Intrinsic Instabilities at Impure Interfaces

薄膜的复杂性和多尺度特性给自然界或工业环境中的许多系统带来了重大的建模挑战，从泡沫到电动汽车的发动机润滑油，从生物膜到非酒精饮料，从隐形眼镜到工业涂层。无意或故意污染界面的薄液体膜的应用是无穷无尽的。这自然会带来大量的研究和经济机会，与理解和控制添加剂和污染物对薄膜界面的影响的能力有关。经过多年的深入研究，这里的主要困难仍然是污染物在界面上的作用通常没有得到很好的理解。我们开始了解表面活性剂的影响，表面活性剂是污染物的一个子集，具有表面活性剂，如洗涤液和洗涤剂，但污染物的一般理论仍然难以捉摸。这不仅是因为表面改变剂的模型有限，直到稀释浓度，这在自然界中并不总是如此，而且还缺乏一个统一的框架来研究非表面活性剂的污染物。这个项目将提供这样一个统一的数学框架来研究薄液体膜上的广义污染物。通过将广义污染物的输入描述为有助于表面张力的有效梯度，由污染物具有的任何特殊性质引起，我们的方法将新机制引入连续体动力学，并允许与通常结合污染物多重效应的实验研究进行比较。解开污染物中各种非线性效应是一个不容忽视的难题。数学框架是对广义污染物溶液的多物理场汤中所有成分进行完整分类的重要的第一步。这种分类不仅使我们能够处理比以前可能的更复杂的污染物，而且还使我们能够为特定应用设计精确的规格或稳定性的薄液体界面，例如具有与酒精版本相同泡沫特性的非酒精啤酒或用于高效电动汽车的非泡沫发动机润滑剂。这两个都是薄液体界面的例子，如果完全了解污染物在表面上的作用，将会受益。

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.