Computational Tools for Active Suspensions

Regents Of The University Of Michigan - Ann Arbor, Ann Arbor MI

Investigators

Abstract

This project will develop advanced computational tools to simulate and optimize the locomotion in a fluid medium of microscopic particles, such as bacteria or specially-designed micro-robots. Understanding how these microswimmers move is crucial for a wide range of applications, from improving our understanding of how biological systems function at the cellular level to creating innovative technologies. For instance, this research could lead to breakthroughs in targeted drug delivery, where microscopic robots deliver medicine precisely where it is needed in the body, or in developing new ways to transport materials within lab-on-a-chip or organ-on-a-chip devices. By making these simulations more efficient and accurate, this project aims to provide fundamental insights that will benefit fields such as biotechnology and materials science, ultimately contributing to scientific discovery and technological advancements that impact people's daily lives. Despite advancements in modeling and simulations of microswimmers, performing control and optimization in complex environments is still daunting, primarily owing to the lack of computational tools that scale to realistic problem sizes and work on arbitrary moving geometries. The primary goal of this project is to develop accurate, computationally efficient, and scalable numerical algorithms necessary for large-scale simulations, as well as shape and functional optimization of microswimmers. The research will address key computational difficulties, including the accurate evaluation of near-singular integrals and periodization schemes in three dimensions that support adaptivity. Adjoint formulations will be derived for various practical scenarios, such as microswimmers in confined flows or in the presence of other active or passive particles. Building on existing work with integral equation methods, the project will specifically develop adjoint-based shape optimization schemes, new high-order nearly-singular integration schemes to simulate flows through confined geometries, and spectrally-accurate, adaptive three-dimensional periodization schemes that can be accelerated by existing fast N-body algorithms. 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.