Optimal control of particle separation in inertial microfluidics

Recently, inertial mircofluidics has emerged as a promising tool to manipulate complex liquids with possible biomedical applications, for example, to particle separation. Indeed, in experiments different particle types were separated based on their sizes (A.J. Mach, D. Di Carlo, Biotechnol. Bioeng. 107, 302 (2010)). In this article we use a theoretical study to demonstrate how concepts from optimal control theory help to design optimized profiles of control forces that allow to steer particles to almost any position at the outlet of a microfluidic channel. We also show that one specific control force profile is sufficient to guide two types of particles to different locations at the channel outlet, where they can be separated from each other. The particles just differ by their size which determines the strength of the inertial lift forces they experience. Our approach greatly enhances the efficiency of particle separation in the inertial regime.