The investigator and collaborators propose to develop a new class of Immersed Boundary-based methods to investigate the interaction of a large number of immersed structures in 2D and 3D with a complex (non-Newtonian) fluid. These innovative methods will have the computational efficiency demanded by some outstanding, formidable problems of flow-structure interaction in complex fluids and will establish new paradigms in the modeling and simulation of these type of systems. To achieve this, the investigator and the project's participants will introduce fundamentally innovative approaches for the fast computation of the influence of the structure on the flow, for the rapid solution of robust, implicit discretizations, and for model building and computation in the presence of a complex fluid in important applications. While the new approaches will be designed with concrete problems in mind (collective sperm motility in a complex fluid and peristaltic pumping), their applicability will be broad.

A myriad of technologically and scientifically important problems can be described as the interaction of a flow and immersed structures that could be elastic or rigid and could come in a broad range of shapes and length scales, from nano to macro. The swimming of micro-organisms like cellular and flagellar locomotion, sperm motility, insect flight, aerodynamic design, cardiac fluid dynamics, and processing of polymeric materials are just a few important examples. There is now a recognized, pressing need to investigate these dynamics in more realistic fluid environments which take into account the frequent viscoelastic character of the underlying complex flow. The project focuses on the development of fluid models and efficient computational tools to investigate this important class of problems. Research and education will be vigorously integrated in a multi-disciplinary environment with a sustained effort to promote and broaden the participation of underrepresented groups, with the active participation of undergraduates, with innovative pedagogic initiatives and modes of collaboration, and with ties with the industrial sector.

Project Report

Many technologically and scientifically important problems can be described as the interaction of a flow and immersed elastic structures. Aerodynamic design, insect flight, swimming of microorganisms, cardiac fluid dynamics, and processing of polymeric materials such as plastics are just a few examples. Often, these immersed structures are the surfaces that bound drops and bubbles composing complex fluids such as emulsions, foams, and polymeric solutions found in a wide variety of industrial applications. Computer simulation plays a key role in the investigation of these important systems. But there are many computational challenges to achieve accurate and physically relevant solutions due to the enormous number of degrees of freedom of these problems. This project focused on the design, implementation, and application of computational methods for the simulation of immersed structures like the swimming of microorganisms and of surfaces separating polymeric and liquid crystalline fluids. Specifically, we advanced a widely used computational methodology (the Immersed Boundary Method) by designing an effective technique to overcome one of the main limitations of this popular method. We applied the new computational approach to the investigation of the flow that occurs between elastic walls that contract and expand periodically, so called peristaltic pumping, as it occurs in gastrointestinal and esophageal transport. Our study showed how viscoelasticity could affect this important type of flow. We also applied our computational method to simulate the locomotion of a microscopic swimmer in a viscoelastic flow and investigated whether viscoelasticity hinders or enhances locomotion. Our study identifies the effects of the different parameters in the model and thus it contributes to a better understanding of this problem. We investigated also, via computer simulation, mixtures consisting of polymers and of liquid crystals. The later can be viewed as suspensions of rigid rod-like molecules whose mean orientation is strongly affected by the flow and by how these rigid molecules stick to the boundaries. Our computational investigation revealed how these affect the dynamics of phase separation of these mixtures and other immersed structures. As part of its broader impacts, this project had a strong educational component. Seven students were directly involved with research activities. Among them four undergraduates, one masters students and two doctoral students. The majority of them were from under-represented groups.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Program Officer
Leland M. Jameson
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University of California Santa Barbara
Santa Barbara
United States
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