LINEAR-STABILITY ANALYSIS OF AN INSOLUBLE SURFACTANT MONOLAYER SPREADING ON A THIN LIQUID-FILM

Recent experiments by several groups have uncovered a novel fingering instability in the spreading of surface active material on a thin liqu id film. The mechanism responsible for this instability is yet to be d etermined. In an effort to understand this phenomenon and isolate a po ssible mechanism, we have investigated the linear stability of a, coup led set of equations describing the Marangoni spreading of a surfactan t monolayer on a thin liquid support. The unperturbed flows, which exh ibit simple linear behavior in the film thickness and surfactant conce ntration, are self-similar solutions of the first kind for spreading i n a rectilinear geometry. The solution of the disturbance equations de termines that the rectilinear base flows are linearly stable. An energ y analysis reveals why these base flows can successfully heal perturba tions of all wavenumbers. The details of this analysis suggest, howeve r, a mechanism by which the spreading can be destabilized. We propose how the inclusion of additional forces acting on the surfactant coated spreading film might give rise to regions of adverse mobility gradien ts known to produce fingering instabilities in other fluid flows. (C) 1997 American Institute of Physics. [S1070-6631(97)00112-8].