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假设重力的影响可以忽略,以气相中圆球形液滴作为参考状态,则对于光滑固体水平面上的球缺形液滴来说,其相对界面自由能F_(rel)与气-液界面和固-液界面通过液体内部的夹角θ(0°<θ≤180°)之间的函数关系为: F_(rel)=1/((4~(1/3)(1-cosθ)~(1/3)(2+cosθ)~(2/3))[2-((γ12-γ23)/γ13)(1+cosθ)] 根据物系的界面自由能自发地趋向于最低的热力学原理,证明了在三个界面张力各种可能组合的情况下,平衡时角θ与它们之间的关系.在1>(γ12-γ23)/γ13>-1范围内,当角θ满足cosθ=(γ12-γ23)/γ13时,物系的界面自由能最低,于是导出了Young氏方程。按照相对界面自由能函数公式,计算了(γ12-γ23)/γ13分别等于2、1、0.5、0、-0.5、-1和-2时,角θ自0°至180°每间隔10°时的F_(rel)值,并绘出了相对界面自由能曲线。
Assuming that the influence of gravity is negligible, taking the spherical droplet in the gas phase as a reference state, the relative free energy F rel for the spherical droplet on the smooth solid surface is proportional to the gas-liquid interface and the solid- The relationship between the liquid interface through the liquid inside angle θ (0 ° <θ ≦ 180 °) is: F rel 1/4 ~ 1/3 (1 - cos θ ~ 1 / 3) (2 + cos θ) ~ (2/3)) [2 - ((γ12 -γ23) / γ13) (1 + cosθ) According to the thermodynamic principle that the interface free energy of a species spontaneously tends to the lowest, When the three interfacial tensions are all possible combinations, the relationship between the angle θ and the angle between them is balanced. When the angle θ satisfies the relationship of cos θ = (γ12-γ23) within the range of 1> (γ12-γ23) / γ13> -1 ) / γ13, the Young’s equation is derived. According to the formula of relative free energy function, (γ12-γ23) / γ13 is equal to 2,1,0.5,0, -0.5, -1 and -2, the angle θ is from 0 ° to 180 ° at every 10 ° F_ (rel), and the relative interfacial free energy curve is plotted.