• id: JME-09-N14
• title: Capillary Action
• tags: capillary, contact-angle, rise

When a narrow tube is dipped in a liquid, the liquid rises (or falls) due to surface tension. The height of capillary rise:

$h = \frac{2S\cos\theta}{\rho g r}$

where $S$ is surface tension, $\theta$ is contact angle, $\rho$ is liquid density, $r$ is tube radius. For water-glass: $\theta \approx 0°$, liquid rises (concave meniscus). For mercury-glass: $\theta \approx 140°$, liquid depresses (convex meniscus). Capillary rise is inversely proportional to tube radius — narrower tubes give higher rise. This is the mechanism behind water transport in plants and wicking in fabrics.