A Lagrangian particle trajectory model is developed to predict the interaction between cell-bead complexes and to track the positions and angles of the particles in a magnetophoretic bio-separation chip. Magnetic flux gradients are simulated in OpenFOAM CFD software and imported to MATLAB to obtain the particle trajectories. A connector vector is introduced to calculate the interaction force between two cell-bead particle 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 degrees with the applied magnetic field. The trajectories of the particles are simulated by solving a system of eight ordinary differential equations using the 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 bead size, cell size, number of beads per cell, and flow rate on the interaction force and trajectories of the particles.