<![CDATA[Mixtures of protein and surfactant have a practical significance in industry, for example in the stabilisation of emulsions and foams. Previous studies on adsorption behaviour of mixed protein-surfactant on the bubble surface [Miller et al., 2000; Kotsmar et al., 2010] were based on experimental data. Mathematical simulation of the adsorption dynamics helps to save time and resources devoted to laboratory experiments in designing processes involving adsorption of mixed protein-surfactant on the bubble surface. In this study, the adsorption of mixed protein-surfactant was simplified using the assumption that conformational changes of the protein on the surface did not occur, therefore there was only one state for the adsorbed protein molecules. The model was developed using the Frumkin isotherm, which is commonly applied to adsorption of mixed protein-surfactant [Kotsmar et al., 2009]. The dynamics of adsorption of both protein and surfactant were modelled using the Ward-Tordai equation that describes the evolution of surface concentration due to transfer from the subsurface. The simultaneous equations of the Frumkin isotherm and the Ward-Tordai equation were solved using a Newton iteration method for simultaneous nonlinear equations. The simulations used parameters based on adsorption of bovine b-lactoglobulin (BLG) protein and nonionic decyl dimethyl phosphine oxide (C10DMPO) surfactant. It was found that protein has a slower rate of mass transfer but a higher affinity for the surface, and therefore protein replaces the surfactant upon reaching the surface. This results in depletion of surfactant concentration on the surface. However there is less protein adsorbed in the presence of more surfactant in the bulk: as surfactant molecules then occupy the surface, there is less space available for protein molecules. In contrast, more protein stays in the subsurface layer when there is a higher concentration of surfactant in the bulk solution: the protein molecules remain in the subsurface because they cannot adsorb to the surface. A parametric study revealed that as the diffusion rate of protein is increased, surfactant on the surface is more quickly replaced by protein. Returning to consider a case where protein diffusion rate is less than that of surfactant, but varying the protein surface affinity, it is observed 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.]]>
