毛细作用的变分法理论

The variational approach to capillary action

以圆柱形毛细管内壁、毛细管内的液体和气体为研究对象.设毛细管液体的表面为旋转面,写出了系统的自由能(表面能及重力势能)的泛函.使自由能泛函取极值的欧拉方程就是关于附加压强的拉普拉斯公式.泛函取极值时在可动边界(毛细管内壁)上的边界条件就可导出关于接触角的杨氏方程.此二方程是自由能取极值的密不可分的两个必要条件.

By studying the internal wall of columniform capillary, the liquid and gas in it, and regarding the surface of the liquid as the rotational surface, we deduce the free energy functional. When the free energy functional arrives maximum, the Euler equation turns to the Laplace formula of additional pressure, and we also derivate the Young＇s equation by use of the moving boundaries conditions. It is a necessary condition for the two functions at the extremum for free energy functional.