# Particle Segregation and Dynamics in Confined Flows

Entry: Chia Wei Hsu, AP 225, Fall 2010

D. Di Carlo, J. F. Edd, K. J. Humphry, H. A. Stone, and M. Toner, "Particle Segregation and Dynamics in Confined Flows," Phys Rev Lett **102**, 094503 (2009)

## Summary

Rigid spherical particles exhibit lateral migration in cylindrical pipes. Such phenomenon cannot be explained by the Stokes equation (ie. linearized Navier-Stokes equation at low Reynolds number). Thus the inertial contribution of the particles must be taken into account, and the full Navier-Stokes equations must be used. In order to simplify the complexity of this problem, previous studies have focused on cases when particles dimension (<math>a</math>) is much smaller than the channel cross section dimension (<math>H</math>). In this paper, the authors show that such "point-particle" assumption is not valid when <math>a</math> approaches <math>H</math>.

## Method

The authors examine rectangular cross-section microchannels. They compare experimental observations with numerical calculations based on finite element method. Fig 1 (a) shows the schematic of the system studied.

The experimental system is prepared using soft-lithography fabrication. They consist of microchannels (length 5 cm; width and height <math>H</math>=20-50 µm) with dilute polystyrene particles (<math>a</math>=5-20 µm) suspended in water. The polystyrene particles flow at controlled rates using a syringe pump.

## Results

Both numerical calculations (fig 1(b)) and experiments (fig 1(c)) reveal four attractors that correspond to the equilibrium position of particles. The authors then study how the location of these fixed points depend on <math>a/H</math>, for the range <math>a/H</math>=0.1~0.9. They observe that particles shift toward channel center as <math>a/H</math> increases. Further, they found that particles rotate at a rate that is slower when <math>a/H</math> increases. Numerical calculations agree quantitatively with experiments.

Then, the authors use numerical calculations to study how the lifting forces scale with <math>a/H</math> across different locations in the channel. They found that the lifting forces depend on <math>a/H</math> and location in a more complex way than the prediction of previous theoretical studies using point-particle assumption (fig 2).

## Connection to Soft Matter

The lateral migration of particles in confined flows is a common phenomenon. It occurs not only for rigid spherical particles, but also for soft deformable particles (such as blood cells) and polymers. It is important for many technical applications and for biology. This works points out that the size of the particles can play an important role in this inertial migration phenomenon, and so that the point-particle assumption should be revisited.