Capillary Rise and Contact Angle

worked-example

In this example, we calculate the capillary rise of water in a glass tube at 20°C using standard physical properties.

1. Identify parameters: Surface tension γ = 0.072 N/m, Contact angle θ = 0°, Radius r = 0.5 mm = 0.0005 m, Density ρ = 1000 kg/m³, Gravity g = 9.81 m/s².
2. Calculate capillary pressure: Pc = 2γ cos(θ) / r = 2(0.072)(1) / 0.0005 = 288 Pa.
3. Calculate height: h = Pc / (ρg) = 288 / (1000 × 9.81) = 0.029357798165137616 m.

experiment

Explore how different parameters affect the capillary action:

1. Open the Capillary Rise interactive module.
2. Change the Contact angle from 0 to 120. Notice how the meniscus curves downward (convex) and the liquid level drops, indicating a capillary depression.
3. Set Surface tension to 0.03 to observe the proportional decrease in height.

limitations

This model uses a simplified 1D force balance approximation:

• Meniscus shape: It assumes a perfectly spherical cap for the meniscus. It does not solve the full Young-Laplace equation for the exact interfacial shape.
• Reservoir curvature: It neglects any finite curvature effects of the surrounding bulk reservoir.
• Dynamics: It calculates static equilibrium heights and does not model dynamic wetting or capillary flow rates.

references

Refer to these authoritative materials for further context on fluid adhesion, cohesion, and equilibrium physics.

• OpenStax College Physics: Cohesion and Adhesion in Liquids: Surface Tension and Capillary Action