Simulation of dynamics of adsorption of mixed protein–surfactant on a bubble surface

The dynamics of adsorption of mixed protein–surfactant on a bubble surface is simulated mathematically. The model for the adsorption dynamics is developed based on the Ward–Tordai equation combined with the Frumkin adsorption isotherm. The simultaneous equations are solved using the Newton method for iteration. Base case adsorption and diffusion parameter values for the simulation were sourced from literature. It was found that protein arrives on the surface at a later time than surfactant. At this later time, the protein replaces the surfactant resulting in depletion of surfactant on the surface. There is, however, less protein adsorbed in the presence of more surfactant in the bulk. In contrast, more protein stays in the subsurface layer under these conditions. In addition to the base case simulation and a comparison to the experimental data available in the literature, a parametric study was performed to explore the effects of varying adsorption and diffusion parameters. The parametric study varying the protein surface affinity revealed that below a certain critical affinity, protein tends not to replace surfactant on the surface, even though the affinity of protein remains higher than that of surfactant. Therefore, protein molecules need to have sufficiently high affinity to displace surfactant molecules from the surface. Another parametric study setting a fixed protein surface affinity and varying relative diffusivity and surface affinity of surfactant (for a specified maximum possible surface capacity of surfactant) concluded that with high relative diffusivity and low surfactant affinity (relative to protein), the displacement of surfactant on the surface is more likely to occur.