Particle pairs and trains in inertial microfluidics

Abstract

Staggered and linear multi-particle trains constitute characteristic structures in inertial microfluidics. Using lattice-Boltzmann simulations, we investigate their properties and stability, when flowing through microfluidic channels. We confirm the stability of cross-streamline pairs by showing how they contract or expand to their equilibrium axial distance. In contrast, same-streamline pairs quickly expand to a characteristic separation but even at long times slowly drift apart. We reproduce the distribution of particle distances with its characteristic peak as measured in experiments. Staggered multi-particle trains initialized with an axial particle spacing larger than the equilibrium distance contract non-uniformly due to collective drag reduction. Linear particle trains, similar to pairs, rapidly expand toward a value about twice the equilibrium distance of staggered trains and then very slowly drift apart non-uniformly. Again, we reproduce the statistics of particle distances and the characteristic peak observed in experiments. Finally, we thoroughly analyze the damped displacement pulse traveling as a microfluidic phonon through a staggered train and show how a defect strongly damps its propagation.

A pair of particles in inertial microfluidics: effect of shape, softness, and position

“…96,101 As we demonstrated in ref. 61 for rigid particles, knowing the bounded two-particle states one can directly infer the lattice constant of the staggered trains, while the lattice constant of linear trains on the same streamline typically have a value determined by the range of the two-particle interaction. In this context, the steady-state value of the axial distance between the leading and lagging particles is summarized in Fig.…”

“…Thus, the present study will help to understand the multi-particle train configurations occurring in inertial microfluidics for soft particles and their mixtures, which will be more involved compared to the case of ref. 61, where only rigid particles of the same size were studied. Fig.…”

“…5 and 9) so that disturbances from the lagging particle can have a significant effect on the motion of the leading particle. The implemented LBFEIBM solver has been employed in a series of works by our group 19,20,60,61 (see Appendix A for benchmarking). According to our previous work we discretize the channel width with 90 lattice nodes for the case of soft particles and 75 lattice nodes for solid particles.…”

“…Schaaf et al 60 reported that for two closely placed solid particles in a channel flow, the inertial lift forces acting on the leading and lagging particles differ significantly. In their subsequent work 61 they extended the understanding of a particle pair to study the behavior of particle trains 62 in inertial microfluidics. At low Reynolds numbers, Lac et al 63 and Aouane et al 64 investigated the interaction of two soft capsules in shear and Poiseuille flows, respectively.…”

Microfluidic formation of crystal-like structures

“…The stability of staggered particle pairs was also confirmed by detailed numerical simulations. 84,87,88 The particles attracted each other over large distances without significant changes of the cross-stream position. Specifically, depending on the initial lateral positions and axial distance, four different kinds of trajectories were possible.…”