Wettability model for various-sized droplets on solid surfaces

The wetting phenomenon is crucial for the formation of stable liquid films on solid surfaces. The wettability of a liquid on a solid surface is characterized by the Young equation, which represents an equilibrium condition of a droplet at the three phase contact line. In general, the surface force in the vertical direction on a solid surface is ignored because of the resistance of the solid surface. However, considering the adhesion energy of the droplet rather than the force balance at the contact line, the vertical component of the surface force can be expected to be an important factor during wetting. Based on this concept, an analytical model is developed herein by considering the energy balance including adhesion forces acting not only in the horizontal but also in the vertical direction, in addition to the effect of gravity on the droplet. The validity of the developed model is then evaluated by experimental observation of the wetting phenomena of droplets on low- and high-surface-energy solids. Existing data are also used for evaluation of our model. The developed model describes the wetting phenomena of droplets with sizes ranging from nano- to millimeters under all experimental conditions and exhibits universality. In addition, on the basis of our model, the line tension is discussed. The results indicate that the line tension approach may be considered as a method to explain wetting phenomena by considering gravitational potential and other macroscopic parameters as a single parameter (i.e., line tension).