Inertial focusing of spherical particles suspended in laminar circular tube flows

Neutrally buoyant spherical particles suspended in laminar circular tube flows migrate laterally due to inertia toward an equilibrium radial position, called the Segre-Silberberg (S-S) annulus. Recent experimental studies reported that another annulus located closer to the tube center, called the inner annulus, appeared at relatively high Reynolds numbers (Re). However, other experimental studies showed the fading of this inner annulus at further downstream cross sections if Re is lower than a certain critical value. Thus, it has not been revealed yet whether the inner annulus is an equilibrium position or not. In this study, we investigated experimentally the cross-sectional distribution of spherical particles in circular tube flows with the particle-to-tube-diameter ratio (size ratio) from 0.083 to 0.15 at Re≲1,000. We found three types of particle focusing patterns in the downstream cross section, depending on Re, such as (A) S-S annulus only, (B) S-S and inner annuli and (C) inner annulus only. The pattern (A) was observed in the lowest Re range, the pattern (B) in higher Re range, and the pattern (C) in the highest Re range. Thus, the inner annulus could be an equilibrium radial position for Re larger than a critical value, which depends on the size ratio.