Theoretical analysis on the effect of liquid droplet geometry on contact angle

This paper is concerned with the development of a first-principle theoretical method to explain the dependence of contact angle on the size of liquid droplets on smooth solid substrates. It has been shown that the contact angle for axisymmetric droplets is size-dependent and, consequently, cannot satisfy the original Young equation. However, this contact angle can be theoretically deduced for any droplet material and mass as a function of the asymptotic contact angle (the limiting value of the contact angle as droplet size decreases). The proposed approach is based on the fact that the two major forces acting on a droplet, that is, the surface force and the gravity force, are independent of each other. It has been demonstrated that for sessile droplets on smooth surfaces, the contact angle can be uniquely determined for given droplet mass (or volume) and liquid/solid/gas properties.