Capillary Condensation - Kelvin Equation

Kelvin Equation

The Kelvin equation can be used to describe the phenomenon of capillary condensation due to the presence of a curved meniscus.

Where...

= equilibrium vapor pressure

= saturation vapor pressure

= mean curvature of meniscus

= liquid/vapor surface tension

= liquid molar volume

= ideal gas constant

= temperature

This equation, shown above, governs all equilibrium systems involving meniscus and provides mathematical reasoning for the fact that condensation of a given species occurs below the saturation vapor pressure (P_v < P_sat) inside a capillary. At the heart of the Kelvin equation is the pressure difference between the liquid and vapor phases, which comes as a contrast to traditional phase diagrams where phase equilibrium occurs at a single pressure, known as P_sat, for a given temperature. This pressure drop is due solely to the liquid/vapor surface tension and curvature of the meniscus, as described in the Young-Laplace equation.

In the Kelvin equation, the saturation vapor pressure, surface tension, and molar volume are all inherent properties of the species at equilibrium and are considered constants with respect to the system. Temperature is also a constant in the Kelvin equation as it is a function of the saturation vapor pressure and vice versa. Therefore, the variables that govern capillary condensation most are the equilibrium vapor pressure and the mean curvature of the meniscus.