Bulk-Interface Coupled Response in Novel Materials: Pattern Formation and Interactive Migration

Purdue University, West Lafayette IN

Investigators

Abstract

Shape-memory alloys and microfluidic bulks with surfactants are examples of so-called novel materials, which are composites of multi-phase bulks connected by single-molecule-thick interfacial layers. In epitaxial growth manufacturing processes, material defects such as dislocations and grain boundaries are interfacial layers, whose migration may lead to fatal plastic deformation. This project will focus on the mathematical analysis of migration patterns of interfacial layers and microfluidic flows in novel materials to understand their mechanisms and predict their patterns. Providing accurate theoretical predictions of their evolution will advance, for instance, the design of microfluidic devices and lower manufacturing costs. The training of undergraduate students and high school students will be integrated into this interdisciplinary research project. The first scientific goal of this project is to develop a novel decomposition for bulk-interface interactive dynamics and use it to predict the pattern formation of a multilayer transition profile. Using quantitative estimates based on the global stability of partial differential equations with dynamic boundary conditions and a reduced invariant manifold for the slow-motion persistence of the multilayer pattern, the main intent is to show that the coupled bulk dynamics does not destroy the slow-motion pattern of material defects at the leading order. The second goal is to systematically generalize Onsager’s linear response principle to obstacle problems for interactive dynamics with topological changes. The investigator aims to derive a new phase field model for geometric motions of microfluidic flows, which automatically builds in migration mechanisms of interfacial layers whenever topological changes happen. This new model, together with mathematical validations, will unveil the hidden variational principle and a selection criterion. This variational principle will incorporate solid-fluid, solid-solid interactive mechanisms, and coherent micro-macro structures for general complex systems. 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.