ΔP = 2γ/r (sphere) or ΔP = 4γ/r (soap bubble)
The Young-Laplace equation ΔP = γ(1/R₁ + 1/R₂) describes the pressure difference across a curved interface due to surface tension. For a sphere: ΔP = 2γ/r. For a soap bubble (two air-liquid interfaces): ΔP = 4γ/r. Smaller bubbles have higher internal pressure, which is why small bubbles inflate large ones when connected (Ostwald ripening). For water (γ = 72.8 mN/m): a 1 μm droplet has ΔP ≈ 1.46 atm. This explains capillary rise: h = 2γcosθ/(ρgr). Applications: lung mechanics (alveolar surfactant reduces γ from 72 to ~25 mN/m, preventing collapse), inkjet printing, emulsion stability, foam science, and microfluidics. The contact angle θ determines wetting behavior: θ < 90° = hydrophilic, θ > 90° = hydrophobic.