Diffusive capture of magnetic particles by an assemblage of random cylindrical collectors

Abstract

Theoretical models describing the capture of ultra-fine weakly magnetic particles in high gradient magnetic field are developed. We begin with the capture of ultra-fine particles in one dimension by a single ferromagnetic cylindrical collector. Later, we extend to the two dimensional case. Finally, we investigate the capture of ultra-fine particles by an assemblage of parallel magnetic cylinders randomly distributed in static fluid in two dimensions. An effective medium treatment is used to improve the theoretical model describing the capture of ultra-fine particle of Davies and Gerber which assumed a single collector in fluid. In our model, only one representative cell is considered while the surrounding cells are replaced by a homogeneous medium with an effective permeability. The continuity equation describing dynamics of particle volume concentration is solved and the steady-state solution is determined analytically while the time-dependent solutions are obtained numerically. In this research, we develop a computer program to simulate the capture of ultra-fine particles in various physical situations. From our results, the concentration contours generated in various physical situations are analyzed which indicate saturation, accumulation and depletion regions around the collector. In the case of the capture of ultra-fine particles by an assemblage of random magnetic collectors, the distribution of concentration around collectors changes insignificantly with varying packing fraction of the collectors in the dilute limit. The amount of particles captured in saturation regions on the collector surface increases, approximately, linearly proportional to the collector packing fraction in the fluid and increases rapidly with the strength of the uniform external magnetic field.