Pattern formation in thin liquid films with insoluble surfactants

The problem of pattern formation in thin liquid films with insoluble surfactants under attractive and repulsive forces is addressed. A thin fluid film bounded by a wall is modeled by a set of two nonlinear evolution equations for the film thickness and surfactant concentration on the free interface. We perform a bifurcation analysis valid for the general case of apolar and polar forces and predict a supercritical bifurcation to new stationary and periodic structures. Numerical simulations for the particular case of a negative apolar spreading coefficient (attractive van der Waals forces) and a positive polar spreading coefficient (repulsive hydration pressure) are discussed in terms of the analytical predictions. Nonlinearities in the competition between attractive and repulsive forces can lead to formation of periodic patterns for the film thickness with homogeneously distributed surfactants. Due to diffusion and Marangoni effects, insoluble surfactants alter the time required for pattern formation but do not alter the final pattern profile itself. Bifurcation analysis allows us then to predict the ranges of film parameters in which pattern formation, rupture, or total film spreading is possible. (C) 1998 American Institute of Physics.