Surfactant instabilities on thin films

Abstract

The deposition of a surfactant drop over a thin liquid film may be accompanied by a fingering instability. In this work, we present experimental results which identify the critical parameters that govern the shape and extend of the fingering phenomena. It was found that the normalized wavelength, [lambda]/t, scales with Marangoni number, Ma=[Delta][gamma]t/[mu]D, to the -1 exponent for any Marangoni higher than 4.3 · 10⁷. On the other end, for Marangoni < 4.3 · 10⁷ the normalized wavelength scales with Ma to the -0.4 but becomes in addition a funcion of the Prandtl number, Pr=[upsilon]/D, which demonstrates the critical significance of bulk diffusion on the spreding behavior. Finally, we present a numerical implementation of a mathematical model which is capable of reproducing the experimentally observed trends.