Particle-Laden Thin Film Flows

This talk will showcase the challenge in the modeling and mathematics for particle-laden thin film flows. 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. In the lubrication limit, the mathematical equations are a system of conservation laws with fluxes that need to be estimated numerically. The speaker will review our current understanding about such systems and will discuss some open problems. Our group at UCLA is just beginning a five-year NSF-sponsored project in this research area and would welcome visitors and collaborators interested in working with us on these problems.