Pressure difference between inside and outside of a drop and its critical radius in dropwise condensation

It was proved using the thermodynamic method that the pressure difference between the inside and outside of a liquid drop sitting on a solid surface follows the classical Laplace equation, and this was further validated using the mechanics method. Such a pressure difference depends only on the surface tension of the liquid and the radius of the drop but is independent of the liquid-solid contact angle. Similarly, the critical radius of a drop in dropwise condensation is also independent of the contact angle and can be calculated using the classical Kalvin equation.