Mathematical modelling of thin liquid films with variable fluid properties

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Thin liquid films are found in many environmental settings and also play an important role in numerous industrial processes and biological functions. These liquid layers can succumb to interfacial instability whereby a flow develops that generates surface waves resulting in a pronounced non uniformity in the thickness of the film. In many cases this occurrence has an adverse effect on the intended purpose of the film. For example, in manufacturing processes involving coating applications the development of interfacial instability can result in an irregular distribution of the coating material. Similarly, liquid films functioning in living organisms such as, for example, the tear film covering the eye or the fluid lining of airways in the lungs can be ineffective if they become too thin or develop holes. In certain industrial sectors, however, interfacial instability can optimize the process. For example, in heat and mass exchangers the formation of interfacial waves improves the operation of the device due to the fact that there is an increase in the surface area of the liquid-gas interface, which facilitates the transport. An important contributor to interfacial instability is variation in surface tension causing what is referred to as the Marangoni effect. Unevenness in surface tension can be due to heating or the presence of chemical agents dissolved in the liquid (surfactants). Theoretical models can be used to predict the conditions that lead to instability and determine the resulting flow pattern. An important research endeavour is to develop models that accurately represent real-world problems by capturing all the relevant physical factors. For instance, heating is known to affect not just surface tension, but also other properties of the liquid such as viscosity and mass density, with the latter also being a function of solutal concentration. This aspect has however remained unexplored in the modelling of liquid films. I propose to implement a mathematical flow model that accounts for variable fluid properties and investigate the effect on the stability of fluid films. I will also study the combined effect with other modelling complexities such as bottom topography (liquid flowing on nonplanar substrates exhibiting periodic undulations or corrugations). In many real-world situations uneven substrates occur naturally, or are an unintended flaw of manufacturing. In other circumstances the shape of the substrate may be a controlled parameter, and a particular profile may be designed so as to mitigate or exploit the onset of instability in the fluid film. Another modelling extension is bottom permeability to the fluid, and is relevant in cases where the fluid film spreads over a porous material. Such situations arise in printing and painting processes as well as the general coating of textiles. Hydraulic permeability is also relevant to tear covered soft contact lenses.