Fig. 3

Magnetic particle characteristics and droplet volume preservation. a Theoretical microparticle velocity in the Y-direction as a function of microparticle diameter according to Eq. (4). The shaded region around the curve indicates the change in distance between the microparticle and the stationary magnet as the microparticle traverses through the channel immediately after injection. b Microparticle recovery under standard flow rates in the two-stage washing microfluidic chip. c High speed video tracking of 22 µm diameter microparticles in the injection region. d High speed video tracking of droplets during wash buffer injection and subsequent splitting into daughter droplets. e Schematic of critical device geometries and operating parameters for efficient recovery of magnetic particles described in Eq. (6)