Intrinsic Instabilities at Impure Interfaces

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The complex and multi-scale nature of thin-films poses significant modelling challenges for many systems which occur in nature or industrial contexts ranging from foams, to engine lubricants in electric vehicles, from biomembranes to non-alcoholic beverages, from contact lenses to industrial coatings. The applications of the thin liquid films where the interface is contaminated either accidentally or on purpose, are endless. This naturally leads to considerable research and economic opportunities associated with the ability to understand and control the effect of additives and contaminants on the thin-film interface. The main difficulty here, after many years of intense research, remains with the fact that the role of a contaminant on the interface is generally not well understood. We are starting to understand the effect of surfactants, which is a subset of contaminants with surface-active agents, such as washing up liquid and detergents, but a generalised theory of contaminants remains elusive. This is due to not only the limited models of surface-altering agents upto dilute concentrations, which is not always the case in nature, but also the lack of an unifying framework upon which to study contaminants that are not surfactants. This project will provide such an unifying mathematical framework to study a generalised contaminant on a thin liquid film. By describing the inputs of the generalised contaminant into the system as contributing to an effective gradient in the surface tension, induced by whichever special property the contaminant possesses, our approach introduces new mechanisms into the continuum dynamics and allows comparisons to be made with experimental studies which often combines multiple effects of the contaminant. Disentangling the various nonlinear effects in the contaminant is a difficult problem which cannot be overlooked. The mathematical framework is a vital first step towards a complete categorisation of all the component in the multiphysics soup of a generalised contaminant solution. This categorisation not only allows us to tackle vastly more complex contaminants than previous possible, but also enables us to engineer thin liquid interfaces to an exacting specification or stability for a particular application, such as a non-alcoholic beer with the same foaming characteristics as an alcoholic version or a non-foaming engine lubricant for high-efficiency electric vehicles, both of which are examples of thin liquid interfaces which would benefit from a complete understanding of the role contaminants play on the surface.