Complex variable methods in transport theory

复杂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高效的方法。基于超疏水、注入液体和表面活性剂的表面的问题提出了适用于这些技术的数学公式。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，正如本项目所着手实现的那样，在这一领域有很大的创新研究空间。该项目的目标是在获得这些材料的诊断量的同时解决几个这样的问题：测量这些表面对所需流动现象的影响，包括减阻、传热和传质。这些结果将为工程师提供信息，为预期这些材料的实验提供理论基础。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的使用。这项工作与EPSRC的可持续技术创新战略主题相一致。

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.