Capillarity — Core Principles

Core Principles

Capillarity is the phenomenon of a liquid rising or falling in a narrow tube, driven by the interplay of surface tension, cohesive forces (liquid-liquid attraction), and adhesive forces (liquid-solid attraction).

When adhesive forces dominate, the liquid wets the surface, forms a concave meniscus, and rises (e.g., water in glass, $\theta < 90^\circ$). When cohesive forces dominate, the liquid doesn't wet, forms a convex meniscus, and falls (e.

g., mercury in glass, $\theta > 90^\circ$). The height of rise or fall ($h$) is given by Jurin's Law: $h = \frac{2T\cos\theta}{r\rho g}$, where $T$ is surface tension, $\theta$ is the angle of contact, $r$ is the tube radius, $\rho$ is liquid density, and $g$ is acceleration due to gravity.

Key factors influencing capillarity are the tube's radius (inversely proportional), liquid's surface tension (directly proportional), and angle of contact. This principle is crucial in plant physiology, ink absorption, and various industrial processes.

Important Differences

vs Capillary Rise vs. Capillary Fall

Aspect	This Topic	Capillary Rise vs. Capillary Fall
Angle of Contact ($\theta$)	Acute ($\theta < 90^\circ$)	Obtuse ($\theta > 90^\circ$)
Wetting Behavior	Liquid 'wets' the solid surface	Liquid does not 'wet' the solid surface
Dominant Forces	Adhesive forces > Cohesive forces	Cohesive forces > Adhesive forces
Meniscus Shape	Concave	Convex
Example	Water in a clean glass tube	Mercury in a glass tube
Sign of $h$ in Jurin's Law	Positive ($h = \frac{2T\cos\theta}{r\rho g}$)	Negative ($h = \frac{2T\cos\theta}{r\rho g}$, as $\cos\theta$ is negative)

Capillary rise occurs when a liquid's adhesive forces to a solid surface are stronger than its internal cohesive forces, leading to an acute angle of contact and a concave meniscus. This causes the liquid to climb the tube. Conversely, capillary fall happens when cohesive forces within the liquid are stronger than its adhesive forces to the solid, resulting in an obtuse angle of contact and a convex meniscus, causing the liquid level to depress. Both phenomena are governed by Jurin's Law, with the sign of the cosine of the angle of contact determining the direction.