Dimensional analysis of magnetophoresis

Abstract

Magnetophoresis is used in various applications requiring selective collection of magnetic particles. This study is aimed at quantitatively describing magnetophoretic systems via dimensional analysis to assess the relative contribution of hydrodynamics, electromagnetism, and particle dynamics. We introduce dimensionless numbers characterizing the transport of magnetic particles in a fluid. Analytical and numerical studies were conducted for magnetophoretic systems where magnetic particles were suspended in a fluid exposed to magnetic fields generated by permanent magnets. The magnetically induced mobility of the magnetic particles was simulated for a range of parameters relevant in biomedical applications, including the particle and fluid properties, flow velocity, and geometries of the particle, flow channel, and magnet. The numerical results obtained in multiphysics modeling of magnetophoretic systems were analyzed based on the proposed dimensionless numbers, resulting in a functional relationship for the particle capture efficiency (CE), defined as the ratio of captured particles to all particles injected in the flow. The performance of magnetophoretic systems predicted with the dimensional analysis was verified in comparison with published experimental data. Using dimensional analysis, 12 input parameters determining the particle CE were reduced to 3 dimensionless numbers characterizing the ratios of magnetophoretic and hydrodynamic forces, cross-sectional areas of the magnet and the flow channel, and length and diameter of the magnet. A set of curves predicting particle CE was obtained using these dimensionless numbers. A close agreement was found between the CEs predicted by the curves and those obtained in both numerical simulations and experiments where cylindrical magnets were placed in a flow through a cylindrical pipe. This study provides a promising framework for analyzing and predicting performance of various magnetophoretic systems for a range of applications.