Liquid Crystal Films Across Scales: Dewetting and Dielectrowetting

研究人员将研究与向列液晶(NLC)的工业应用直接相关的问题，以及基本的数学和科学兴趣。该项目首先将重点放在开发新的方法来模拟和准确模拟已经在NLCS超薄膜中观察到的复杂的去湿现象。然后，研究人员将对由精心调整的外加电场驱动的介电润湿现象进行建模。所要考虑的铺展和除湿问题直接适用于各种依赖于在衬底上涂覆NLC薄膜的工业过程，例如用于电子设备的NLC基微显示器的制造，因此开发稳健的预测模型将是非常有价值的。这项工作还将介绍介电流体作为光学快门和可控透镜的使用，以及NLCS在各种生物传感应用中的应用。为实验观察到的去湿现象建立一个坚实的理论框架，并建立可控电润湿的模型，这将是工业研究人员和来自数学、物理和工程界的一大批学术研究人员的重大兴趣。这两位研究人员都积极参与了NJIT在数学、工程和物理领域的本科生和研究生的教学和指导工作。这个项目的很大一部分研究将由研究生进行，他们将接受优秀的研究入门和研究实践方面的全面培训。研究人员将在本项目下继续参与本科教育，为NJIT的应用数学顶峰课程开发一个新的电润湿实验模块，为参与其中的学生提供独特的教育和研究体验，为他们加入美国科学工作队伍做好准备。该项目将开发新的方法来模拟和准确模拟在NLCS超薄膜中观察到的复杂的去湿现象，并模拟电场梯度驱动的电润湿现象。这项工作将把精细的数学建模与广泛的分析方法相结合，例如匹配渐近分析、多尺度分析、奇点的局部分析、偏微分方程组的稳定性分析、边际稳定性分析和正则化技术。同时，将改进和发展由自由表面膜扩散模型(ADI方法)产生的四阶非线性抛物型偏微分方程组的数值方法，以及由电场引起的耦合椭圆模型的数值方法。这些代码将在GPU计算环境中实现，以实现最大的效率和速度。重大挑战包括推导物理上合适但数学上容易处理的模型，这对于深入了解所考虑的问题是必要的；理解导致NLC膜破裂的机制；以及正确处理外加的非均匀电场和运动的NLC膜之间的耦合，特别是在电场在整个NLC层都很重要的情况下。只要有可能，结果将与现有的或新的实验进行比较，这些实验将与本项目所关注的理论和计算工作相协调地进行。除了潜在的产业影响，该项目还将为研究生和本科生提供重要的教育和研究培训机会。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

The investigators will study problems of direct relevance to industrial applications of Nematic Liquid Crystals (NLCs), as well as of fundamental mathematical and scientific interest. The project will first focus on developing new approaches to model and accurately simulate the complex dewetting phenomena that have been observed in ultra-thin films of NLCs. The investigators will then model the phenomenon of dielectrowetting, driven by carefully-tuned applied electric fields. The spreading and dewetting problems to be considered are directly applicable to various industrial processes that rely on coating thin films of NLC onto substrates, such as the manufacture of NLC-based microdisplays for electronic devices, for which the development of robust predictive models would be very valuable. The work will also inform the use of dielectric fluids as optical shutters and as controllable lenses, and of NLCs in various biosensing applications. Establishing a firm theoretical framework for the experimentally-observed dewetting phenomena, and establishing models for controllable dielectrowetting, will be of significant interest both to researchers in industry and to a large class of academic researchers from the mathematics, physics and engineering communities. Both investigators are actively involved in teaching and mentoring undergraduate and graduate students at NJIT, within both mathematics and the engineering and physical sciences. A significant portion of the research for this project will be carried out by graduate students, who will receive an excellent introduction to research and a thorough training in research practices. The investigators will continue their involvement with undergraduate education under the present project, with the development of a new dielectrowetting experimental module for NJIT's Capstone Course in Applied Mathematics, providing the involved students with a unique educational and research experience that will ready them to join the U.S. scientific workforce.The project will develop new approaches to model and accurately simulate the complex dewetting phenomena observed in ultra-thin films of NLCs and model the phenomenon of dielectrowetting, driven by electric field gradients. The proposed work will combine careful mathematical modeling with a broad range of analytical approaches, such as matched asymptotic analysis, multiple scales analysis, local analysis of singularities, stability analysis of PDEs, marginal stability analysis, and regularization techniques. In parallel, numerical methods will be refined and developed for 4th order nonlinear parabolic PDEs arising from the free surface film-spreading models (ADI methods), and for the coupled elliptic models that will arise from the electric field. The codes will be implemented in a GPU computing environment for maximum efficiency and speed. Significant challenges include the derivation of physically-appropriate yet mathematically tractable models, necessary to gain insight into the problems considered; understanding the mechanisms leading to NLC film breakup; and dealing properly with the coupling between an applied nonuniform field and a moving NLC film, particularly in the case where the electric field is significant throughout the NLC layer. Wherever possible, the results will be compared either with existing, or new experiments that will be carried out in coordination with the theoretical and computational work on which this project centers. In addition to the potential industrial impacts, the project will provide both graduate and undergraduate students with significant educational and research training opportunities.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.