关键词: 自由能最小化, 重心插值配点法, 超铺展

Abstract: The surface shape of the droplets in the vacuum is determined by the principle of surface free energy minimization. In the case of ignoring droplet gravity，the minimum free energy corresponds to the minimum surfacearea of the droplet. We derive the equations satisfied by the minimum surface under fixed volume constraints，and use the linearized iterative method to numerically solve the equation to prove that the surface is spherical. In addition，we prove that if the final thickness of the super-spreading liquid film is constant，the liquid film spreading shape is also determined by the principle of minimum free energy，and its shape is circular.

Key words: free energy minimization, barycentric interpolation collocation method, super-spreading