Numerical investigation on the forming and ordering of staggered particle train in a square microchannel

Abstract

An in-depth understanding of inertial-focusing mechanism is significant to developing high-throughput microfluidic devices. This paper numerically studies the forming and ordering of a staggered particle train in a square microchannel using the immersed boundary-lattice Boltzmann method. Effects of the particle Reynolds number (Rep) and average length fraction (⟨Lf⟩) are mainly concerned, where ⟨Lf⟩ describes the initial particle concentration. Results reveal that the staggered particle train has two distribution patterns depending on ⟨Lf⟩, namely, Continuous Pattern that particles uniformly distributed in the channel and Discontinuous Pattern that an interruption occurs in the train. A detailed train-forming process is provided. Particles within the train are approximately uniformly distributed in both patterns; thus, influencing factors of this uniform interparticle spacing [(L/D)uni] are investigated. A critical ⟨Lf⟩ (⟨Lf⟩*) is defined, dividing determinants of (L/D)uni into Rep-dependent and ⟨Lf⟩-dependent areas. The flow fields and forces acting on the particles were analyzed for further investigation. Four forces are considered: shear gradient lift force, wall-induced lift force, attractive forces, and repulsive forces. Analysis shows that the latter two forces play an essential role in forming a train and the vortex or counterflow is crucial in determining interparticle spacing. Finally, the lagging, translational, and angular velocities were employed to describe particle dynamic characteristics. These parameters are decisively affected by Rep and slightly by ⟨Lf⟩. Inertial-focusing behaviors of a single particle are also compared. The present study is expected to help understand the inertial-focusing behaviors of staggered particle trains and provide a reference for practical applications of microfluidics devices.