text: The earliest study on the relationship between contact angle and surface tensions for sessile droplets on flat surfaces was reported by Thomas Young in 1805. A century later Gibbs proposed a modification to Young's equation to account for the volumetric dependence of the contact angle. Gibbs postulated the existence of a line tension, which acts at the three-phase boundary and accounts for the excess energy at the confluence of the solid-liquid-gas phase interface, and is given as:
  where  is the line tension in Newtons and  is the droplet radius in meters.  Although experimental data validates an affine relationship between the cosine of the contact angle and the inverse line radius, it does not account for the correct sign of  and overestimates its value by several orders of magnitude.