The Climb of Liquids
Capillary action (or capillarity) is the fascinating phenomenon where a liquid spontaneously flows into narrow spaces without the assistance of, or even in strict opposition to, external forces like gravity.
This occurs because of an intermolecular battle between cohesive forces (the liquid molecules wanting to stick to each other) and adhesive forces (the liquid molecules wanting to stick to the solid walls of the tube). If the adhesive forces to the wall are stronger, the liquid will literally climb up the walls until the weight of the climbing water column is perfectly balanced by the upward pulling force.
Capillary Action in Nature
Life on Earth depends entirely on this principle:
- Trees and Plants: A $300$-foot California Redwood tree doesn't have a mechanical pump. It relies almost entirely on the microscopic capillary action within its xylem tubes to pull heavy water from the deep roots all the way up to the highest leaves.
- Paper Towels: The microscopic gaps between the cellulose fibers in a paper towel act as tiny capillary tubes, aggressively sucking up liquid spills against gravity.
- Tears: Your tear ducts use capillary action to constantly draw fluid across your eyeball to keep it moist.
The Formula
Example Calculation
A perfectly clean glass capillary tube with a tiny radius of $0.0001 , \text{m}$ (0.1 mm) is placed in water (surface tension $0.0728 , \text{N/m}$, density $1000 , \text{kg/m}^3$). Assuming a contact angle of $0^\circ$ (so $\cos(0) = 1$).
- Numerator: $2 \cdot 0.0728 \cdot 1 = 0.1456$.
- Denominator: $1000 \cdot 9.81 \cdot 0.0001 = 0.981$.
- Divide: $0.1456 / 0.981 \approx 0.148 , \text{meters}$.
The water will miraculously climb almost $15 , \text{cm}$ (about 6 inches) straight up the tiny glass tube, completely defying gravity until it reaches equilibrium.