Intrinsic Instabilities at Impure Interfaces

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.

The work proposed in this Fellowship can impact upon our wealth of knowledge, the society at large, the economy and finally myself as an academic looking to building a broad collaborative group of scientists with a wide variety of expertise to tackle the challenging and multi-disciplinary problem of contaminated interfaces.

Knowledge-wise, this project developes novel simulation and optimisation tools in aid of the analytical models, are of value to the thin-film academic community at large as well as the numerous industries working with thin-film flows in general. As the models become more sophisticated, the link between complex mathematical models of contaminants in a Navier-Stokes fluid dynamics framework and powerful numerical tools in various fields of engineering, such as the automotive industry, aeronautics, bioengineering and gastroengineering, will be made.

A second question which we will try to answer is that "What and how do patterns form on contaminated surfaces?" The model as outlined in my fellowship will attempt to generalise a special case of the pattern-formation developed previously. This is important since pattern formation is a key component to the indication of evolution of biomatter which is very often a contaminated surface, e.g. sites of potential cancer tumours, anomalies in cells and etc. A correct identification of pattern formation can be critical to diagnosis or developments of key insights into dynamics of the biomatter. Moreover, pattern formation on a contaminated surface can be suggestive of its underlying physical properties which are sometimes hard or even impossible to measure experimentally. Work proposed in this fellowship will help to categorise pattern formations based on specific contaminant properties.

One of the direct impacts of my work in trying to understand contaminants on the thin liquid film is to design a bespoke antifoam solution for engine lubricants to be used in the next generation of electric vehicles (EVs), which is an important part of the plan to transition our society into a cleaner and greener economy. The mathematical understanding of contaminated surfaces allows specific foaming properties to be optimised when added to oils or lubricants, achieving a more precise result demanded by the newest innovations in EVs. The resultant technology increases overall efficiency of the fuels and lubricants, leading to both lower downtime overall and more efficient running of the vehicle. I will work closely with my industrial partner, Shell, on this problem.

This Fellowship will also entail significant postgraduate (doctoral) and undergraduate training activities. The proposed research provides excellent opportunities for a number of interesting projects for undergraduate and (taught) postgraduate students. Planned student projects conduct testing using the experimental foaming rig, augmenting it with new ways to measure foamability and also generating novel analytical, computational and machine-learning models to interpret the full-spectrum of the rich data generated with the rig.