Capillarity

Capillarity, or capillary action, is the movement of a liquid within narrow spaces such as thin tubes or porous materials due to the balance of cohesive forces within the liquid and adhesive forces between the liquid and surfaces. This interaction causes liquids to rise or fall in small channels relative to the surrounding liquid level, driven by surface tension and wetting.

A key feature is the liquid’s meniscus, whose curvature is governed by surface tension and the contact angle between the liquid and solid. In a vertical capillary tube of radius r, the rise height h is described by Jurin’s law: h = (2 γ cos θ) / (ρ g r), where γ is the liquid’s surface tension, θ is the contact angle, ρ is the liquid density, and g is gravitational acceleration. Capillary pressure at a curved meniscus is ∆P = 2 γ cos θ / r. When θ < 90°, capillary rise occurs; if θ > 90°, capillary depression or wetting failure can occur.

Dynamic capillarity in tubes and porous media is often described by Washburn’s law, which states that the square of the penetration length L grows linearly with time: L^2 = (r γ cos θ / (2 μ)) t, where μ is the liquid’s dynamic viscosity. This relation highlights the influence of radius, surface tension, wettability, and viscosity on capillary spreading.

Applications of capillarity are widespread and include plant water transport, soil moisture movement, inkjet printing, paper and textile wetting, and microfluidic devices. Capillarity also underpins phenomena in porous materials and coatings where liquid transport through small pores governs performance.