Capillary Action
Capillary action is the spontaneous rise (or depression) of a liquid in a narrow tube or porous medium against or with gravity, driven by the interplay between adhesive forces (liquid to solid) and cohesive forces (liquid to liquid), as characterised by surface tension. When adhesion exceeds cohesion — as in water in glass — the liquid rises and forms a concave meniscus; when cohesion exceeds adhesion — as in mercury in glass — the liquid is depressed and forms a convex meniscus. Capillary action is vital in plant water transport, paper chromatography, inkjet printing, and soil hydrology.
Key Formula
h = (2γ cosθ) / (ρ g r)
LaTeX: h = \frac{2\gamma \cos\theta}{\rho g r}
| Symbol | Meaning | Unit |
|---|---|---|
| h | Height of capillary rise (or depression) | m |
| γ | Surface tension of the liquid | N/m |
| θ | Contact angle between liquid and tube wall | degrees (°) |
| ρ | Density of the liquid | kg/m³ |
| g | Acceleration due to gravity | m/s² |
| r | Inner radius of the capillary tube | m |
Worked Example
Problem
Calculate the height to which water rises in a glass capillary tube of radius 0.2 mm at 20 °C. Given: γ = 0.0728 N/m, contact angle θ = 0°, ρ = 1000 kg/m³, g = 9.81 m/s².
Solution
Step 1 — cos θ = cos 0° = 1. Step 2 — r = 0.2 × 10⁻³ = 2 × 10⁻⁴ m. Step 3 — h = (2 × 0.0728 × 1) / (1000 × 9.81 × 2 × 10⁻⁴). Step 4 — Numerator: 0.1456. Denominator: 1.962. Step 5 — h = 0.1456 / 1.962 ≈ 0.0742 m.
Answer
h ≈ 74.2 mm ≈ 7.4 cm
Capillary Rise in Water (γ = 72.8 mN/m, θ = 0°, ρ = 1000 kg/m³)
| Tube Radius (mm) | Capillary Rise (mm) | Rise Height (cm) | Application Context |
|---|---|---|---|
| 0.05 | 297 | 29.7 | Xylem vessels in trees |
| 0.10 | 148 | 14.8 | Paper fibres, soil pores |
| 0.20 | 74 | 7.4 | Thin glass capillary tubes |
| 0.50 | 30 | 3.0 | Porous concrete, ceramics |
| 1.00 | 15 | 1.5 | Coarse sand grains |
| 2.00 | 7 | 0.7 | Wide laboratory tube |
Interactive Tools
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Related Terms
Surface Tension
Surface tension is the cohesive force per unit length acting along the surface of a liquid, arising because molecules at the surface experience a net inward attractive force from neighbouring molecules and therefore resist increases in surface area. It causes liquids to form droplets, allows certain insects to walk on water, and governs the rise of liquids in narrow tubes through capillary action. Surface tension decreases with temperature and is reduced by surfactants (detergents), which disrupt intermolecular cohesion.
Fluid Pressure
Fluid pressure is the force exerted per unit area by a fluid on any surface in contact with it, arising from the continuous collisions of fluid molecules. In a static fluid, pressure at a given depth depends on the fluid's density, gravitational acceleration, and the depth below the free surface. It is fundamental to hydraulics, hydrostatics, and the design of dams, pipelines, and pressure vessels.
Viscosity
Viscosity is a measure of a fluid's resistance to deformation or flow under an applied shear stress, arising from internal friction between adjacent fluid layers moving at different velocities. Dynamic (absolute) viscosity quantifies the shear stress needed to produce a unit velocity gradient, while kinematic viscosity is the ratio of dynamic viscosity to fluid density. Viscosity governs flow behaviour in lubrication, blood circulation, polymer processing, and aerodynamics.
From Latin "capillaris" (of hair), derived from "capillus" (hair), referring to the hair-thin bore of the tubes in which the phenomenon is most visible. The term "capillary" was applied to fine tubes in the 17th century; quantitative treatment was developed by Thomas Young and Carl Friedrich Gauss around 1805.