Relationship between contact angle and contact line radius for micro to atto [10-6 to 10-18] liter size oil droplets

Contact angles of liquids on surfaces characterize wettability and have been studied extensively, especially for sessile droplets on flat surfaces. Continuum models that incorporate the contact line energy into Young's equation predict a linear dependence between the cosine of the contact angle and the inverse line radius. Experimental evidence for non-volatile nanodroplets suggests a non-linear relationship. At these dimensions (femto and atto liter sized droplets), experimental evidence suggests a flattening of the curve which can be explained by the addition of internal Laplace pressures. This, in turn, indicates that the contact angle for ultra small droplets is less than that measured for macro droplets. (C) 2017 Elsevier B.V. All rights reserved.