Numerical simulation of two-phase droplets on a curved surface using Surface Evolver

In this paper, we present a new approach for using the Surface Evolver (SE) finite element program to simulate the 3-D shape of a droplet on a curved surface. The approach proposed in this paper circumvents the need for carrying out complicated derivations to obtain analytical expressions for the total energy of the interfacial areas between air, liquid, and solid surfaces. More specifically, we use the solid-liquid surface energy in place of the contact angle when simulating a droplet using SE. This approach also makes it easier to use SE to model a twophase droplet (e.g., a compound droplet) on a solid surface. To better illustrate our approach, the 3-D shape of single-phase and compound pendant droplets are simulated on a hydrophobic spherical surface in the presence of gravitational and magnetic fields. For validation purposes, our computational results are compared to dedicated experimental data obtained by compounding water droplets with oil-based ferrofluids of different surface tensions.