Complex variable methods in transport theory

复变分析的应用为建模和理解特定的物理系统提供了一种优雅且计算效率高的方法。基于超疏水性，液体注入，和表面活性剂负载表面的问题提出了数学公式服从这些技术。由于最近对这些材料的研究的增长，以及这些方法的技术性质，在这个领域有很多新的研究范围，因为这个项目要实现。该项目的目标是解决几个这样的问题，在头脑中获得这些材料的诊断量：测量这些表面对所需的流动现象，包括减阻，传热和传质的影响。这些结果将为工程师提供信息，为这些材料的实验预期提供理论基础。这项工作还发展了数学方法背后的理论，特别是在计算这些诊断量时。这项工作符合EPSRC的可持续技术创新战略主题。

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.