球形液滴表面形状形成与自由能最小化原则关系的证明

Proof of the relationship between the shape of the spherical droplet surface and the principle of free energy minimization

真空中的液滴表面形状由表面自由能最小化原则所决定.忽略液滴重力的情况下,最小自由能对应于液滴最小表面积.我们推导出固定体积约束下的最小曲面所满足的方程,并运用线性化迭代法数值求解方程,从而证明该曲面为球面.此外,我们证明在超铺展效应中,当液膜的最终厚度一定时,液膜铺展形状也是由最小自由能原则决定,其形状为圆形.

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 surface area 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.