The inertial migration of neutrally buoyant spherical particles suspended in tube flows of square cross sections was investigated experimentally in the range of Reynolds numbers ($\text{Re}$) from 1 to 800 for particle-to-tube-size ratios from 0.075 to 0.175. Direct observations of the particle distribution in the cross section at various distances from the tube inlet revealed that at low $\text{Re}$, smaller than a certain critical value, particles were focused on four equilibrium positions, located at the center of channel faces, consistent with previous studies on microchannel flows, whereas at higher $\text{Re}$, larger than another critical value, four additional equilibrium positions were observed near the channel corners. At intermediate $\text{Re}$, between these two critical values, we observed new focusing positions of particles, located on a heteroclinic orbit joining the channel face and corner equilibrium positions. Comparing these results with corresponding numerical simulations, we examined the migration properties in detail and categorized their types. It was found that the critical $\text{Re}$ values depended considerably on the particle-to-tube-size ratio.

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• Microfluidics
• Particle-laden flows
• Suspensions