Measurements of the cross-sectional distributions of spherical particles suspended in rectangular channel flows

We investigated the inertial migration of neutrally buoyant spherical particles using millimeter-sized rectangular channels of various aspect ratios (\textit{AR} $=$ 1 -- 4.2), in the range of Reynolds numbers (\textit{Re}) from 100 to 2000. The Reynolds number was defined as \textit{UH}/$\nu $, where $U$ is the maximum flow velocity, $H$ is the length of the shorter face of the channel cross-section, and $\nu $ is the kinematic viscosity. Dilute suspensions of polystyrene particles of diameter $d =$ 300 - 650 $\mu $m were used. For the size ratio $d/H \quad =$ 0.1 -- 0.25, the observation of particle positions at downstream cross-sections revealed that the particles were aligned in a straight or curved line nearly parallel to the longer face of the channel cross-section and their probability density function showed a sharp peak at a certain distance from the channel centerline. These focusing positions of particles were found to depend on \textit{Re}, $d/H$ and \textit{AR}. They approached the channel centerline with increasing \textit{Re}. As \textit{AR} increased for constant \textit{Re} and constant $d/H$, focusing positions moved closer to the channel centerline, and reached asymptotic positions for \textit{AR }\textgreater 2.