Modeling Draining Flow in Mobile and Immobile Soap Films

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

“…(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.…”

A mathematical model for an expanding foam

“…Each of these functions vary in space and time. The model is an adaptation and significant extension of a model developed by us to explain the behavior of draining soap films [5]. For a soap film on a vertical wire frame that is draining under the influence of gravity, it has been observed experimentally that rapid thinning occurs at low surfactant levels while high surfactant concentrations result in thick films that drain quite slowly.…”

Marangoni effect from density variations in apolar ultrathin films

“…However, the fact that a surface tension gradient will produce a Marangoni flow effect was not taken into account. This phenomenon is usually associated with concentration gradients in soap films [8] or with temperature gradients c EDP Sciences Article published by EDP Sciences and available at http://www.edpsciences.org/epl or http://dx.doi.org/10.1209/epl/i2005-10582-3 in heated films [9,10]. In this work we theoretically investigate the effect of a Marangoni flow induced by density gradients (density-capillary effect) on the stability of a thin film.…”

“…into the two-dimensional version of the thin film equation (8) and taking the limit ξ → 0 for the amplitude of the perturbations. The sign of the growth rate Ω determines the stability of the film.…”

“…-We simulate the temporal evolution of a liquid thin film with lateral density variations by numerically solving the partial differential equation (8). The simulated film covers a domain size of 4Λ m with periodic boundary conditions.…”