Surfactant effects on the Rayleigh instability in capillary tubes – non-ideal systems

In a previous work, the instability of a liquid film deposited on the inner walls of a capillary under the presence of insoluble surfactant was analyzed; for that purpose the surface tension was related to the interfacial concentration of surfactant by a linear equation. In general, that assumption is valid when just trace amounts of surfactant are present. The present work extends previous analysis by considering a non-linear surface equation of state derived from the Frumkin adsorption isotherm. This equation of state account not only for the existing quantities of surfactant but also for non-ideal interactions between adsorbed molecules. Except for the equation of state, both the model and the numerical technique employed do not differ from those used in the preceding work. The new predictions here presented show that a linear surface equation of state gives reasonable results for strong surfactants. However, the action of weaker surfactants strongly depends on other parameters: the initial concentration and the type and strength of interaction between adsorbed molecules. Thus, the use of a linear equation of state in these circumstances might give erroneous results.