Force acting along a line on the liquid surface

Measured in newtons per meter (N/m) or dynes per centimeter (dyn/cm). If you imagine a frame with a movable side in contact with a liquid film, surface tension is the force pulling on that side divided by its length. This is the mechanical definition.

Formula: γ = F/L where F = force, L = length of the edge

Example: Water @ 20°C = 72.8 mN/m means 0.0728 N of force per meter of edge

Energy required to create new surface area

Measured in joules per square meter (J/m²) or ergs per square centimeter (erg/cm²). Creating new surface area requires work against intermolecular forces. Numerically identical to surface tension but represents the energy perspective rather than force perspective.

Formula: γ = E/A where E = energy, A = surface area increase

Example: Water @ 20°C = 72.8 mJ/m² = 72.8 mN/m (same number, dual interpretation)

Intermolecular forces determine surface behavior

Cohesion: attraction between like molecules (liquid-liquid). Adhesion: attraction between unlike molecules (liquid-solid). High cohesion → high surface tension → droplets bead up. High adhesion → liquid spreads (wetting). The balance determines contact angle and capillary action.

Contact angle θ: cos θ = (γ_SV - γ_SL) / γ_LV (Young's equation)

Example: Water on glass has low θ (adhesion > cohesion) → spreads. Mercury on glass has high θ (cohesion >> adhesion) → beads up.

First quantitative experiments on surface tension

German physicist Segner studied floating needles and observed that water surfaces behave like stretched membranes. He calculated forces but lacked molecular theory to explain the phenomenon.

Young's equation for contact angle

British polymath Young derived the relationship between surface tension, contact angle, and wetting: cos θ = (γ_SV - γ_SL)/γ_LV. This fundamental equation is still used today in materials science and microfluidics.

Young-Laplace equation for pressure

Laplace derived ΔP = γ(1/R₁ + 1/R₂) showing that curved interfaces have pressure differences. Explains why small bubbles have higher internal pressure than large ones—critical for understanding lung physiology and emulsion stability.

Molecular theory of surface tension

Dutch physicist van der Waals explained surface tension using intermolecular forces. His work on molecular attraction earned the 1910 Nobel Prize and laid groundwork for understanding capillarity, adhesion, and the critical point.

Monolayers and surface chemistry

Langmuir studied molecular films on water surfaces, creating the field of surface chemistry. His work on surfactants, adsorption, and molecular orientation earned the 1932 Nobel Prize. Langmuir-Blodgett films are named after him.

Surface tension determines wetting, spreading, and adhesion:

• Paint formulation: Adjust γ to 25-35 mN/m for optimal spreading on substrates
• Ink-jet printing: Ink must have γ < substrate for wetting (typical 25-40 mN/m)
• Corona treatment: Increases polymer surface energy from 30 → 50+ mN/m for adhesion
• Powder coatings: Low surface tension helps leveling and gloss development
• Anti-graffiti coatings: Low γ (15-20 mN/m) prevents paint adhesion
• Quality control: Du Noüy ring tensiometer for batch-to-batch consistency

Detergents work by reducing surface tension:

• Pure water: γ = 72.8 mN/m (doesn't penetrate fabrics well)
• Water + soap: γ = 25-30 mN/m (penetrates, wets, removes oil)
• Critical Micelle Concentration (CMC): γ drops sharply until CMC, then plateaus
• Wetting agents: Industrial cleaners reduce γ to <30 mN/m
• Dishwashing liquid: Formulated to γ ≈ 27-30 mN/m for grease removal
• Pesticide sprayers: Add surfactants to reduce γ for better leaf coverage

Interfacial tension between oil and water affects extraction:

• Oil-water interfacial tension: Typically 20-50 mN/m
• Enhanced oil recovery (EOR): Inject surfactants to reduce γ to <0.01 mN/m
• Low γ → oil droplets emulsify → flow through porous rock → increased recovery
• Crude oil characterization: Aromatic content affects surface tension
• Pipeline flow: Lower γ reduces emulsion stability, aids separation
• Pendant drop method measures γ at reservoir temperature/pressure

Surface tension is critical for life processes:

• Lung surfactant: Reduces alveolar γ from 70 to 25 mN/m, preventing collapse
• Premature infants: Respiratory distress syndrome due to insufficient surfactant
• Cell membranes: Lipid bilayer γ ≈ 0.1-2 mN/m (very low for flexibility)
• Blood plasma: γ ≈ 50-60 mN/m, increased in disease (diabetes, atherosclerosis)
• Tear film: Multi-layer structure with lipid layer reducing evaporation
• Insect respiration: Tracheal system relies on surface tension to prevent water entry

Water striders (Gerridae) exploit water's high surface tension (72.8 mN/m) to support 15× their body weight. Their legs are coated with waxy hairs that are superhydrophobic (contact angle >150°). Each leg creates a dimple in the water surface, and surface tension provides the upward force. If you add soap (reducing γ to 30 mN/m), they sink immediately!

Surface tension acts to minimize surface area for a given volume. The sphere has the minimum surface area for any volume (isoperimetric inequality). Soap bubbles demonstrate this beautifully: the air inside pushes outward, surface tension pulls inward, and equilibrium creates a perfect sphere. Non-spherical bubbles (like cubic ones in wire frames) have higher energy and are unstable.

