| NSF Org: |
CMMI Division of Civil, Mechanical, and Manufacturing Innovation |
| Recipient: |
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| Initial Amendment Date: | August 12, 2020 |
| Latest Amendment Date: | August 12, 2020 |
| Award Number: | 2029540 |
| Award Instrument: | Standard Grant |
| Program Manager: |
Marcello Canova
mcanova@nsf.gov (703)292-2576 CMMI Division of Civil, Mechanical, and Manufacturing Innovation ENG Directorate for Engineering |
| Start Date: | September 1, 2020 |
| End Date: | August 31, 2024 (Estimated) |
| Total Intended Award Amount: | $387,724.00 |
| Total Awarded Amount to Date: | $387,724.00 |
| Funds Obligated to Date: |
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| History of Investigator: |
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| Recipient Sponsored Research Office: |
2550 NORTHWESTERN AVE # 1100 WEST LAFAYETTE IN US 47906-1332 (765)494-1055 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
Young Hall West Lafayette IN US 47907-2114 |
| Primary Place of
Performance Congressional District: |
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| Unique Entity Identifier (UEI): |
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| Parent UEI: |
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| NSF Program(s): | Dynamics, Control and System D |
| Primary Program Source: |
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| Program Reference Code(s): |
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| Program Element Code(s): |
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| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.041 |
ABSTRACT
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.
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH
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PROJECT OUTCOMES REPORT
Disclaimer
This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.
In his Dirac Memorial Lecture, Nobel Laureate P. G. de Gennes wrote, "the interfaces between two forms of bulk matter are responsible for some of the most unexpected actions." One reason is that interfacial mechanics deals not just with the boundaries between fluids (and solids) but also with the boundaries between scientific disciplines. Interfaces are abundant in our daily lives, from the deformation of a soap bubble to the progression of a cold front on a weather report. Thus, from both a fundamental scientific and a practical technological point of view, and even out of pure curiosity, we wish to model, simulate, predict, and control these complex patterns. The methods of dynamical systems allow us to do so.
This NSF award enabled the discovery of how to configure a magnetic field to cause a circular droplet of a magnetic (ferro) fluid to become a spinning gear. Searching for "ferrofluid" on YouTube reveals our innate fascination with how these science-fiction-like fluids behave. Analyzing and controlling their motion through mathematical models is much more challenging. We discovered that a stationary force can lead to nonlinear dynamics through instability. Magnetic fluids are but one example of active materials responsive to non-invasive external fields. Through further analysis, we developed a reduced model --- a single nonlinear partial differential equation encompassing all the multiphysics of the problem --- that demonstrated how a misalignment of the magnetic field and the interface surface normal causes it to "chase its tail" and makes the droplet rotate. More precisely, we discovered that a balance between energy production and dissipation on a magnetic fluid's interface supports dissipative solitons. Under extreme conditions, these interfacial waves can even "break," much like water waves overturn approaching a beach. Despite ferrofluids being the featured example in much of our work under this award, the underlying physics are generic, rooted in deep concepts of bifurcation theory and nonlinear dynamical systems. For example, we demonstrated how the notion of bifurcation delay allows time-dependent targeted control of the interface's motion via the external field. The novel dynamical phenomena discovered in the course of the research supported by this NSF award could become the building block of new technologies (say, 3D printing, micromixing or microchip droplet logic) that require the precise manipulation of spreading and confined layers of fluids. The potential economic impact of such a breakthrough in additive manufacturing is enormous.
PI Christov and his team have been highly productive in the course of the research supported by this NSF award, producing many peer-reviewed journal publications and conference proceedings. The scientific results from this NSF award were disseminated in top field-specific and multidisciplinary scientific journals, including Physical Review E, the Proceedings of the Royal Society A, and the Journal of Fluid Mechanics, amongst others. The PI and the graduate students participating in this research have also presented their research to international scientific audiences at the 74th through 76th Annual Meetings of the American Physical Society's Division of Fluid Dynamics, and the 2021 and 2023 SIAM Conferences on Applications of Dynamical Systems, amongst other conferences.
PI Christov's activities under this NSF award have led to an impact on the development of human resources. Specifically, this NSF award fully or partially supported the completion of 3 female PhD student's dissertations, two of them continuing on to competitive academic postdocs and one going into industrial R&D. One Master's student was able to interact with the PhD students working on this research, completing a thesis. Several other graduate students had a chance to participate in the project during summers, specifically to mentor undergraduates. For example, PI Christov and his team provided unique R1-university-level research experiences to 4 undergraduates from Savannah State University, motivating some of them to apply to graduate programs in engineering.
PI Christov's activities under this NSF award have also led to an impact on teaching and educational experiences. For example, PI Christov and PhD students supported under this award developed a summer seminar course in 2021, which they co-mingled with an undergraduate research experience for students from Savannah State, on developing Python-based tools for studying basic interface dynamics problems. Students learned to code, use SciPy to solve nonlinear differential equations related to interface dynamics, and use Matplotlib for visualization. Undergraduate research engagement was continued through Purdue's Summer Undergraduate Research Fellowship in 2022, 2023, and 2024.
Last Modified: 01/23/2025
Modified by: Ivan C Christov
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