An unrecognized force in inertial microfluidics

Abstract: Describing effects of small but finite inertia on suspended particles is a fundamental fluid dynamical problem that has never been solved in full generality. Modern microfluidics has turned this academic problem into a practical challenge through the use of high-frequency oscillatory flows, perhaps the most efficient way to take advantage of inertial effects at low Reynolds numbers, to precisely manipulate particles, cells and vesicles without the need for charges or chemistry. The theoretical understanding of flow forces on particles has so far hinged on the pioneering work of Maxey and Riley (MR in the following), almost 40 years ago. We demonstrate here theoretically and computationally that oscillatory flows exert previously unexplained, significant and persistent forces, that these emerge from a combination of particle inertia and spatial flow variation, and that they can be quantitatively predicted through a generalization of MR.