Membrane Tension & Laplace Pressure
Pressure balance across curved interfaces: ΔP = γ(1/R₁ + 1/R₂)
Young-Laplace Equation: The pressure difference across a curved interface is ΔP = γ(1/R₁ + 1/R₂), where R₁ and R₂ are the principal radii of curvature and γ is surface tension. For a sphere: R₁=R₂=R, so ΔP=2γ/R (soap bubble gets 4γ/R for two surfaces). For a cylinder: R₁=r, R₂=∞, so ΔP=γ/r. For a saddle surface: opposite curvatures can cancel — a minimal surface has ΔP=0 (e.g., soap films spanning a wire frame). This drives capillary rise, droplet formation, and membrane vesicle shapes.