Theoretical study of the generation of soap films: role of interfacial visco-elasticity

Abstract

In this work, we study theoretically the thickness of a liquid film (typically made of a surfactant solution) pulled out of a bath at constant speed in the absence of gravity, when it features a viscous or an elastic interfacial rheology. We show that a purely viscous rheology does not lead to the extraction of a steady state film of constant thickness. In contrast, the thickness of the film is well defined in the elastic case, which allows us to compute it. This thickness depends on the capillary number of the experiment, and on the elasticity of the interface. It is always lower than or equal to that obtained for an incompressible interface predicted by Frankel (Mysels, Shinoda and Frankel, Soap Films: Studies of their Thinning and a Bibliography, 1959), which is recovered in the limit of an arbitrary large elasticity.

Surfactant-induced rigidity of interfaces: a unified approach to free and dip-coated films

“…27 but not in ref. 5 . The influence of these choices on the results will be discussed later in the text and in appendix A.…”

“…Unlike in references 5,27 , we have kept the non-linearized form of the equation of state (14) instead of using its linearized version:…”

“…Understanding the influence of physical chemistry on film thickness is all the more crucial as complex liquids, such as colloidal dispersions or emulsions, are often used as coating agents 3 . The major difference between free and coated films is that liquid films can be coated onto a solid substrate by viscous entrainment, whereas viscous forces alone are not sufficient to generate a free standing film 4,5 . The additional support that helps pulling a soap film upwards stems from interfacial shear stress, which usually results from spatial gradients in the concentration of surface active agents adsorbed at the liquid/air interfaces 6,7 , but can also be generated by temperature gradients 8,9 .…”

“…(1) observed at higher capillary numbers (Ca ∼ 10 −5 − 10 −4 ), where the condition Ca 1/3 ≪ 1 still holds 13,17,25,26 , remain unexplained. To go beyond the assumption of rigid interfaces, several models have been proposed to account for the elastic and/or viscous behavior of the liquid/air interfaces for both LLD [27][28][29][30] and Frankel 5,31,32 configurations. Because the mechanical response of the interfaces is dictated by the interfacial dynamics of surfactants, most of the models make the assumption of water-insoluble surfactants, for which the complex adsorption-desorption dynamics can be disregarded.…”

“…Still, the surface rheological parameters involved in the models -surface elasticity and viscosity -are difficult to measure experimentally. Quantitative comparison between thin film models including surface rheology and experimental data is scarce in the literature 5,33,34 . Moreover, most experimental data available on thin films were obtained with water-soluble surfactant: comparison to models neglecting mass exchange between the surface and the bulk is thus to be done with caution -but remains possible 35 in certain conditions, as will be discussed later on.…”