Simulation of surfactant transport during the rheological relaxation of two-dimensional dry foams

Abstract

We describe a numerical model to predict the rheology of two-dimensional dry foams. The model accurately describes soap film curvature and viscous friction with the walls, and includes the transport of surfactant within the films and across the vertices where films meet. It accommodates the changes in foam topology that occur when a foam flows and, in particular, accurately represents the relaxation of the foam following a topological change. The model is validated against experimental data, allowing the prediction of elastic and viscous parameters associated with different surfactant solutions.

Dynamical Coupling between Connected Foam Films: Interface Transfer across the Menisci

“…At higher deformation rate, in contrast, tangential velocities become crucial, as they are strongly coupled to the viscous forces and surface tension variations which govern the dynamics. In this viscous regime, foam dynamics at the local scale has been partially characterized in the literature: interfacial stress have been determined by a measure of the angles between adjacent films during imposed deformation [4][5][6][7] or by force measurements [8]; film thicknesses have been measured by interferometry [9] or light absorption [10]; and velocities in a stretched film by particle tracking [10]. These measurements provide important information, but are not exhaustive enough to fully determine the flow in the liquid phase.…”

Micro-mechanical prediction of the effect of surfactant concentration and external friction on the visco-elasto-plastic response of an aqueous foam

“…Knowing the surface tension gradient along each film, we define a "convection equation", similar to the Marangoni effect 26 . We assume that the gradient of surface tension is balanced by the drag experienced by the surfactant molecules which move along the film 5 . In this way our surfactant transport model allows the calculation of the tangential component of the surface velocity v t in terms of a surfactant drag coefficient µ:…”

“…From a dimensional analysis of equations 1, 2 and 3 5 , we find the free parameters of the model: we defineÊ = E γ eq andμ = µ λ . In our previous publication 5 we optimizedÊ andμ in order to fit ex-perimental data and predict the Gibbs elasticity E and the surface viscosity µ for common anionic surfactants and dairy proteins.…”

“…From a dimensional analysis of equations 1, 2 and 3 5 , we find the free parameters of the model: we defineÊ = E γ eq andμ = µ λ . In our previous publication 5 we optimizedÊ andμ in order to fit ex-perimental data and predict the Gibbs elasticity E and the surface viscosity µ for common anionic surfactants and dairy proteins. Experimental values for these physical parameters are available in literature, for the anionic surfactant SDS, for example, E is 30 mN/m while the surface viscosity µ is 1-10 mPa m s 5,27 .…”

“…Here, we combine the Viscous Froth model 22 with a surfactant transfer model, as described in our previous publication 5 , to analyse the rheological behaviour of dry two-dimensional foams. This model extends the two-dimensional Viscous Froth model 22 , which includes the curvature of the films to simulate dry foams between parallel plates, by including the movement of surfactant molecules during foam flow 23 .…”