Surfactant transport onto a foam film in the presence of surface viscous stress

Surfactant transport onto a foam film in the presence of surface viscosity has been simulated as a model for processes occurring during foam fractionation with reflux. A boundary condition is specified determining the velocity at the end of the film where it joins up with a Plateau border containing surfactant rich reflux material. The evolutions of surface velocity and surfactant surface concentration on the film are computed numerically using a finite difference method coupled with the material point method. Results are analysed both for low and high surface viscosities. Evolution is comparatively rapid when surface viscosity is low, but the larger the surface viscosity becomes, the slower the surface flow, and the lower the surfactant surface concentration on the film at any given time . For a large surface viscosity, the surface concentration of surfactant is maintained nearly uniform except at positions near the Plateau border where the velocity and surfactant concentration fields need to adjust to satisfy the boundary condition at the end of the film. The boundary condition imposed at the end of the film implies also that a drier foam (i.e. smaller radius of curvature of the Plateau border) leads to less surfactant transport onto the films. Moreover, the shorter the film length is, also the shorter the characteristic time for surfactant transport onto the film surface. Thinner films however give longer characteristic times for surfactant transport

Computational analysis of single rising bubbles influenced by soluble surfactant

This paper presents novel insights about the influence of soluble surfactants on bubble flows obtained by Direct Numerical Simulation (DNS). Surfactants are amphiphilic compounds which accumulate at fluid interfaces and significantly modify the respective interfacial properties, influencing also the overall dynamics of the flow. With the aid of DNS local quantities like the surfactant distribution on the bubble surface can be accessed for a better understanding of the physical phenomena occurring close to the interface. The core part of the physical model consists in the description of the surfactant transport in the bulk and on the deformable interface. The solution procedure is based on an Arbitrary Lagrangian-Eulerian (ALE) Interface-Tracking method. The existing methodology was enhanced to describe a wider range of physical phenomena. A subgrid-scale (SGS) model is employed in the cases where a fully resolved DNS for the species transport is not feasible due to high mesh resolution requirements and, therefore, high computational costs. After an exhaustive validation of the latest numerical developments, the DNS of single rising bubbles in contaminated solutions is compared to experimental results. The full velocity transients of the rising bubbles, especially the contaminated ones, are correctly reproduced by the DNS. The simulation results are then studied to gain a better understanding of the local bubble dynamics under the effect of soluble surfactant. One of the main insights is that the quasi-steady state of the rise velocity is reached without ad- and desorption being necessarily in local equilibrium