Nonlinear Dynamics of Confined Interfaces: Beyond Linear Analysis and Towards Control

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From the acrobatics of fluids that respond to magnetic fields, to the extraction of oil from the Earth, to electrode operation in consumer device batteries, the motion of interfaces must be modeled, analyzed and controlled towards achieving a desired flow pattern, improving the efficiency of energy recovery, or assuring safety. This award will support fundamental scientific research that will contribute new knowledge and understanding of the dynamics of interfaces between fluids. The outcomes of this research program could become the building blocks for new approaches towards the precise manipulation of spreading and confined layers of fluids, which is needed to advance additive manufacturing (also called 3D printing) processes, as well as lab-on-a-chip devices that use motion of droplets (closed fluid-fluid interfaces) to perform chemical diagnostics. Therefore, this award will promote both the progress of a scientific field, as well as potentially contribute to the science behind new technologies that benefit the U.S. economy and society, thus advancing national prosperity. Furthermore, the research will engage undergraduate, graduate and postdoctoral researchers within the PI's established culture of mentorship and diversity efforts, towards championing scientific excellence and broadening participation in this research field.Fluid interfaces do not always move and deform in an orderly fashion. They can be unstable, and their shapes can be unpredictable from the inputs to the system. The current research on such instabilities has focused on the initiation stage of the unpredictable behavior, which is called the linear regime. At the same time, the dynamics are influenced by multiple physical effects, whose coupled influence remains relatively unexplored. To address these knowledge gaps, the fundamental research will derive mathematical models and construct numerical methods to understand the late stage (termed nonlinear) time evolution of interfaces, eventually yielding methods to manipulate instability. Specifically, the research team will: (i) derive sharp-interface mathematical models of the dynamics of immiscible fluid-fluid interfaces confined in nonstandard Hele-Shaw geometries, including multiphysics interactions due to domain boundary motion and non-invasive forcing via magnetic fields; (ii) construct efficient numerical methods for Lagrangian sharp-interface tracking, based on the vortex sheet method, to enable analysis of the nonlinear evolution of interfaces, including their ability to sustain permanent traveling excitations (solitons); and (iii) harness (i) and (ii), in conjunction with optimization and control strategies from dynamical systems theory, to update the external forcing of the confined system on-the-fly and, thus, achieve pre-determined interfacial shapes and motions.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.