Newborn lungs contain pulmonary surfactant (phospholipids + proteins) that reduces alveolar surface tension from 70 to 25 mN/m. Without it, alveoli collapse during exhalation (atelectasis). Premature infants lack sufficient surfactant, causing Respiratory Distress Syndrome (RDS). Before synthetic surfactant therapy (1990s), RDS was a leading cause of neonatal death. Now, survival rates exceed 95%.

Pour wine in a glass and watch: droplets form on the sides, climb upward, and fall back down—the 'tears of wine.' This is the Marangoni effect: alcohol evaporates faster than water, creating surface tension gradients (γ varies spatially). Liquid flows from low-γ to high-γ regions, pulling wine upward. When droplets get heavy enough, gravity wins and they fall. Marangoni flows are critical in welding, coating, and crystal growth.

Soap molecules are amphiphilic: hydrophobic tail (hates water) + hydrophilic head (loves water). In solution, tails stick out of the water surface, disrupting hydrogen bonding and reducing γ from 72 to 25-30 mN/m. At the Critical Micelle Concentration (CMC), molecules form spherical micelles with tails inside (trapping oil) and heads outside. This is why soap removes grease: oil is solubilized inside micelles and washes away.

Drop a camphor crystal on water and it zooms around the surface like a tiny boat. Camphor dissolves asymmetrically, creating a surface tension gradient (higher γ behind, lower ahead). The surface pulls the crystal toward high-γ regions—a surface tension motor! This was demonstrated by physicist C.V. Boys in 1890. Modern chemists use similar Marangoni propulsion for microrobots and drug delivery vehicles.

This is a fundamental thermodynamic relationship, not a coincidence. Dimensionally: [N/m] = (kg·m/s²)/m = kg/s² and [J/m²] = (kg·m²/s²)/m² = kg/s². They have identical base dimensions! Physically: creating 1 m² of new surface requires work = force × distance = (γ N/m) × (1 m) × (1 m) = γ J. So γ measured as force/length equals γ measured as energy/area. Water @ 20°C: 72.8 mN/m = 72.8 mJ/m² (same number, dual interpretation).

Cohesion: attraction between like molecules (water-water). Adhesion: attraction between unlike molecules (water-glass). High cohesion → high surface tension → droplets bead up (mercury on glass). High adhesion relative to cohesion → liquid spreads (water on clean glass). The balance determines contact angle θ via Young's equation: cos θ = (γ_SV - γ_SL)/γ_LV. Wetting occurs when θ < 90°; beading when θ > 90°. Superhydrophobic surfaces (lotus leaf) have θ > 150°.

Soap molecules are amphiphilic: hydrophobic tail + hydrophilic head. At the water-air interface, tails orient outward (avoiding water), heads orient inward (attracted to water). This disrupts hydrogen bonding between water molecules at the surface, reducing surface tension from 72.8 to 25-30 mN/m. Lower γ allows water to wet fabrics and penetrate grease. At Critical Micelle Concentration (CMC, typically 0.1-1%), molecules form micelles that solubilize oil.

Higher temperature gives molecules more kinetic energy, weakening intermolecular attractions (hydrogen bonds, van der Waals forces). Surface molecules have less net inward pull → lower surface tension. For water: γ decreases ~0.15 mN/m per °C. At the critical temperature (374°C for water, 647 K), liquid-gas distinction disappears and γ → 0. Eötvös rule quantifies this: γ·V^(2/3) = k(T_c - T) where V = molar volume, T_c = critical temperature.

Four main methods: (1) Du Noüy ring: Platinum ring pulled from surface, force measured (most common, ±0.1 mN/m). (2) Wilhelmy plate: Thin plate suspended touching surface, force measured continuously (highest precision, ±0.01 mN/m). (3) Pendant drop: Drop shape analyzed optically using Young-Laplace equation (works at high T/P). (4) Capillary rise: Liquid climbs narrow tube, height measured: γ = ρghr/(2cosθ) where ρ = density, h = height, r = radius, θ = contact angle.

ΔP = γ(1/R₁ + 1/R₂) describes the pressure difference across a curved interface. R₁, R₂ are principal radii of curvature. For a sphere (bubble, droplet): ΔP = 2γ/R. Small bubbles have higher internal pressure than large ones. Example: 1 mm water droplet has ΔP = 2×0.0728/0.0005 = 291 Pa (0.003 atm). This explains why small bubbles in foam shrink (gas diffuses from small to large) and why lung alveoli need surfactant (reduces γ so they don't collapse).

Mercury: Strong cohesion (metallic bonding, γ = 486 mN/m) >> weak adhesion to glass → contact angle θ ≈ 140° → beads up. Water: Moderate cohesion (hydrogen bonding, γ = 72.8 mN/m) < strong adhesion to glass (hydrogen bonds with surface -OH groups) → θ ≈ 0-20° → spreads. Young's equation: cos θ = (γ_solid-vapor - γ_solid-liquid)/γ_liquid-vapor. When adhesion > cohesion, cos θ > 0, so θ < 90° (wetting).

No. Surface tension is always positive—it represents the energy cost to create new surface area. Negative γ would mean surfaces spontaneously expand, violating thermodynamics (entropy increases, but bulk phase is more stable). However, interfacial tension between two liquids can be very low (near-zero): in enhanced oil recovery, surfactants reduce oil-water γ to <0.01 mN/m, causing spontaneous emulsification. At the critical point, γ = 0 exactly (liquid-gas distinction disappears).