Particle focusing mechanisms in curving confined flows

Particles in finite-inertia confined channel flows are known to segregate and focus to equilibrium positions whose number corresponds with the fold of symmetry of the channel's cross section. The addition of curvature into channels presumably modifies these equilibrium inertial focusing positions, because of the secondary flow induced in curved channels. Here, we identify the critical interaction of the secondary flow field with inertial lift forces to create complex sets of particle focusing positions that vary with the channel Reynolds number (Re(C)) and the inertial force ratio, which is a new dimensionless parameter that is based on the ratio of inertial lift to drag forces from the secondary flow. We use these results to identify microfluidic channel geometries to focus particles at rates an order of magnitude higher than previously shown (channel Reynolds number, Re(C) = 270) and develop design criteria for the focusing of potentially arbitrary-sized particles. In addition, our results indicate that channel curvature can lead to microfluidic designs with reduced fluidic resistance, useful for lower power inertial focusing or separation. These results will enable design of practical particle/cell separation, filtration, and focusing systems for critical applications in biomedicine and environmental cleanup.