Holographic analysis of three-dimensional inertial migration of spherical particles in micro-scale pipe flow

The inertial migration of neutrally buoyant spherical particles suspended in a micro-scale pipe flow was investigated in a Reynolds number range of 1.6 <= Re <= 77.4. A microtube, 350 mu m in diameter, was used for the micro-scale pipe flow, and the ratios of the tube diameter (D) to the particle diameter (d) were D/d = 50, 23, and 12. The three-dimensional positions of the particles were measured using a digital holography technique, and the detailed structures of the Segre-Silberberg annulus were visualized. By analyzing the probability density distributions of the particles, the quantitative data of the equilibrium particle positions were obtained and compared to those of previous experimental and numerical studies. Several characteristics of the inertial migration in a microscale pipe flow, including the effects of Re and D/d, were analyzed. The results were found to be similar to those obtained in macro-scale flows. The degree of inertial migration was also quantified using the obtained probability density function. Based on these results, simple criteria were suggested on the entry lengths required in the design of inertial microfluidic devices.