FRG: Collaborative Research: Dynamics of elastic biostructures in complex fluids

New York University, New York NY

Investigators

Abstract

Problems in biological fluid dynamics typically involve the interaction of an elastic structure with a surrounding fluid. Mucus transport by cilia in the respiratory tract, sperm penetration of the oocyte in fertilization, and peristaltic contractions of the oviduct are examples of such interactions. Many biological fluids are actually complex; that is they are not liquids or mixtures of a simple molecular structure that yields Newtonian responses, but instead have complicated non-Newtonian mechanical responses that arise, usually, because they have suspended microstructure. While much progress has been made in the development of mathematical models and numerical methods for fluid-structure interactions in a Newtonian fluid, much work needs to be done in the case of complex fluids. This focused research group will use a combination of analytical, computational and experimental tools to investigate the dynamics of elastic structures coupled to a complex fluid. Accurate and robust numerical methods for viscoelastic fluids coupled to moving and flexible boundaries will be developed that build upon classical immersed boundary methods and particle methods previously designed for Newtonian fluids. Continuum descriptions of the viscoelastic fluid will be implemented, as well as models that track discrete viscoelastic microstructure of the fluid. While the methods developed will be widely applicable, the team will focus upon the biofluidmechanics of reproduction, nematode motility in microfluidic chambers, as well as mucus-ciliary transport. Computational models will be coordinated with physical and biological experiments performed at the Applied Mathematics Lab at the Courant Institute. Mathematics has had a huge impact on engineering and the physical sciences through its development of theoretical analyses and numerical methods for Newtonian fluid flows. The dynamics of complex fluids is emerging as another such opportunity, and is one which draws some of its richest problems from new areas in biophysics and engineering, medicine and reproductive health, and from core biology. The integration of mathematical and computational analysis into biological science presents educational challenges and great opportunities. This research project embraces these challenges, and is based upon collaborations of investigators at four institutions - Tulane University, New York University, Washington State University and the University of California, Los Angeles. A central component of this project is the training of graduate students and postdoctoral researchers. This FRG project will sponsor two summer programs, where the postdoctoral researchers and graduate students will spend six weeks at the Applied Mathematics Lab at Courant Institute. This will provide opportunities for all the students and postdocs involved in the project to work together side by side, develop a comprehensive understanding of the various aspects of the research, and experience and participate in the life of a working fluids lab.