Utilizing bifurcations to separate particles in spiral inertial microfluidics

Particles suspended in fluid flow through a closed duct can focus to specific stable locations in the duct cross section due to hydrodynamic forces arising from the inertia of the disturbed fluid. Such particle focusing is exploited in biomedical and industrial technologies to separate particles by size. In curved ducts, the particle focusing is a result of balance between two dominant forces on the particle: (i) inertial lift arising from small inertia of the fluid and (ii) drag arising from cross-sectional vortices induced by the centrifugal force on the fluid. Bifurcations of particle equilibria take place as the bend radius of the curved duct varies. By using the mathematical model of Harding et al. [J. Fluid Mech. 875, 1–43 (2019)], we illustrate via numerical simulations that these bifurcations can be leveraged in a spiral duct to achieve a large separation between different sized neutrally buoyant particles and identify a separation mechanism, not previously reported, which exploits the transient focusing of smaller particles near saddle points. We demonstrate this for similar sized particles, as well as particles that have a large difference in size, using spiral ducts with a square cross section. The novel formalism of using bifurcations to manipulate particle focusing can be applied more broadly to different geometries in inertial microfluidics, which may open new avenues in particle separation techniques.