A tracking algorithm for finite-size particles.

Particle-wall interaction is important in various applications such as cell sorting, particle separation, the entire class of hydrodynamic filtration and its derivatives, etc. Yet, accurate implementation of interactions between the wall and finite-size particles is not trivial when working with the currently available particle tracking algorithms/packages as they typically work with point-wise particles. Herein, we report a particle tracking algorithm that takes into account interactions between particles of finite size and nearby solid objects. A particle is modeled as a set of circumferential points. While fluid-particle interactions are captured during the track of particle center, interactions between particles and nearby solid objects are modeled explicitly by examining circumferential points and applying a reflection scheme as needed to ensure impenetrability of solid objects. We also report a modified variant of auxiliary structured grid method to locate hosting cells, which in conjunction with a boundary condition scheme enables the capture of interactions between particles and solid objects. As a proof-of-concept, we numerically and experimentally study the particles' motion within a deterministic lateral displacement microfluidic device. The results successfully demonstrate the zigzag and bump modes observed in our experiments. We also study a microfluidic device with pinched flow numerically and validate our results against experimental data from the literature. By demonstrating an almost 8 $\times$ speedup on a system with eight performance threads, our investigations suggest that the algorithm can benefit from parallel processing on multi-thread systems. We believe that the proposed framework can pave the way for designing related microfluidic chips precisely and conveniently.