Spherical Droplet Deposition—Mechanistic Model

Abstract

In the currently existing physical models of wetting a solid substrate by a liquid drop, the contact angle is determined on the basis of the equilibrium of forces acting tangentially to the wetted surface at any point in the perimeter of the wetted area, ignoring the forces (or their components) acting perpendicular to this area. In the solution shown in the paper, the equilibrium state of forces acting on a droplet was determined based on the minimum mechanical energy that the droplet achieves in the state of equilibrium. This approach allows one to take into account in the model, in addition to the forces tangential to the wetted surface, also forces perpendicular to it (also the force of adhesion), moreover, these may be dispersed forces acting on the entire interface, not on a single point. The correctness of this approach is confirmed by the derived equations concerning the forces acting on the liquid both tangentially and perpendicularly to the wetted surface. The paper also identifies the areas of solutions in which the obtained equilibrium of forces is stable and areas of unstable equilibrium of forces. The solution is formulated both for isothermal and isochoric system. Based on the experimental data accessible in the literature, the condition that has to be met by the droplets (and their surroundings) during measurements performed under gravity conditions was formulated.