Inertial lift forces are exploited within inertial microfluidic devices to position, segregate and sort particles or droplets. However, the forces and their focusing positions can currently only be predicted by numerical simulations, making rational device design very difficult. Here we develop theory for the forces on particles in microchannel geometries. We use numerical experiments to dissect the dominant balances within the Navier-Stokes equations and derive an asymptotic model to predict the lateral force on the particle as a function of particle size. Our asymptotic model is valid for a wide array of particle sizes and Reynolds numbers, and allows us to predict how focusing position depends on particle size.
Bibliographical noteFunding Information:
This work was partly supported by the National Science Foundation through grants DGE-1144087 (to K.H.) and DMS-1312543 (to M.R.) and by a research fellowship from the Alfred P. Sloan Foundation to M.R. We thank Dino Di Carlo, Howard Stone and Z. Jane Wang for useful discussions.
- low-Reynolds-number flows
- particle/fluid flows