Modeling and Analysis of Particle Laden Flow

This project involves modeling and analysis of particle laden flows using nonlinear partial differential equations (PDEs) for the flow thickness and volume fraction of particles in the flow. Such flows arise in many applications including the food industry, mining, and environmental cleanup. These flows are notoriously difficult to model because the dominant physics, especially for viscous flows, is due to many body interactions of the particles.

There are no "first principles" continuum models for the physics and instead modelers rely on semi-empirical rules for particle settling and migration. Even at the elementary level of reduced order continuum theory, the mathematical equations are a system of conservation laws with fluxes that need to be estimated numerically. This project addresses fundamental mathematics problems related to these models.

The project also develops new models for flows in complex geometries such as spiral separators used in the mining industry. This project is a five-year study that impacts our understanding of particle laden flow dynamics and analysis of PDEs for the novel fluid equations that model the physics of particle laden flows. In addition, this project provides research training for two doctoral students, five undergraduate researchers, and two postdoctoral scholars over a five-year period.

This project addresses several interrelated problems in particle laden flow models. (a) Flux functions in conservation law models for particle laden flow must be computed or estimated numerically. This raises the question of structural stability of multi-wave solutions of conservation laws under perturbation of the flux function. (b) Singular shocks have been shown to exist in conservation laws that model particle laden flow.

Such solutions have largely, to date, been a curiosity in the mathematics literature. This project considers the actual physics that leads to singular shocks and studies how to continue those solutions after the singular shock formation in a way that is consistent with experimental observations. (c) This project considers models for bidisperse flows with direct comparison to experiments, building on earlier work for bidensity flows. (d) Spiral Separators are devices used in the mining industry in which slurries flow under gravity in a helical trough and species within the slurry naturally separate through turns of the spiral, coming out as stripes at the end.

This project develops an asymptotic model for two species flows in spiral separators and studies how to optimally separate the species.

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.