The Kelvin equation describes the relationship between the vapor pressure of a liquid droplet (or a bubble) and its radius, accounting for the effects of surface tension. It is particularly important in the study of thermodynamics and physical chemistry, especially when dealing with phase transitions and small systems such as droplets and nanoparticles.
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In the ideal-vapor, incompressible-liquid capillarity approximation, a spherical droplet of radius has the displayed equilibrium vapor-pressure relation. Here is liquid volume per molecule, is surface tension, and is the flat-interface saturation pressure at the same temperature. The Young–Laplace equation raises liquid pressure by , increasing its chemical potential by approximately . Matching this with the ideal-vapor chemical-potential increase proves the formula. The liquid contribution from the vapor-pressure change itself is neglected relative to its curvature pressure, and bulk properties are taken independent of radius. A convex small drop therefore requires a higher ambient vapor pressure than a flat interface.