Laplace's Law

the dependence of the hydrostatic pressure drop Δp at the boundary surface between two phases (liquid-liquid, liquid-gas, or liquid-vapor) on the interphase surface tension σ and the mean curvature ∊ of the surface at a given point: Δp = P₁ — P₂ = ∊σ, where p₁ is the pressure on the concave side of the surface, p₂ is the pressure on the convex side, and ∊ = 1/R₁ + 1/R₂ where R₁ and R₂ are the radii of curvature in two mutually perpendicular normal sections of the surface at the given point (see Figure 1).

Figure 1. Example of application of Laplace’s law to water vapor interface in a capillary: Δ_p = p₁— p₂. R₁, and R₂, the radii of curvature at point 0 of the concave surface (R₁, = OA and R₂ = OB), are determined in two mutually perpendicular sections ACD and BEF.

The Laplace law, established in 1806 by P. Laplace, determines the magnitude of the capillary pressure, and thereby makes it possible to write down the conditions of mechanical equilibrium for movable (liquid) interfaces.