CAREER: Model Fluid-Solid Interactions, Networks REUs, and BioCalculus

University Of North Carolina At Chapel Hill, Chapel Hill NC

Investigators

Abstract

This project includes a collection of activities spanning research in low Reynolds number fluid dynamics, mentoring of undergraduate research in networks science, and curriculum development for improved presentation of mathematics to biology undergraduates. The project explores the computational modeling of fluid-solid interactions from suspensions phenomena obeying simple rules between interacting solids, to flows where key features can be effectively approximated by distributed Lagrange multiplier (DLM) techniques. In studying suspensions, the "sort-and-sweep" simulation method developed by the PI will be employed and extended to investigate sedimentation instabilities, including some analogous to classic fluid instabilities (e.g., the Rayleigh-Taylor heavy-over-light instability) and others that appear to be special to suspensions (e.g., in electrophoretic levitation and breakup of particle-laden drops). A main goal is testing macroscopic models of sedimentation processes. Model DLM calculations will be extended to explore important hydrodynamic phenomena at the scale of interaction between small numbers of rigid, jointed, or deformable solids, including investigation of natural and artificial modes of propulsion in liquids at small but non-zero Reynolds numbers. Research and mentoring activities are bridged in this project through Research Experiences for Undergraduates in networks science, including tools for identifying hierarchical community structures and the application of such tools to novel datasets, including the potential of investigating effective networks of hydrodynamically-interacting components. The project also includes extensive curriculum development aimed at optimizing the set of mathematical tools covered in courses for undergraduate students majoring in biology and the health sciences. Continuing advances in capabilities for developing micro- and nano-systems and machines lead to design questions about fluid dynamics at small scales that must be addressed with different tools than those used at large scales. At small scales viscosity plays an increased role (an air pump doesn't do a good job pumping more viscous maple syrup), and external boundary conditions become more important (the walls of blood vessels). Also important are interactions between solids and the complex viscoelastic fluids in which they are suspended, a common occurrence in biological situations. Developing computational tools for more efficiently and effectively handling such interactions is a goal. Other fundamental fluid-dynamic phenomena are further investigated, both for their own importance and for the validation of the proposed computational approaches to these regimes. For instance, the investigation of general questions about propulsion of small-scale objects through liquids leads to computational techniques that can be used to study scenarios of potential biological and medical importance.