| Summary: | <p>In this thesis we derive and solve mathematical models for surfactant systems with differing adsorption structures at interfaces. The first part of this thesis considers two dynamic experimental set-ups for which we derive the associated mathematical surfactant–fluid description. Firstly we consider the behaviour of a weakly interacting polymer–surfactant solution under the influence of a steady straining flow. We reduce the model using asymptotic methods to predict the regimes under which we observe phase transitions of the species in the system and show how the bulk dynamics couple to the surfactant adsorption. Secondly we model an experiment to observe the desorption kinetics of a surfactant monolayer, designed to emulate the 'rinse mechanism' used for the removal of surfactant-containing products using water. Through the comparison of our model with experimental data we derive a semi-empirical relationship that describes the variation in depth of a near-surface diffusive boundary layer with the reduced Peclet number. We then employ a combination of asymptotic and numerical techniques that validate this result.</p> <p>The second part of this thesis is concerned with surfactant systems that exhibit more pronounced adsorption at the interface due to the surfactant monomers no longer arranging themselves in a single layer, as is typically the case, but rather in multiple layers. Such self-assembled structures are commonly referred to as multilayers. We derive a simplified model that describes the rearrangement of surfactant within the multilayer structure and draw comparisons between the features of our model and experimental observations. We consider an extension of the theory to the situation of multilayer formation between two adsorbing interfaces, which is governed by an implicit free-boundary problem. We also consider incorporation of bulk solution effects, such as the addition of an electrolyte. Finally, we draw our conclusions and suggest further theoretical and experimental work related to the models presented in this thesis.</p>
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