YoungLaplaceGesetz

YoungLaplaceGesetz (Young–Laplace law) is the physical relation that links the pressure difference across a curved fluid interface to the interface's surface tension and curvature. It is named after Thomas Young and Pierre-Simon Laplace, who formulated the concepts in the early 19th century. The law is commonly written as ΔP = γ(1/R1 + 1/R2), where ΔP is the pressure inside minus outside the interface, γ is the surface tension, and R1 and R2 are the principal radii of curvature. Equivalently, ΔP = 2γH with H the mean curvature.

The Young–Laplace law explains why small droplets and bubbles have higher internal pressure than the surrounding medium and governs the shape of menisci in contact with solids. Special cases include a spherical surface (ΔP = 2γ/R) and a cylindrical surface (ΔP = γ/R). The relation follows from a force or energy balance that minimizes surface free energy for a given volume.

Applications span fluid mechanics, capillarity, materials science and physiology (for example, understanding lung alveoli behavior and the role of pulmonary surfactant). Limitations include neglect of gravity, dynamic effects, contact-line friction, complex rheology, and molecular-scale interactions; corrections are needed for very small length scales or non-ideal surfaces. The Young–Laplace law remains a fundamental tool for analyzing interfaces in both natural and engineered systems.