This study presents a method for continuous inertial focusing, ordering, and separation of particles in microchannels. The researchers demonstrate that particles in laminar flow can migrate across streamlines due to inertial lift forces, which become significant when the flow is not purely viscous. By engineering symmetric and asymmetric channel geometries, they can bias particle equilibrium positions to create continuous streams of ordered particles in three spatial dimensions. Particles can be ordered laterally with >80-nm accuracy and longitudinally in regular chains along the flow direction. For discoidal red blood cells, a fourth dimension of rotational alignment is observed. The ordering is independent of particle buoyant direction, suggesting minimal centrifugal contributions. Theoretical analysis shows that the physical principles are operational over a range of channel and particle length scales. The ability to differentially order particles of different sizes continuously, at high rates, and without external forces in microchannels has broad applications in continuous bioparticle separation, high-throughput cytometry, and large-scale filtration systems. The study shows that inertial lift forces dominate particle behavior when the particle Reynolds number is of order 1. In microscale channels, particle flow is typically dominated by viscous interactions with R_p << 1. In these systems, particles are accelerated to the local fluid velocity due to viscous drag. Dilute suspensions of neutrally buoyant particles do not migrate across streamlines, resulting in the same distribution seen at the inlet, along the length, and at the outlet of a channel. As R_p increases, migration across streamlines has been observed in macroscale systems. In a cylindrical tube, particles migrate away from the tube center and walls to form a focused annulus. The theoretical basis for this "tubular pinch" effect is a combination of inertial lift forces acting on particles at high particle Reynolds numbers. The dominant forces on rigid particles are the "wall effect," where an asymmetric wake of a particle near the wall leads to a lift force away from the wall, and the shear-gradient-induced lift that is directed down the shear gradient and toward the wall. Inertial lift forces acting on a particle lead to migration away from the channel center. The particle migration velocity can be developed assuming Stokes drag balances this lift force. An estimate of the transverse migration velocity out from the channel center line can be made by using an average value of f_c ~ 0.5 for flow through parallel plates. This calculation yields a value of 3.5 cm/s for 10-μm particles in a flow with U_m = 1.8 m/s. Traveling a lateral distance of 40 μm requires traveling ≈2 mm downstream in the main flow. The lateral distance traveled will depend heavily on particle diameter, indicating the possibility of separations based on differential migration. In curved channels, secondary rotational flow caused by inertia of the fluid itself, called Dean flow, can alter the position of flowing particles. TheThis study presents a method for continuous inertial focusing, ordering, and separation of particles in microchannels. The researchers demonstrate that particles in laminar flow can migrate across streamlines due to inertial lift forces, which become significant when the flow is not purely viscous. By engineering symmetric and asymmetric channel geometries, they can bias particle equilibrium positions to create continuous streams of ordered particles in three spatial dimensions. Particles can be ordered laterally with >80-nm accuracy and longitudinally in regular chains along the flow direction. For discoidal red blood cells, a fourth dimension of rotational alignment is observed. The ordering is independent of particle buoyant direction, suggesting minimal centrifugal contributions. Theoretical analysis shows that the physical principles are operational over a range of channel and particle length scales. The ability to differentially order particles of different sizes continuously, at high rates, and without external forces in microchannels has broad applications in continuous bioparticle separation, high-throughput cytometry, and large-scale filtration systems. The study shows that inertial lift forces dominate particle behavior when the particle Reynolds number is of order 1. In microscale channels, particle flow is typically dominated by viscous interactions with R_p << 1. In these systems, particles are accelerated to the local fluid velocity due to viscous drag. Dilute suspensions of neutrally buoyant particles do not migrate across streamlines, resulting in the same distribution seen at the inlet, along the length, and at the outlet of a channel. As R_p increases, migration across streamlines has been observed in macroscale systems. In a cylindrical tube, particles migrate away from the tube center and walls to form a focused annulus. The theoretical basis for this "tubular pinch" effect is a combination of inertial lift forces acting on particles at high particle Reynolds numbers. The dominant forces on rigid particles are the "wall effect," where an asymmetric wake of a particle near the wall leads to a lift force away from the wall, and the shear-gradient-induced lift that is directed down the shear gradient and toward the wall. Inertial lift forces acting on a particle lead to migration away from the channel center. The particle migration velocity can be developed assuming Stokes drag balances this lift force. An estimate of the transverse migration velocity out from the channel center line can be made by using an average value of f_c ~ 0.5 for flow through parallel plates. This calculation yields a value of 3.5 cm/s for 10-μm particles in a flow with U_m = 1.8 m/s. Traveling a lateral distance of 40 μm requires traveling ≈2 mm downstream in the main flow. The lateral distance traveled will depend heavily on particle diameter, indicating the possibility of separations based on differential migration. In curved channels, secondary rotational flow caused by inertia of the fluid itself, called Dean flow, can alter the position of flowing particles. The