A computational design of a magnetic field applied to control magnetic adsorbent used in liquid/gas adsorption processes

Recently in our research studies, ferroferric oxide magnetic micro particles were used as seeds combined with chitosan and activated carbon respectively in a nutrition recovery process for post hemodialysis (HD) and in a mixed-gas adsorbate analysis. Initially, these magnetic adsorbents used in the experiments were all sealed inside a cylinder vessel by molecular sieve filters. However, this design led to a very slow liquid or gas flow rate during adsorption. To increase the flow rate, a novel design applying a nonlinear gradient magnetic field in the reverse direction of liquid or gas flow was proposed in this paper. The objective of the design was to retain the magnetic adsorbent inside the vessel maintaining a high flow rate. The magnetic field inside an infinite solenoid coil was derived using Ampere Circuit Law and the Langevin equation. An equation, showing the relationship between the ampere-turns of the magnetic field and their positions, was outlined in this paper. We finally proved that this equation is suitable for the practical design of a magnetic field with finite length. Thus, this mathematic model could help the development of adsorption device utilizing magnetic particles.