Surface Tension Simulator: Laplace Pressure & Capillary Rise

simulator beginner ~9 min
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h = 27.5 mm — capillary rise of water

Water (γ = 72 mN/m, θ = 20°) rises 27.5 mm in a 0.5 mm radius glass capillary. The Laplace pressure across the meniscus is 288 Pa, balancing the hydrostatic pressure of the raised liquid column.

Formula

h = 2γ cos θ / (ρgr) (Jurin's law)
ΔP = 2γ / R (Laplace pressure for sphere)
λ_c = √(γ / ρg) (capillary length)

The Invisible Skin of Liquids

Every liquid surface behaves like a stretched elastic membrane. Molecules at the interface experience an imbalance of attractive forces — pulled inward by their liquid neighbors but with no corresponding pull from the vapor side. This net inward force creates surface tension, a quantity with units of energy per area or force per length. It is the reason raindrops are spherical, insects walk on ponds, and soap bubbles form.

Laplace Pressure

A curved liquid interface generates a pressure difference between the inside and outside. The Young-Laplace equation ΔP = 2γ/R (for a sphere of radius R) explains why small bubbles are under higher pressure than large ones, why soap bubbles left to themselves merge into larger ones, and why the alveoli in your lungs need surfactant to prevent the smallest ones from collapsing. This simulation lets you see how curvature and surface tension combine to create surprisingly large pressures at small scales.

Capillary Rise

When a narrow tube is dipped into a wetting liquid, surface tension pulls the liquid upward along the walls, creating a concave meniscus. The liquid rises until gravity balances the capillary force. Jurin's law h = 2γcosθ/(ρgr) shows that the height is inversely proportional to tube radius — explaining why water wicks through paper towels, soil absorbs moisture, and trees can transport water to heights exceeding 100 meters through microscopic xylem channels.

Engineering Surface Tension

Surfactants (surface-active agents) reduce surface tension by accumulating at interfaces. Soaps and detergents use this principle to help water wet oily surfaces. In industrial printing, carefully tuned surface tensions ensure ink spreads uniformly on substrates. Microfluidic lab-on-a-chip devices exploit capillary forces to move nanoliter samples without pumps, enabling rapid medical diagnostics in resource-limited settings.

FAQ

What is surface tension?

Surface tension is the energy per unit area (or equivalently, force per unit length) at a liquid-vapor interface. It arises because molecules at the surface have fewer neighbors than those in the bulk, creating a net inward force. Water has a high surface tension (72.8 mN/m at 20°C) due to hydrogen bonding.

What is the Laplace pressure?

The Laplace pressure is the pressure difference across a curved liquid interface: ΔP = 2γ/r for a sphere. It explains why small bubbles have higher internal pressure than large ones, why soap bubbles are spherical, and why emulsion droplets tend to coarsen over time (Ostwald ripening).

How does capillary rise work?

When a narrow tube contacts a wetting liquid, surface tension pulls the liquid up the tube walls. The liquid rises until the upward capillary force (2πrγcosθ) balances the weight of the raised column (πr²hρg), giving h = 2γcosθ/(ρgr). Narrower tubes produce greater rise.

Why is surface tension important in biology?

Surface tension governs lung function (pulmonary surfactant prevents alveoli collapse), enables insects to walk on water, drives capillary action in plant xylem, and controls cell membrane deformation. Without surfactant, the Laplace pressure would collapse small alveoli into larger ones.

Sources

Embed

<iframe src="https://homo-deus.com/lab/surface-chemistry/surface-tension/embed" width="100%" height="400" frameborder="0"></iframe>
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