Development of an experimentally-validated analytical framework to study particle-laden flows for biomedical regimes

In this work, an analytical framework is developed to describe the motion of a single particle or a system of particles within an unsteady, non-uniform, incompressible flow, focusing on rigid spheres translating in Newtonian fluids in two-way and four-way coupled regimes. The study aims to formulate particle motion using force terms that are more inclusive and general, yet theoretically feasible. For example, the non-linear fluid forces due to the convective term in the Navier-Stokes equation are obtained analytically. In addition, theoretical formulations for the coupling forces between particles and the resulting velocity field are developed. Both steady-state and transient portions of the forces are calculated. The regions where coupling force fields are significant with respect to chosen thresholds will be quantified. Additionally, these force fields will be used in a time-marching module to demonstrate the motion of particles and the resulting disturbed flow field in two-way coupled regimes. These formulations are validated against a variety of experimental test cases in both Eulerian and Lagrangian frameworks, using measurements from image-based methods such as particle image velocimetry (PIV) and particle tracking velocimetry (PTV).