Mathematical Modelling and Analysis of Industrially-Important Flows of Liquid Crystals: Spreading and Channel Filling

摘要：该项目由工程与物理科学研究委员会（EPSRC）工业案例博士奖学金与默克化学有限公司（默克）共同支持。该项目将得到史密斯工业数学和系统工程研究所的支持。项目背景：液晶显示器作为显示器在现代电子设备中无处不在，如平板大屏幕电视、笔记本电脑、手机、数码相机和电子玩具。然而，随着显示技术应用的数量和规模不断增长，技术需求也随之增长，默克在液晶领域拥有40年的经验，在开发新的、更高效的显示器和更便宜、更高效的制造技术（有时被称为“工艺强化”）方面处于领先地位。液晶显示器制造是一个价值数十亿英镑的国际产业，因此即使是相对较小的科学和技术改进也可以对相关公司（就增加的利润而言）和更广泛的社会（就更广泛地获得更实惠和更可靠的设备而言）产生实质性的经济效益。背景：格拉斯哥斯特拉斯克莱德大学在液晶的理论分析方面有着良好的记录，可以追溯到Frank Leslie FRS教授的开创性工作，他与Jerry Ericksen教授一起制定了著名的并被广泛研究的Ericksen-Leslie方程。斯特拉斯克莱德的连续介质力学和工业数学（CMIM）研究小组（由威尔逊教授领导）在研究复杂流体（特别是液晶）的流动和各种各样的薄膜流动方面具有特殊的专业知识。项目目标：拟建项目的目的是结合分析和数值技术，为与液晶显示技术制造相关的基本科学问题带来新的见解和理解，特别是液晶在物理和/或化学非均质衬底上的扩散，以及用液晶填充狭窄的通道。监督：该项目将由斯特拉斯克莱德大学数学与统计学系的Stephen Wilson教授和Nigel Mottram教授以及David Wilkes博士（默克德国）和Rachel Tuffin博士（默克英国）监督。该学生将在斯特拉斯克莱德工作，并定期访问位于南安普顿和德国的默克公司。

Summary: This project is supported by an Engineering and Physical Sciences Research Council (EPSRC) Industrial CASE PhD studentship in conjunction with Merck Chemicals Ltd (Merck). The project will be supported by the Smith Institute for Industrial Mathematics and System Engineering.Project Background: Liquid crystal displays are now ubiquitous as displays in modern electronic devices, such as flat large-screen televisions, laptops, mobile phones, digital cameras and electronic toys. However, as the number and scale of display technology applications continue to grow the technical demands grow alongside them, and with 40 years of experience in the field of liquid crystals Merck are at the cutting edge of developing new and more efficient displays and the techniques for manufacturing them more cheaply and efficiently (sometimes called "process intensification"). Liquid crystal display manufacturing is a multi-billion pound international industry, and so even relatively small scientific and technological improvements can have substantial economic benefits both to the companies involved (in terms of increased profits) and to wider society (in terms of more widespread access to more affordable and more reliable devices).Strathclyde Context: The University of Strathclyde in Glasgow has a well-established track record in the theoretical analysis of liquid crystals, dating back to the pioneering work by Professor Frank Leslie FRS who, together with Professor Jerry Ericksen, formulated the famous and widely-studied Ericksen-Leslie equations for nematic liquid crystals. The Continuum Mechanics and Industrial Mathematics (CMIM) research group at Strathclyde (led by Professor Wilson) has particular expertise in studying the flow of complex fluids (and, in particular, liquid crystals) and a wide variety of thin-film flows.Project Aims: The aim of the proposed project is to use a combination of analytical and numerical techniques to bring new insight and understanding to fundamental scientific problems associated with the manufacturing of liquid crystal display technologies, specifically the spreading of a liquid crystal over a physically and/or chemically heterogeneous substrate, and the filling of a narrow channel with a liquid crystal.Supervision: The project will be supervised by Professors Stephen Wilson and Nigel Mottram in the Department of Mathematics and Statistics at the University of Strathclyde and Dr David Wilkes (Merck Germany) and Dr Rachel Tuffin (Merck UK). The student will be based at Strathclyde, with regular visits to Merck in Southampton and Germany.