Kelvin equation

The Kelvin equation was established by Lord Kelvin in 1871 and describes the vapor pressure over a curved surface (also called Kelvin - pressure ).

Calculation

The following applies:

With

• The ( usual ) vapor pressure over a non- curved surface ( Index: = eng vapor steam. )
• The gas constant
• Temperature in K
• Interfacial tension
• The molar volume of the fluid
• The radii of curvature of the surface in two mutually perpendicular trajectories

Drops

The best-known special case of the Kelvin equation describes a drop with radius:

The interfacial tension of a liquid to its vapor pressure increases with decreasing radius. It follows one of the most important consequences of this equation: large droplets have a smaller Kelvin pressure than smaller ones. Therefore, in a mixture of different sized droplets grow on the large drops, while the smaller ones disappear ( Ostwald ripening ). The molecules of the regions of higher pressure areas move into the lower pressure This explains why supersaturated vapor condenses into the liquid phase.

This same equation is also valid for spherical bubbles in liquids. Examples are carbon dioxide bubbles in mineral water bottles, vapor bubbles during boiling of water or evaporation of precursor molecules in bubblers in CVD and CVS.

Cylindrical pore

Another special case of the Kelvin equation is valid for a wetted with liquid cylindrical pore with radius

Derivation

The Kelvin equation can be derived from the equations of state of equilibrium thermodynamics under various approximations; in particular the liquid phase is treated as an incompressible fluid and the gaseous phase as an ideal gas. Furthermore, it is believed that the surface tension and curvature, determined by the difference of pressure in the interior and outer drop is much greater than the difference between Kelvin - pressure and steam pressure (). Detailed derivations can be found in