

The scaling descriptions of the deformation of the air-water interface due to van der Waals attractive forces induced by a paraboloid shaped solid as well as of the force vs distance behavior are systematically discussed theoretically and experimentally. It is demonstrated that the force-distance curves at the proximity of the solid to the air-water interface without contact satisfy a simple and universal scaling law, which can be useful to help study various systems involved in the deformable interface. Moreover, an analytical solution to the E-L differential equation governing the deformation of the water surface profile is obtained from the scaling relation, and the two length scales that quantitatively evaluate the lateral and longitudinal deformation of the air-water interface respectively are hence determined.