中文摘要：

本文建立了固体表面上静止液滴的势能方程，根据能量最小化原理，当系统总势能取得最小值时，液滴将处于平衡状态。采用有限元方法，将初始自由液面离散化，通过曲面上节点的虚拟位移，改变自由液面的拓扑结构，使系统总势能取得最小值，从而得到静止液滴的形状。并应用该方法对均质表面和梯度表面能材料表面上的液滴界面进行了数值模拟，得到了均质材料表面和梯度表面能材料表面上静止液滴的界面形状及分布。

英文摘要：

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.