Mathematical modelling of a droplet sitting on super hydrophobic surface with Hertz model

Abstract

In this paper, Hertz contact model is applied to predict the contact area of a water droplet sitting on hydrophobic surface. Unlike Molotskii's model, the volume of the water droplet is treated invariant before and after sitting on the surface. Mathematical model is derived to obtain the contact area of water droplet in the gravitational field. A number of experimental testing has been conducted to verify the established model. The copper sheets treated with the silver nitrate and n-octadecanethiol solutions are utilized as the superhydrophobic surfaces, which have a contact angel 145°. The volume of the water droplets changes to obtain the data of different contact areas and radius. Based on the experimental tests, the parameter α in the analytical model is obtained by least square fitting method. It is demonstrated that the established mathematical model is in good agreement with experimental data for the superhydrophobic surfaces.