Penetration of a small drop into a capillary

Abstract

The theory of capillary penetration, which has so far considered only infinite liquid reservoirs, has been extended to include the case of drops of a finite size. A thermodynamic discussion and a kinetic theory are presented. It is found that the borderline value of the contact angle, which distinguishes between penetration and nonpenetration, depends on the drop size, and can be much higher than 90°. Practically complete penetration into a capillary can be achieved in a microgravity environment for contact angles up to about 114°, for sufficiently small drops. The fraction of the drop volume, which can penetrate the capillary, is markedly decreased for higher contact angles. Capillary rise under the effect of gravity is found to be higher for a finite drop than for an infinite reservoir (as long as the drop volume is sufficient to accommodate the equilibrium height). Also, the rate of capillary penetration by a drop is higher when the drop is smaller. In general, the difference between the behavior of a small drop and an infinite reservoir becomes bigger as the contact angle increases. An analytical approximation for the kinetics of capillary penetration has been developed. It is in excellent aggrement with the exact solutiOn for the initial period of penetration, and fits it well also at later times, for low contact angles. © 1988.