The effect of surfactants on expanding free surfaces

This paper develops a systematic theory for the flow observed in the so-cal led "overflowing cylinder" experiment. The basic phenomenon to be explained is the order of magnitude increase in the surface velocity of a slowly ove rflowing beaker of water that is caused by the addition of a small amount o f soluble surfactant. We perform analyses of (i) an inviscid bulk flow in w hich diffusion is negligible, (ii) a hydrodynamic boundary layer in which v iscous effects become important, and (iii) a diffusive boundary layer where diffusion is significant, and by matching these together arrive at a coupl ed problem for the liquid velocity and surfactant concentration. Our model predicts a relation between surface velocity and surface concentration whic h is in good agreement with experiment. However, a degeneracy in the bounda ry conditions leaves one free parameter which must be taken from experiment al data. We suggest an investigation that may resolve this indeterminacy. ( C) 2001 Elsevier Science Ltd. All rights reserved.