Date of Award

5-2026

Document Type

Thesis

Degree Name

Master of Science (MS)

College/School

College of Science and Mathematics

Department/Program

School of Computing

Thesis Sponsor/Dissertation Chair/Project Chair

Eric Forgoston

Committee Member

Baojun Song

Committee Member

David Trubatch

Abstract

We investigate the dynamics of small inertial spherical and non-spherical particles in fluid flows. We consider the Maxey-Riley-Gatignol (MRG) equation, which models well the motion of spherical inertial particles in low Reynolds number flows. To study how shape affects the dynamics, we implement a corrective factor on the Stokes drag term in the MRG equation. This corrective factor, or shape factor, is based on the geometric properties of the particles. The Basset-Boussinesq history term in the MRG equation is often neglected to simplify analytical and computational studies involving the equation. We include this history term and implement a multi-step integration scheme to solve the MRG equation with history term. We consider a solid-body rotation vortex flow, a double-gyre flow and the Taylor-Green vortex flow and study how particle paths and particle aggregation patterns generated by the inclusion of the history term differ from particle paths and aggregation patterns generated by an often-used simplified version of the MRG model which ignores the history term. We also consider the combined effects of shape factor and the history term.

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