The separation and sorting of living cells play an important role for

medical, biological and industrial applications. Current research

focuses on the inertial migration mechanism for a label-free,

passive and continuous separation of neutrally buoyant

particles. The physical effects and different particle behaviours,

however, are not completely understood. To elucidate the

migration and focusing of particles in a microfluidic channel

direct numerical simulations of geometrically resolved particles

using the Immersed-Boundary Method are presented. The

analysis in this work is structured based on the geometry of the

channel. In straight channels, particle focusing is dominated

by the inertial migration. In spirals the curvature introduces

a new phenomenon which increases the complexity of the

flow. The numerical simulation of particles in curved channels,

however, still presents a challenge. To allow such simulations

at a reasonable computational cost, a coordinate transformation

is implemented and validated against experimental

results. The simulation results provide another insight on

the migration process concerning migration time, particle

positioning in the cross-section, streamwise particle spacing,

and the surrounding fluid flow. Focus is given to the migration

of nospherical particles.