A Lagrangian particle trajectory model is developed to predict the interaction between cell-bead particle complexes and to track their trajectories in a magnetophoretic bio-separation chip. Magnetic flux gradients are simulated in the OpenFOAM CFD software and imported into MATLAB to obtain the trapping lengths and trajectories of the particles. A connector vector is introduced to calculate the interaction force between cell-bead complexes as they flow through a microfluidic device. The interaction force calculations are performed for cases where the connector vector is parallel, perpendicular, and at an angle of 45° with the applied magnetic field. The trajectories of the particles are simulated by solving a system of eight ordinary differential equations using a fourth order Runge-Kutta method. The model is then used to study the effects of geometric positions and angles of the connector vector between the particles as well as the cell size, number of beads per cell, and flow rate on the interaction force and trajectories of the particles. The results show that the interaction forces may be attractive or repulsive, depending on the orientation of the connector vector distance between the particle complexes and the applied magnetic field. When the interaction force is attractive, the particles are observed to merge and trap sooner than a single particle, whereas a repulsive interaction force has little or no effect on the trapping length.
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