Jurinlagen

Jurinlagen are a concept in capillarity describing the equilibrium height to which a liquid rises or falls when placed in a narrow tube, due to the balance of surface tension forces at the liquid–solid and liquid–gas interfaces with gravity. The term is named after James Jurin, who studied capillary action in the early 18th century.

In a cylindrical capillary of inner radius r, and assuming the liquid wets the tube with contact angle θ, the Jurin height h at equilibrium is given by the formula h = 2 γ cos θ / (ρ g r). Here γ is the liquid–air surface tension, ρ is the liquid density, and g is the acceleration due to gravity. If the liquid does not wet the surface well (cos θ negative), the liquid depresses in the tube, yielding a negative height. The relation applies under static, ideal conditions for a uniformly cylindrical tube; it neglects dynamic effects, vapor pressure, and molecular-scale forces that may become relevant at very small radii.

Jurinlagen illustrate how capillary rise depends strongly on tube radius: smaller r gives higher rise, all else being equal. They are used experimentally to determine surface tension or contact angle by measuring h for known r, or to study wetting properties of liquids on different solids. The concept is foundational in capillarity, with applications in microfluidics, porous media, and related fields.