Liquid Crystal Films Across Scales: Dewetting and Dielectrowetting

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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.