The effect of adsorption modeling on the stability of surfactant-laden liquid film flow

Abstract

The primary instability of gravity-driven, liquid film flow is examined when the liquid contains a soluble surfactant. It is shown that the model adopted for the description of adsorption equilibrium affects significantly the prediction of the critical Reynolds number, \(Re_\mathrm{c} \). Weak attractive/repulsive van der Waals forces between adsorbed molecules stabilize/destabilize the film, whereas strong, attractive van der Waals forces result in non-monotonic variation of \(Re_\mathrm{c} \) with surface coverage. Ionic surfactants form an electric double layer at the interface, whose repulsive potential destabilizes the film. The intensity of electrostatic effects varies inversely with the solution ionic strength, and two asymptotic limits—zero and high concentration of an indifferent salt—are examined. The competition between electrostatic and van der Waals forces results in a very rich behavior, with the critical Reynolds number increasing or decreasing with surface coverage. The parametric variation of \(Re_\mathrm{c} \) is physically understood in terms of the effectiveness of surfactant mass exchange (between the interface and the bulk) in short-circuiting the basic stabilization mechanism, i.e., Marangoni stresses.