Complex flows and optics to model topographical substrate design: Solar panel application balancing superhydrophobicity and concentrated photovoltaics

Fluids interract with surfaces in a vast variety of natural phenomena, and technological and industrial applications. Theoretical work over the last few decades on the motion of contact lines---the location between two immiscible fluids and a solid surface---has enabled increasingly efficient oil extraction, contributed to a wide variety of printing and coating applications, and opened up the fields of micro and nanofluidics. In these applications, the focus is on the motion and profile of the fluid and has to take account of many physical effects across a wide range of lengthscales. However, the physical effects are predominately those that affect the motion of the fluid, rather than any impact from the presence of the fluid on optical, thermal or other electromagnetic wave properties.

Whilst optical materials, and wetting and spreading, have received attention individually for several decades, their combined effects have not been scrutinised in detail, and several unresolved issues still elude us. In particular the coupling of the physics of fluid dynamics with electromagnetic radiation: Whenever a surface that is designed for its light, ultra-violet, or other properties, interacts with fluids such as rainwater there will be both fluid dynamics and electromagnetic wave propagation challenges to model. A prototype situation in this proposal is that of rain on solar panels, but many other examples exist: car windscreens, coated windows on buildings, radar or infra-red sensors on cars (e.g. for automatic braking systems), or at smaller scales multiphase fluids in microfluidic devices probed via visible light or other electromagnetic waves. In essence we consider any advanced optical material that has an interplay with fluids.

This project will explore the fundamental relationships between light, microstructure, and hydrodynamics for the design of advanced optical materials, in a synergistic and interdisciplinary framework combining theory and computations---with the ultimate goal being optimal design leading to more efficient, safer, and lower cost materials/surfaces. In particular for the prototype of photovoltaic surfaces, it is to understand how best to achieve the objectives of self-cleaning, reflection reduction, and concentrated photovoltaics with one substrate design, whilst modelling the situation in a generality to be able to inform the myriad of other applications where electromagnetic waves interact with moving fluids.

Using modelling to design efficient solar panels is at the heart of this project, and thus long-term the key impacts are for the industrial manufacturers of panels, who can build more efficient and cost-effective products, and those who buy them. This proposal seeks to model the design of the surface of solar panels to have a focussing effect such that the more expensive photovoltaic material that coverts light into electricity can be located efficiently in smaller amounts-leading to reduced costs; alongside this the surface will be textured to aid self-cleaning, where rainwater runs off naturally and collects dust and debris (thus maintaining good efficiency of the solar panel even without regular cleaning and maintenance). Beyond advanced optical materials such as solar panels, the fundamental generalisations of this work will have long-term impact for the design of advanced and meta materials, in situations where both the optical/electromagnetic radiation properties and the interaction with fluids are important. As the modelling in this project will deal with broad and general situations, in the long-term and further down the pipeline such advances in material design will lead to new companies and wealth creation.

As well as being an economic impact, society will also benefit from greater deployment of clean and secure energy sources through reduction of greenhouse gases and improvements in air quality, key to improving health and quality of life. Cost reduction and lower maintenance of panels enables more citizens to produce their own energy, promoting self-sufficiency in energy production nationally. Microgeneration, where more citizens are encouraged to produce small-scale, renewable, electricity and feed back any excess to the national grid, will have a positive impact on society more generally by making everyone more aware of power generation and usage.

With this being a mathematical modelling project at a fundamental level, these impacts are long-term and admittedly would require further intermediate steps, in particular from the engineering community to develop prototype methods to manufacture panel surfaces with designs developed in this project. As such, much of the immediate impact of this project is in nucleating the concept of bringing the large and mature field of fluid dynamics to the modelling of green energy devices. Specifically in this project the coupling of electromagnetic ray tracing to cutting edge dynamic droplet motion computations will begin an interdisciplinary niche to grow.

Furthermore, a more public dissemination of research will be created. A very successful CD-ROM and website explaining the aspects of photovoltaics have been developed over a number of years by S. Bowden and C. Honsberg at the Solar Power Labs in Arizona State University (supported by a number of NSF grants), at http://pveducation.org. With the smaller scale of this proposal, the initial plan will be to create an accessible personal website, including a blog about applied maths and youtube videos, using the detailed visualisations that will be possible from the mathematical modelling research done. The website will give a visually appealing overview of the benefits of mathematical modelling for solar panel design, with the expectation that the underlying research is of a high level and thus can generate institutional news articles, and articles further afield. An accessible site such as this, with associated visuals, will be advertised more widely at outreach events at Loughborough to be used to excite the next generation of applied mathematicians. It will also provide a clear place to send potential industrial and academic colleagues to strengthen the case for encouraging traditional fluid mechanicists to bring their expertise to new fields, and to promote the value of mathematical modelling to engineers and industry.