  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,
Stokes, and Bertozzi [1], we illustrate via numerical simulations that these
bifurcations can be leveraged in a spiral duct to achieve large separation
between different sized particles by transiently focusing smaller particles
near saddle-points. We demonstrate this by separating similar-sized particles,
as well as particles that have a large difference in size, using spiral ducts
with square cross-section. The 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.
