High gradient magnetic particle separation in viscous flows by 3D BEM

The boundary element method was applied to study the motion of magnetic particles in fluid flow under the action of external nonuniform magnetic field. The derived formulation combines the velocity-vorticity resolved Navier–Stokes equations with the Lagrange based particle tracking model, where the one-way coupling with fluid phase was considered. The derived algorithm was used to test a possible design of high gradient magnetic separation in a narrow channel by computing particles trajectories in channel flow under the influence of hydrodynamic and magnetic forces. Magnetic field gradient was obtained by magnetization wires placed outside of the channel. Simulations with varying external magnetic field and flow rate were preformed in order to asses the collection efficiency of the proposed device. We found that the collection efficiency decreases linearly with increasing flow rate. Also, the collection efficiency was found to increase with magnetic field strength only up a saturation point. Furthermore, we found that high collection efficiently is not feasible at high flow velocity and/or at weak magnetic field. Recommendation for optimal choice of external magnetic field and flow rate is discussed.