The spreading of a drop by capillary action

Abstract

A small drop placed on a horizontal surface will spread under the action of capillary forces until it reaches an equilibrium position. The rate at which it spreads provides a means for testing certain hypotheses about moving contact lines; namely that there must be slip between the fluid and the solid boundary near the rim of the drop to avoid a force singularity there, and that the contact angle measured at the rim itself does not show the dynamic behaviour observed by measurements that ignore rapid changes in slope in the immediate vicinity of the rim but remains equal to its static value.By the use of matched asymptotic expansions, an equation for the rate of spread of a drop as a function of the radius of the contact circle is obtained. Experiments on the spreading of small drops of molten glass allow a comparison to be made between the spreading of a drop determined experimentally and that predicted theoretically, which supports the use of the proposed hypotheses as appropriate for the study of fluid motions containing moving contact lines.