Collaborative Research: Kinetic to Continuum Modeling of Active Anisotropic Fluids

The principal investigators use mathematics and computation to model fluid-particle mixtures in which the individual particles are anisotropic (e.g., rod-like) and have their own propulsion mechanism. Examples arise in nature with suspensions of rod-like, flagella-propelled bacteria, in living cells where actin filaments provide structural integrity and molecular motors propel the filaments to achieve cellular function, and in high performance materials where catalytic nano-rods are suspended in a reactive solvent and propelled by chemical reactions. These systems share the remarkable feature of self-organization on scales in space and time far greater than those of the individual particles, translating to functionality across many scales. These diverse active particle-fluid systems have been previously modeled. Here the investigators undertake a unified theoretical and computational platform for such problems, which offers multiple benefits. A common mathematical structure reveals how these systems achieve their functional properties, informs which physical and chemical features allow the most efficient steering and optimization of the system toward desired properties, allows for a common computational platform, and allows one to incorporate additional degrees of freedom or perturb existing particle and fluid properties and predict their consequences. These advances have applications to enhance beneficial bacterial colonies and to disrupt harmful ones, to repair damaged cellular functions, and to design nano-composite materials with optimal properties. Graduate students are involved in the work of the project.

The principal investigators develop a modeling and computational platform for active, anisotropic fluids, unifying three apparently diverse fluid systems (catalytic nano-rod dispersions, swimming bacterial suspensions, and motor-driven actin filament gels) for which models, analysis, algorithms, and simulations have so far evolved independently. The mathematical platform unifies previous results, spans kinetic to continuum spatial and temporal scales, and identifies a common leading-order mathematical structure at each scale of description as well as the lower-order structure that distinguishes among different active, anisotropic fluids. This structure guides analysis and algorithm development toward an understanding of, and predictive control over, the remarkable observed behavior of these fluid systems. The project aims to distinguish sensitivity to particle dimensions, aspect ratio, concentration, and activation energy, with direct application to active nano-rod dispersions, actin filament gels, and bacterial suspensions in confined and free surface flows.