# Axial and lateral particle ordering in finite Reynolds number channel flows

Original entry by Sagar Bhandari, APPHY 225 Fall 2010

## Reference

Axial and lateral particle ordering in finite Reynolds number channel flows, Katherine J. Humphry, Pandurang M. Kulkarni, David A. Weitz, Jeffrey F. Morris and Howard A. Stone, Physics of Fluids, 22, 081703 (2010)

## Keywords

Axial, Lateral, Particle order, Reynolds, Microfluidic

## Summary

In case of rectangular cross section microfluidic channel and particle size comparable to the channel size, consequences of the combination of confining geometries, inertia, and particle concentration have not been characterized. In this paper, the authors study the effects of particle concentration and channel geometry on inertial focusing. The authors find that the location and number of focusing positions depend on the linear number density of particles along the channel. The linear number density is a function of channel cross section and number of particles. 6 cm long microfluidic channels with a uniform rectangular cross-section in PDMS are used in their experiment. Polystyrene beads of diameter d=9.9 um are dispersed in water. As shown in Fig 1 , the particles, initially randomly located, migrate in the directions transverse to the flow and settle in characteristics focusing positions and spacings.

Figure 1:

The authors use relative occupancy function "p(r)" to quantify the particle ordering in both the axial and lateral directions which is computed by building a histogram for the location of all neighbors around each reference particle and normalizing by the bin size.When 'p(r)" is plotted against the particle fraction volume, "p(r)" exhibits maxima in both the lateral and axial directions as shown in Fig. 2.

Figure 2:

To understand the physical mechanisms underlying the observed regular axial spacing, the authors perform numerical simulations at finite Re in a wall-bounded geometry using the lattice Boltzmann method. Using the results from simulations to investigate the mechanism for this regular spacing , the authors find that confinement in the channel leads to fixed points in the flow with respect to the particle, and these roughly define the positions of neighboring particles in the axial direction. They infer "inertially influenced hydrodynamic interaction" as the source for this kind of behavior.