Modeling of an axisymmetric shape of an equilibrium drop resting on a horizontal plane

The problem of calculating the equilibrium axisymmetric shape of a liquid drop resting on a non-deformable horizontal plane is formulated. For the first time, an equation for the balance of forces acting on a drop in the vertical direction has been obtained, which completes the formulation of the problem under consideration. A high-precision numerical method for solving the formulated nonlinear problem has been developed. The dependence of the wetting angles of drops on variation of the input data of the problem: the chemical composition of the drop, gas pressure, and the strength of additional weak interaction (for example, van der Waals or electrochemical origin) is studied. For drops of small diameters, the possibility of the existence of two solutions is shown, which correspond to significantly different contact angles: in the first solution, the contact angles are less than 90°, and in the second, they are greater than 90°, reaching values of 160° and more. The existence of two equilibrium forms of a small-diameter drop is confirmed by full-scale experiments. Equilibrium forms of droplets of large diameters can exist only in the presence of an additional weak repulsive force between the liquid and the supporting surface, having an intensity of the order of 10–7…10–5 Pa. In this case, for drops of large diameters, there is only one solution.