Algorithms, Theory, and Applications for Fiber Coating Systems

North Carolina State University, Raleigh NC

Investigators

Abstract

Thin liquid films flowing down a vertical fiber, a phenomenon known as fiber coating, is a fundamental component in various engineering applications such as mass and heat exchangers for thermal desalination, water vapor, and ultra-fine particle capture. These liquid films spontaneously exhibit intriguing interfacial instabilities, leading to trains of traveling droplets and irregular wavy patterns. Although there have been extensive studies on the modeling of fiber coating dynamics, the inherent nonlinearity and degeneracy of these models often present analytical and computational challenges in broader applications. This research project aims to develop a hybrid numerical and machine learning framework that accelerates the computation and facilitates the control of large-scale stiff problems associated with fiber coating systems. The development of these techniques can lead to a prototype for real-time simulation and prediction in fiber coating applications. Parts of the project will be incorporated into the investigator’s courses on scientific computing and data science. This project will also provide research training opportunities for both undergraduate and graduate students. This project will employ analytical approaches, numerical simulations, and machine learning techniques to develop theory and algorithms for challenging free-surface flow problems that arise from fiber coating systems. Such problems are characterized by fourth-order highly-nonlinear partial differential equation (PDE) systems, which are sensitive to traditional numerical methods and data-driven machine-learning approaches. The objectives of the project are organized around three interconnected aspects: 1) Analysis of the regularity and structure of traveling droplets described by coupled PDE systems. The derived structures will be utilized to develop simplified dynamical systems from full-order models for individual droplets. A prototype control problem will be studied to establish the foundation for control design of general fiber coating systems; 2) Development of robust and structural-preserving algorithms for simulating and learning fiber coating dynamics. This involves bridging physics-based modeling principles, PDE theory, and neural ordinary differential equation techniques for long-time sequential learning and reduced-order modeling. The data-driven learning techniques developed for high-order nonlinear degenerate PDEs in this project are expected to advance scientific machine learning for stiff physical systems; 3) A real-world large-scale application will serve as a case study for the theoretical understanding and verification of the developed algorithms. 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.