Young Equation

Surface tension and the Young–Laplace equation

Surface tension γ is the force per unit length acting along a liquid's surface (N/m), and it comes from cohesive forces that don't cancel out at the interface. The Young–Laplace equation ties the pressure jump across a curved interface to γ and the radii of curvature: ΔP = γ·(1/R₁ + 1/R₂). A spherical droplet gives ΔP = 2γ/r, while a cylinder gives ΔP = γ/r. Some reference values at 20 °C: water sits at γ = 72.8 mN/m, mercury at 485 mN/m (so high it beads into round droplets) and ethanol at just 22 mN/m. Surfactants such as soap and detergents knock γ down sharply. As an example, a water droplet of 1 mm radius carries an internal overpressure of ΔP = 2·0.0728/0.001 ≈ 146 Pa.

Applications

Formulating detergents and shampoos, where lowering γ helps "wet" surfaces. Cosmetics. Agricultural spraying, where adjuvants boost leaf coverage. Pulmonary mechanics, since lung surfactant keeps alveoli from collapsing, and its absence brings on respiratory distress syndrome in premature infants. Then microfluidics, ink-jet printing and inkjet droplet formation.

FAQ

Why does mercury form beads and water spreads? Mercury has a very high γ and barely sticks to most surfaces, so cohesion wins over adhesion. Water carries a lower γ and wets clean glass nicely, because its adhesion to silica beats its own cohesion.

How does soap lower surface tension? Surfactant molecules carry a hydrophilic head and a hydrophobic tail. They crowd the interface and break up the hydrogen bonding between water molecules, which pulls γ down from about 72 to roughly 30 mN/m.

Does temperature affect γ? It does. γ falls off roughly linearly as temperature rises. Water goes from 75.6 mN/m at 0 °C down to 58.9 mN/m at 100 °C, and near the critical point γ drops all the way to zero.