The interfacial modulus of a solid surface and the young's equilibrium contact angle using line energy

We review here three theories: The first is for the equilibrium contact angle as a function of line energy; the second is for the force as a function of the Shanahan-de Gennes triple line protrusion; and the third is for the force according to Furmidge and Dussan. The three theories relate to different regimes: The first and third assumes a flat and infinitely rigid surface and second assumes a protrusion of the solid surface at the triple line. We discuss what systems are appropriate for each of the theories. The Shanahan-de Gennes protrusion induced force relates to the onset of the drop motion; the Furmidge-Dussan equation relates to a slowly moving drop or the condition for a drop to stop moving. The contact angle equilibrium relates to a system that is statistically isotropic (the surface is uniform in all orientations and does not have surface deformities or irregularities). We also review the Shanahan-de Gennes approach to find the modulus associated with the deformation of the surface during drop motion.