Numerical simulation for drop shape on the surface with gradient surface energy

A potential formulation was established for the system of a static drop on solid surface. Base on the minimum energy principle, the shape of static drop on the homogenous solid surface and the solid surface with gradient surface energy was numerically simulated by using the finite element method, respectively. The numerical method was proposed to obtain the equilibrium shape of the free surface of static drop on the solid surface. The numerical results show that the equilibrium shape of static drop on the homogenous surface behaves as an axially symmetric shape and the drop on the solid surface with a larger contact angle has a larger altitude and a smaller liquid-solid contact surface area for a constant drop size. The drop on the surface with gradient surface energy has an asymmetric shape along the direction of surface energy gradient, the contact angle at the rear of drop being significantly larger than the one at the front of drop close to the hydrophilic side. A large surface energy gradient leads to a larger extension of drop and smaller altitude of drop for a fixed drop size.