Generation of soap films with instantaneously adsorbed surfactants: Concentration-dependent film thinning

• Deviation from the Frankel's law predicting the soap film thickness is computed.
• The film thickness varies non-monotonically with the surfactant bulk concentration.
• The elastic interface behavior is recovered at small solubility.
• The predictions are compatible with available experimental data.

In this theoretical work, we predict the steady state thickness of soap films pulled from a bath of surfactants. Assuming simplified thermodynamical properties for the surfactants, we compute the interfacial stresses by taking explicitly into account surfactant convection along the film. We make no assumption on interfacial rheology: the rigidification of the interfaces results entirely from confinement and depletion effects. Two main approximations are used: the concentration of surfactants is supposed homogeneous within the thickness of the film, and at equilibrium with the adsorbed layer. With these hypotheses, we show that the thickness of the film follows Frankel's law at low capillary numbers, and that deviations occur at higher pulling velocities. We study the dependence of the film thickness with the characteristics of the surfactant used and especially with its initial concentration, and we show that our predictions are compatible with available data by Saulnier and coworkers.

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