A dynamic buildup growth model for magnetic particle accumulation on single wires in high-gradient magnetic separation



Magnetic fluids containing nano or submicron magnetic particles and their applications to food, biological, and pharmaceutical systems have recently attracted considerable attention. Magnetic particles can be collected efficiently in magnetizable matrices (e.g., iron wires) in high-gradient magnetic separation processes. However, capture efficiencies based on results for clean, particle-free, wires may be seriously in error because the particle accumulation on the wire distorts the flow and the magnetic fields, and thus influences the capture efficiency. A model is developed here in which the dynamic growth process is treated as a moving boundary problem, with the growing front tracked explicitly by marker points distributed evenly over its surface. The flow field and magnetic field are calculated using a finite element method, and a particle trajectory model is used to calculate the deposition flux on the surface. The marker point distribution and the buildup shape are updated at each simulation step. Simulation results show that, for weakly magnetic particles, the accumulation exhibits a smoothly growing front, whereas for strongly magnetic particles, an instability occurs, leading to dendritic growth. The capture efficiency decreases dramatically as particle accumulation increases; and this trend is more prominent for the transverse configuration than it is for the longitudinal configuration. The simulation results show good agreement with experimental results from the literature. © 2011 American Institute of Chemical Engineers AIChE J, 2012