Kelvin方程的一种理论推导

Derivation of the Kelvin Equation

从液滴平衡条件推导出严格意义的Kelvin方程,验证了其在宏观尺度可以转化为经典形式.利用Tolman方程,在考虑表面张力与曲率半径关系的条件下,给出在液体压缩性可忽略时,饱和蒸气压、蒸气密度、蒸气摩尔体积和曲率半径等关系;液体压缩性不可忽略时,得出以等温压缩系数和Tolman长度表示的饱和蒸气压与液滴半径的关系.

The exact Kelvin equation is deduced from the equilibrium condition of liquid drops. It is easily translated into the classical macroscale expression. The relationship between surface tension and curvature radius is a key point in microscale. Use of the Tolman equation allows us to obtain formulae for incompressible liquid drops and this relates the curvature radius to saturation vapor pressure,vapor density,and vapor molar volume. The Kelvin equation for a compressible liquid is also given while the compression coefficient and the Tolman length are introduced into the expression.