Surface Tension

Have you ever watched a water strider glide across a pond without sinking, or noticed how a needle can float on still water even though steel is far denser than water? These phenomena arise from surface tension — a force that acts along the surface of a liquid, pulling the surface taut like an invisible elastic film. Surface tension is not magic; it emerges directly from the intermolecular forces between liquid molecules and is one of the most elegant examples of microscopic interactions producing macroscopic, visible effects. Inside a liquid, every molecule is surrounded on all sides by neighbours, so the attractive forces — van der Waals forces or hydrogen bonds in water's case — cancel out in all directions. A molecule sitting right at the surface, however, has neighbours below and to the sides but almost none above (only a thin layer of vapour). The net force on a surface molecule is therefore directed inward, into the bulk of the liquid. This inward pull means the surface behaves as if it is under tension: it resists being stretched and will contract to the smallest possible area for a given volume. That is why free-falling water droplets form spheres — a sphere has the minimum surface area for its volume. Surface tension is quantified in two complementary ways: as a force per unit length (γ, in N/m) acting along the surface, or as surface energy per unit area (J/m²). These two descriptions are mathematically identical because 1 N/m = 1 J/m², and they reflect the same physical reality from different perspectives. Surface tension decreases as temperature rises because thermal energy disrupts intermolecular cohesion. For water at 20 °C, γ ≈ 0.0728 N/m — small by everyday standards, but entirely sufficient to support small insects or produce capillary rise in narrow tubes.

Key takeaways
  • Molecular Origin: Cohesion and the Surface Layer
  • Surface Tension as Force per Unit Length
  • Surface Energy Equivalence
  • Excess Pressure Inside Curved Surfaces
  • Contact Angle and Wetting
  • Capillary Rise

Molecular Origin: Cohesion and the Surface Layer

Every molecule in a liquid experiences cohesive forces from its neighbours. In the bulk, these forces are isotropic — they cancel. At the surface, the net force is inward (toward the bulk). This asymmetry means energy is required to bring molecules from the interior to the surface, so the surface possesses excess potential energy per unit area, called surface energy.

Surface Tension as Force per Unit Length

Imagine a thin soap film stretched across a rectangular wire frame, with one side free to slide. The film pulls the sliding wire inward with a force F. If the wire has length L, then the surface tension is γ = F / (2L). The factor of 2 appears because the soap film has two surfaces (front and back). This definition makes γ a force per unit length measured perpendicular to any line drawn on the surface.

Surface Energy Equivalence

If you pull the sliding wire outward by a small distance dx, increasing the film area by dA = 2L·dx, the work done is W = F·dx = γ·2L·dx = γ·dA. Therefore γ = W/dA, showing that surface tension equals the energy needed to create one square metre of new surface. The units N/m and J/m² are numerically identical — both descriptions are equally valid.

Excess Pressure Inside Curved Surfaces

A curved liquid surface — such as a spherical droplet or bubble — has higher pressure inside than outside. For a liquid droplet of radius R, the excess pressure is ΔP = 2γ/R (two surfaces contribute for a soap bubble: ΔP = 4γ/R). This is the Young–Laplace equation in its simplest spherical form. Small bubbles have large internal pressure; large bubbles have small internal pressure — which is why small bubbles in foam are absorbed by larger ones.

Contact Angle and Wetting

When a liquid meets a solid surface, the equilibrium shape is determined by the balance between cohesion (liquid–liquid attraction) and adhesion (liquid–solid attraction). The contact angle θ is measured through the liquid at the liquid–solid–vapour boundary. If θ < 90°, the liquid wets the surface (water on glass). If θ > 90°, the liquid beads up (mercury on glass). Young's equation relates the contact angle to the three interfacial tensions: γ_SV = γ_SL + γ_LV cos θ.

Capillary Rise

In a tube of small radius r, surface tension pulls the liquid upward along the walls (for a wetting liquid). The liquid rises until the upward surface-tension force equals the weight of the liquid column: 2πr·γ cos θ = πr²·h·ρ·g. Solving gives the capillary rise height h = 2γ cos θ / (ρgr). Narrower tubes produce greater rise — a phenomenon crucial to water transport in plants and in many industrial processes.

The Key Equation

ΔP=2γR\Delta P = \frac{2\gamma}{R}
  • \Delta P — Excess pressure (Pa (N/m²)): The pressure inside the droplet minus the pressure outside. Always positive — interior is always at higher pressure.
  • \gamma — Surface tension coefficient (N/m or J/m²): The force per unit length (or energy per unit area) acting along the liquid surface. For water at 20 °C, γ ≈ 0.0728 N/m.
  • R — Radius of curvature (m): The radius of the spherical droplet. Smaller droplets have greater internal excess pressure.

Worked Example

Problem. A spherical soap bubble (which has two surfaces) is blown to a radius of R = 3.0 cm. The surface tension of the soap solution is γ = 0.040 N/m. Calculate the excess pressure inside the bubble compared to the surrounding air.

ΔP=4γR=4×0.0400.030≈5.3 Pa\Delta P = \frac{4\gamma}{R} = \frac{4 \times 0.040}{0.030} \approx 5.3 \text{ Pa}

Answer. The excess pressure inside the soap bubble is approximately 5.3 Pa.

Figure
Diagram
Surface Tension: Molecular Forces and Droplet PressurebulkForces cancelsurfaceNet inwardforcesurfaceP_inΔP = 2γ/Rmeniscuscapillary rise
Origins · 1 minThomas Young and how this was discovered
TY
Thomas Young
1773–1829 · British

Thomas Young was a polymath who made foundational contributions to wave optics (the double-slit experiment), the theory of elasticity (Young's modulus), and fluid physics. In 1805 he introduced the concept of surface tension and derived the relationship between contact angle and interfacial tensions — now known as Young's equation — providing the mathematical framework that still underpins wetting and adhesion science today. Young was also a key figure in deciphering the Rosetta Stone, contributing to the translation of Egyptian hieroglyphics. His breadth of expertise led his contemporaries to call him 'The Last Man Who Knew Everything.'

  • Capillarity and Capillary Rise — Capillary rise is a direct application of surface tension: the balance between surface-tension forces and gravity determines how high a liquid climbs in a narrow tube.
  • Viscosity and Fluid Flow — Both surface tension and viscosity arise from intermolecular forces in liquids, and both influence how fluids behave in narrow channels and at interfaces.
  • Cohesion and Adhesion — Surface tension is a macroscopic manifestation of cohesive forces between like molecules; the contact angle is set by the competition between cohesion and adhesion.
  • Pressure in Fluids — The Young–Laplace equation links surface tension directly to pressure differences across curved surfaces, connecting surface phenomena to fluid statics.