2024 Physics Oral Defense: Two-Phase Continuum Dynamics of Suspensions at Low Reynolds Number

Abstract: Many fluid flows central to biological and industrial interests are actually suspension flows, characterized by the coupled transport of solid particles and their suspending fluid medium. Yet, despite more than a century of earnest theoretical effort, a universally accepted theory of suspension fluid dynamics has remained elusive. Here, we present a mathematical framework which is used to derive a continuum-level description of a suspension of identical spherical particles at low Reynolds number. Applying our equations to an isotropic suspension of identical rigid no-slip particles, we correct and extend results obtained separately by A. Einstein and G.K. Batchelor. Next, we develop an asymptotic procedure which is used to derive effective continuum boundary conditions by analyzing particle-wall effects through a Green’s function approach. Finally, we extend our original framework to allow for small spatial variations in the particle singularity strengths. We find new dynamical contributions to the bulk suspension stress and average particle velocity that arise in nonuniform suspensions or flows with curvature. Our approach clarifies the methods required to model suspensions beyond the dilute limit and corrects inconsistencies in previously proposed suspension models, resulting in dynamical equations which are stable and may be expanded to any desired order of accuracy.

Zoom:  https://us05web.zoom.us/j/81519931238?pwd=8jiSx7VX0hpGtZbvQJF12Od6aN7mB8.1  Passcode: 4152024