Focusing patterns of spherical particles in a viscoelastic flow through square channels

The inertial migration of neutrally buoyant spherical particles in viscoelastic fluids flowing through square channels is experimentally and numerically studied. In the experiments, using dilute aqueous solutions of polymers with various concentrations that have nearly constant viscosities, we measured the distribution of suspended particles in downstream cross-sections for the Reynolds number ( $\textit{Re}$ ) up to 100 and the elasticity number ( $El$ ) up to 0.07. There are several focusing patterns of the particles, such as four-point focusing near the centre of the channel faces on the midlines for low $\textit{El}$ and/or high $\textit{Re}$ , four-point focusing on the diagonals for medium $\textit{El}$ , single-point focusing at the channel centre for relatively high $\textit{El}$ and low $\textit{Re}$ , and five-point focusing near the four corners and the channel centre for high $\textit{El}$ and very low $\textit{Re}$ . Among these focusing patterns, various types of particle distributions suggesting the presence of a new equilibrium position located between the midline and the diagonal, and multistable states of different equilibrium positions were observed. In general, as $\textit{El}$ increases from 0 at a constant $\textit{Re}$ , the particle focusing positions shift from the midline to the diagonal in the azimuthal direction first, and then inward in the radial direction to the channel centre. These focusing patterns and their transitions were numerically well reproduced based on a FENE-P model with measured values of viscosity and relaxation time. Using the numerical results, the experimentally observed focusing patterns of particles are elucidated in terms of the fluid elasticity-induced lift and the wall-induced elastic lift.