Complex variable methods in transport theory

The application of complex analysis provides an elegant and computationally efficient method for
modelling and understanding particular physical systems. Problems based on superhydrophobic,
liquid-infused, and surfactant-laden surfaces pose mathematical formulations amenable to these
techniques. Due to the recent growth of study into these materials, and the technical nature of these
methods, there is plenty of scope for novel research in this field, as this project sets out to achieve.
The objective of the project is to solve several such problems in the mind of obtaining diagnostic
quantities for these materials: measuring the effect of these surfaces on desirable flow phenomena
including drag reduction, and heat and mass transfer. These results will be informative to engineers,
offering a theoretical basis for expectations from experimentation with these materials. This work also
develops the theory behind the mathematical methods, particularly in its use in calculating these
diagnostic quantities.
This work aligns with EPSRC's strategic themes of innovation in sustainable technologies.