Testing the Thin Capillary Model

Abstract

We provide a detailed and accessible introduction to the exact theory of capillary phenomena in a cylindrical tube of finite radius. We demonstrate explicitly that Jurin's law always somewhat underestimates the height of liquid rise. The largest deviations occur for small contact angles. In the limiting case of a very large capillary radius, the true column height becomes independent of the radius and approaches a finite limiting value. The mean curvature of a real meniscus is a monotonically increasing function of the capillary radius. We argue that the force balance method is most appropriate for deriving Jurin’s law, whereas the exact capillary equation requires the use of the pressure balance method or the Helmholtz energy minimization procedure.