The Eect of Surfactants on Expanding Free Surfaces

This paper develops a systematic theory for the ow observed in the so-called \over-owing cylinder " experiment. The basic phenomenon to be explained is the order of magnitude increase in the surface velocity of a slowly over owing beaker of water that is caused by the addition of a small amount of soluble surfactant. We perform analyses of (i) an inviscid bulk ow in which diusion is negligible, (ii) a hydrody-namic boundary layer in which viscous eects become important, (iii) a diusive boundary layer where diusion is signicant, and by matching these together ar-rive at a coupled problem for the liquid velocity and surfactant concentration. Our model predicts a relation between surface velocity and surface concentration which is in good agreement with experiment. However a degeneracy in the boundary con-ditions leaves one free parameter which must be taken from experimental data. We suggest an investigation that may resolve this indeterminacy