Collaborative Research: Self-Assembly and Aggregate Formation in Stratified Fluids

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The atmospheres, lakes, and oceans of our world typically involve density variability, with layers of lighter fluid sitting on top of heavier fluid. In this project, we are exploring a novel mechanism we have discovered through which particles suspended within such layered systems are seen to attract each other and self-assemble, forming large disc like clusters. The mechanism for this attraction involves fluid flows which the particles themselves create from being in a layered fluid. Such clusters occur ubiquitously in lakes and oceans, where they can provide food sources for a variety of organisms, or result in concentrations of polluting particles. The origins of these clusters may well lie within this new aggregate formation mechanism under exploration within this award. Graduate students will be involved in the project. Specifically, the award will undertake a combined theoretical, numerical, and experimental investigation of a newly discovered hydrodynamic interaction between particles in a stratified ambient environment. Recent experimental work by the PIs at the UNC Joint Fluids Lab have demonstrated that passive particles suspended in a density-stratified environment interact through self-induced flows which can result in approaching one and another over time until coming into contact. Collections of many particles tend to aggregate and self-assemble into large-scale 2D structures due to this newly identified attraction mechanism. The project aims to characterize this newly-identified interaction effect in nature for the first time, through novel asymptotic methods, numerical simulations, and careful experimentation. The research will explore the complex interplay between diffusion, advection, and geometry (through physical boundary conditions) in inducing new collective phenomena. This requires developing novel computational, asymptotic, and experimental methods for extracting quantitative predictions from the parent Navier-Stokes equations coupled through the viscous stress tensor to particles suspended in stratified environments. The new asymptotic methods developed as part of this proposal will also prove useful for a wider range of problems in fluid dynamics and potential theory.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.