Surfactant adsorption and transport onto a foam lamella in a foam fractionation column with reflux

Abstract

The adsorption and transport of surface active material such as surfactant and/or protein onto the surface of a lamella in a foam fractionation column with reflux is investigated using mathematical simulation. The dynamics of adsorption of protein and/or surfactant from the bulk solution onto the surface of the foam lamella is modelled using the Ward-Tordai equation combined with relevant adsorption isotherms such as the Henry, Langmuir or Frumkin isotherms. Once the surface active material is attached to the surface of the lamella and the surface of the Plateau border, the transport of that material (in this study is represented by surfactant in the first instance) is modelled based on the continuity equation. There are two approaches to the transport of surfactant discussed in this study. One is the transport of surfactant onto a foam lamella in the absence of surface viscosity and in the presence of film drainage. The second approach to the transport of surfactant onto a foam lamella includes the surface viscosity, however the effect of film drainage is neglected to simplify the problem thus the model provides a benchmark for a more complicated system that would involve film drainage. Competition between protein and surfactant may occurs in the absorption of mixed protein-surfactant. The protein arrives onto the interface at a later time due to a slower diffusion rate and it displaces the surfactant molecules already on the surface since protein has a higher affinity for that surface than surfactant. In the absence of surface viscosity, the Marangoni effect dominates the film drainage results in accumulation of surfactant on the surface of the foam lamella in the case of a lamella with a rigid interface. In the case of a film with a mobile interface, the film drainage dominates the Marangoni effect and surfactant is washed away from the surface of the lamella. When the drainage is very fast, such as that which is achieved by a film with a mobile interface, the film could be predicted to attain the thickness of a common black film, well within the residence time in a foam fractionation column, at which point the film stops draining and surfactant starts to accumulate on the lamella surface. The desirable condition in operation of a foam fractionation column however is when the Marangoni effect dominates the film drainage and surfactant accumulates on the surface of a foam lamella such as the one achieved by film with a rigid interface. In the presence of surface viscosity and the absence of film drainage, the surface viscous forces oppose the Marangoni effect and reduce the amount of surfactant transport onto the foam lamella. A larger surface viscosity results in less surfactant transport onto the foam lamella.