FRG: Collaborative Research: Computational Methods for Complex Fluids: Adaptivity, Fluid-Structure Interaction, and Applications in Biology

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Many biological systems involve flexible structures immersed in viscoelastic fluids (e.g., sperm in the reproductive tract, bacteria in the gut and lung, ciliary transport of mucus in the lung). In some cases, such as cilia-driven transport in the lung, these structures operate in a multi-fluid environment. Despite decades of work explicit challenges remain with developing suitable computational tools for the modeling of the complex fluid-structure interactions. The goal of this project is to develop and analyze accurate computational methods for these simulations, and to establish high-performance open-source implementations of these tools to be used by other researchers. The new computational tools together with experimental measurements will be used to generate new insight into the mechanical behavior of mucus. Mucus provides a protective barrier for every human organ, and many diseases and disorders are associated with mucus pathology (e.g., in the lung (COPD, cystic fibrosis, asthma), stomach (ulcers), reproductive tract (infertility)). Moreover, tools developed as part of these projects have applications beyond mucus: to the food industry, for personal care products, as well as pharmaceutical applications, including drugs and drug delivery systems. The project will also provide broad interdisciplinary training for graduate students and postdoctoral researchers in the mathematical sciences.The specific research objectives of this project are 1) to develop and analyze efficient higher-order accurate numerical methods for fluid-structure interaction and fluid-fluid interaction problems involving complex fluids, 2) to validate these methods by comparison to experimental data of project collaborators, and 3) to develop mathematical models of industrial and biological systems, including microbead rheology, ciliar synchronization and transport, and phase separation of suspensions. Previous research on numerical methods for viscoelastic fluids has been driven by engineering applications, while biological applications pose new challenges: large deformations of active soft structures and complex rheology. Despite past efforts to understand the dynamics of active structures in complex fluids, a significant bottleneck persists: the lack of accurate, efficient, adaptive numerical methods and software for viscoelasstic fluid-structure interaction and fluid-fluid interfaces. The research team aims to build, validate, and apply this technology, guided by applications and experimental data from biology and engineering.