Kelvin equation ($\ln (p/p_{\mathrm{sat}})\simeq 2\Gamma v_l/(R{k}_{B}T)$)

In the ideal-vapor, incompressible-liquid capillarity approximation, a spherical droplet of radius $R$ has the displayed equilibrium vapor-pressure relation. Here $v_l$ is liquid volume per molecule, $\Gamma$ is surface tension, and $p_{\mathrm{sat}}$ is the flat-interface saturation pressure at the same temperature. The Young–Laplace equation raises liquid pressure by $2\Gamma /R$, increasing its chemical potential by approximately $2\Gamma v_l/R$. Matching this with the ideal-vapor chemical-potential increase $k_{B}T\ln (p/p_{\mathrm{sat}})$ 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.

Condensation in a wetting confined geometry at a vapor pressure below planar-interface saturation. A concave liquid meniscus has lower equilibrium vapor pressure in the capillarity approximation. Gap size, contact angle and surface adsorption affect the actual onset.