FIG. 4.

Overview of the magnetic, hydrodynamic drag and surface tension forces acting on the magnetic beads. The magnet is at a 45° angle to the direction of motion, and the separation between the magnet and the bead is $d=7.5\hspace{0.17em}\hspace{0.17em}\text{mm}$. (a) The change in dB/dx as the distance between the magnet and bead increases. (b) The change in the magnetic force as the distance between the magnet and the bead increases. (c) The minimum number of magnetic beads in a clump required for the magnetic driving force F_M to overcome the viscous drag force in the microchannel. (d) The minimum number of magnetic beads required for the driving force to overcome the surface tension at the center and at the peripheral of the water and oil interphase. The angle, θ, of the interface is approximated to be 45°.