A universal law for capillary rise in corners

Abstract

We study the capillary rise of wetting liquids in the corners of different geometries and show that the meniscus rises without limit following the universal law: h ( t )/ a ≈ (γ t /η a ) 1/3 , where γ and η stand for the surface tension and viscosity of the liquid while $a\,{=}\,\sqrt{\gamma/\rho g}$ is the capillary length, based on the liquid density ρ and gravity g . This law is universal in the sense that it does not depend on the geometry of the corner.