Capillary Action

Interactive visualization of capillary action and Jurin's law - Explore liquid rise in narrow tubes, contact angle, and force balance analysis

Visualization Mode

Real-time Statistics

Height (h) 0.00 mm
Surface Tension (γ) 72.8 mN/m
Contact Angle (θ) 30 °
Tube Radius (r) 0.5 mm
Density (ρ) 998 kg/m³
Gravity (g) 9.81 m/s²
h = 2γcosθ ρgr
h = 2 × 72.8 × cos(30°) / (998 × 9.81 × 0.0005)

Liquid & Tube Properties

Liquid Water
Wetting Hydrophilic (θ < 90°)
Meniscus Concave
Tube Material Glass

Parameters

Smaller radius → Higher rise
θ < 90°: Rise | θ > 90°: Fall
Affects surface tension
Moon:1.6 | Earth:9.8 | Jupiter:24.8

Applications of Capillary Action

🌱

Plants

Water transport from roots to leaves through xylem vessels

📄

Paper & Fabric

Ink absorption in paper, sweat wicking in athletic fabrics

🖨️

Inket Printing

Precise ink delivery through microscopic nozzles

🔬

Medical Testing

Blood samples in capillary tubes, pregnancy tests

🧽

Sponges

Porous structure absorbs water via capillary action

🛢️

Oil Recovery

Oil migration through porous rock formations

What is Capillary Action?

Capillary action is the ability of a liquid to flow in narrow spaces without external forces. When a thin tube is placed vertically in a liquid, the liquid level inside the tube is different from the level outside. This phenomenon occurs due to the balance between surface tension forces (pulling the liquid up) and gravitational forces (pulling the liquid down).

Jurin's Law (1718)

James Jurin formulated the mathematical relationship describing capillary rise: h = 2γcosθ/(ρgr), where h is the height difference, γ is surface tension, θ is the contact angle, ρ is liquid density, g is gravitational acceleration, and r is the tube radius. The law shows that capillary rise is inversely proportional to tube radius - smaller tubes produce higher rise.

Role of Contact Angle

The contact angle determines whether liquid rises or falls in the capillary. When θ < 90° (wetting liquids like water on glass), cosθ is positive and liquid rises. When θ > 90° (non-wetting liquids like mercury on glass), cosθ is negative and liquid falls below the external level. At θ = 90°, there is no capillary effect.

Effect of Tube Radius

Jurin's law shows that capillary height is inversely proportional to tube radius (h ∝ 1/r). Halving the tube radius doubles the capillary rise. This explains why capillary action is significant in microscopic tubes (like plant xylem vessels, typically 10-100 μm in diameter) but negligible in large containers. This relationship is demonstrated in the Tube Comparison mode.

Wetting vs Non-wetting Liquids

Water exhibits strong capillary rise in glass tubes (θ ≈ 30°, h can reach several centimeters in sub-millimeter tubes). In contrast, mercury shows capillary depression in glass (θ ≈ 140°) because mercury does not wet glass. The contact angle depends on the relative strengths of cohesive forces (within the liquid) and adhesive forces (between liquid and solid). Changing the tube material (e.g., glass to Teflon) dramatically affects the contact angle and thus the capillary behavior.

Gravity Effects

Capillary rise is inversely proportional to gravitational acceleration (h ∝ 1/g). In low-gravity environments like the Moon (g = 1.6 m/s², about 1/6 of Earth's), capillary rise would be 6 times higher for the same tube and liquid. Conversely, on Jupiter (g ≈ 24.8 m/s²), capillary rise would be only about 40% of the Earth value. This demonstrates that capillary action would be much more significant in space exploration contexts.

Limitations of Jurin's Law

Jurin's law assumes: (1) Perfectly cylindrical tube with constant radius, (2) Contact angle is constant and independent of tube size, (3) Liquid completely wets the tube wall above the meniscus, (4) No evaporation or condensation effects, (5) Static equilibrium (not considering dynamic effects during rise). Real capillary systems may deviate from these assumptions, especially for very small tubes (nanoscale) or very large heights where the meniscus shape changes significantly.