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# Control of Inertial Microfluidics

Christopher Prohm:

Inertial microfluidics studies the motion of particles in microchannels at intermediate Reynolds numbers. First observed by SegrÃ© and Silberbeg [1], particles organize themselves at a fixed distance from the center and the channel walls, irrespective of their initial distribution. Devices utilizing this inertial focusing for particle separation have recently been demonstrated [2, 3].

To solve the full Navier-Stokes equations numerically, we employ Multi-Particle Collision Dynamics (MPCD) [4]. This simulation method introduces ballistic and collision steps of coarse-grained fluid particles and recovers the Navier-Stokes equations on length scales larger than the particle distance. Explicit expressions for transport coeffcients such as the shear viscosity exist. MPCD has successfully been applied to colloid dynamics. Here, we present numerical studies of spherical particles embedded in a pressure driven flow in microchannels at intermediate Reynolds numbers. The lift force, which drives the particle to its preferred position within the channel, depends on the Reynolds number, the particle size, and particle speed relative to the Poiseuille flow.

We investigate this dependence in detail. The colloid dynamics in a circular channel perpendicular to the flow can be described in terms of a one-dimensional nonlinear equation of motion, for which the central channel axis is an unstable fix point. By employing external feedback mechanisms we demonstrate the stabilization of this unstable fix-point and its application to particle sorting.

[1] G. SegrÃ© and A. Silberberg. Radial particle displacements in Poiseuille flow of suspensions. Nature, 189:209 - 210, 1961.

[2] S. C. Hur, H. T. K. Tse, and D. Di Carlo. Sheathless inertial cell ordering for extreme throughput flow cytometry. Lab on a Chip, 10:274 - 280, 2009.

[3] D. Di Carlo, D. Irimia, R. G. Tompkins, and M. Toner. Continuous inertial focusing, ordering, and separation of particles in microchannels. Proceedings of the National Academy of Sciences, 104:18892 - 18897, 2007.

[4] R. Kapral. Multi-particle collision dynamics: Simulation of complex systems on mesoscales. Advances in Chemical Physics, 140:89 - 146, 2008.