Longitudinal particle separation
Owing to inertial effects, the flow through a three-dimensional curved duct focuses finite-sized spherical particles in the two-dimensional cross-section onto either stable equilibrium points or limit cycles. This hydrodynamic inertial focusing underpins various biomedical and industrial applications for size-based particle and cell sorting. Departing from conventional particle separation in the channel cross-section, we instead focus on particle separation in the primary flow direction, i.e., longitudinal separation. We consider a duct with an elliptical centreline and a tall rectangular cross-section. For a given particle size, the nature of the cross-sectional equilibrium points depends on the local radius of curvature of the duct, and a periodical variation of the radius of curvature can result in a periodical bifurcation behaviour along its length. In particular, a duct geometry that undergoes a periodically varying saddle-node infinite-period (SNIPER) bifurcation can be used to improve longitudinal, at the expense of cross-sectional, particle clustering. For sufficiently large particles, this longitudinal clustering weakens at higher Reynolds numbers and with decreasing eccentricity, in contrast to small particles whose longitudinal clustering remains unaffected across a wide range of geometric configurations and flow conditions. Then, ducts with smaller eccentricities enable simultaneous separation along both the flow direction and the cross-section. In contrast, for larger eccentricities, the emergence of a SNIPER bifurcation promotes more pronounced longitudinal separation while compromising cross-sectional separation. These preliminary findings suggest that elliptically wound microfluidic devices might be used for longitudinal separation of particles by size, with potential biomedical and industrial applications.