Absolute limit for the capillary rise of a fluid

¹  Laboratoire de Physique Statistique de l'Ecole Normale Supérieure, associé au CNRS et aux Universités Paris 6 et Paris 7 - 24 rue Lhomond 75005 Paris, France
²  Physics Department, Pennsylvania State University - University Park, PA 16802, USA
³  Université Pierre-et-Marie-Curie - 4 Place Jussieu, 75005 Paris, France

Corresponding author: caupin@lps.ens.fr

Received: 6 November 2007
Accepted: 14 April 2008

Abstract

Small capillaries can provide strong binding to fluids confined within them. We analyze this behavior with a simple microscopic theory, considering two geometries, a slit pore and a cylindrical pore. A goal is to achieve the maximum possible capillary rise (H) within each type of pore. The attraction for very small capillaries can result in a large value of H, exceeding 100 km in a number of cases (e.g., hydrogen, methane and water in cylindrical graphitic pores). The specific value of H depends on the details of the pore and the fluid-surface interaction. It is maximized in the case of small cylindrical pores, strong interactions and small adsorbate mass. Explicit calculations are presented for graphite and MgO substrates. Experimental tests are possible with an ultracentrifuge, where the high effective gravitational field reduces H.