(237n) Thin Free Liquid Film Stability in Various Interaction Regimes Arising Due to Surface Active Agents

A hydrodynamic model that addresses the interplay between surface rheological effects, and surface tension and its gradients is used to predict the stability of a thin liquid film containing surface active agents. The model traces the evolution of a Newtonian liquid film, covered with insoluble surface active particles, until rupture, assisted by a van der Waals type disjoining pressure. The particles are assumed to have a significant effect on the surface viscosity of the film, which in turn depends on the particle concentration. In addition, they may also cause gradients in surface tension due to diffusion-driven local concentration variations, and induce a Marangoni flow. Four distinct interaction regimes, emerging from local concentration variations are identified, such that either, both, or neither of Marangoni and surface viscosity effects would be present at leading order in the lubrication limit.

In the model, the free film is covered by passive air phases on both sides, considering a free film in the squeezing mode [1], symmetric about the horizontal axis (see Figure 1). Hence, a symmetry condition is used, wherein the vertical gradient of the horizontal velocity vanishes at the symmetry plane. The surface tension is assumed to decrease linearly with increasing concentration of the surface active particles, whereas a nonlinear phenomenological model [2] is used to examine the effect of particle concentration on surface viscosity. At sufficiently high concentrations, the particles could form an apparently rigid shell around the liquid free surface due to enhanced surface viscosity. Depending on whether the Marangoni or surface viscosity effects are weak or strong, these effects are correspondingly present or absent in the tangential stress balance condition at the free surface.

Standard linear stability analysis reveals the nature of growth or decay of small amplitude interfacial perturbations. When the system has weak Marangoni and weak surface viscosity effects, both these factors act as film stabilizers against van der Waals - driven rupture. The nonlinear evolution of the system exhibits emergence of a fastest growing interfacial perturbation wavelength as predicted by linear theory. However, when either of these effects are important at leading order, the surface viscosity and the Marangoni effects retard the rupture process more drastically, resulting in a steady-state solution in the nonlinear numerics. When both the effects are assumed important at leading order, the free film could rupture or stabilize according to the relative strengths of surface viscosity effect and Marangoni stress. The numerical challenges encountered while solving for these regimes are emphasized and the results are compared with earlier studies in the literature.

Figure 1: Schematic of a free film with surface active agents in squeezing mode.

References

[1] De Wit, A., Gallez D. (1994) Phys. Fluids. 6(10), 3256-3266.

[2] Maki, K.L., and Kumar, S. (2011) Langmuir. 27, 11347-11363.