This paper presents the theory and development, validation, and results of a transient computational multi-physics model for analyzing the magnetic field, particle dynamics, and capture efficiency of magnetic and non-magnetic (e.g., Red Blood Cells and E. Coli bacteria) microparticles in a travelling wave ferro-magnetic microfluidic device. This computational model demonstrates proof-of-concept of a method for greatly enhancing magnetic bio-separation in ferro-microfluidic systems using an array of copper conductive elements arranged in quadrature to create a periodic potential energy landscape. In contrast to previous works, our approach theoretically uses a microfluidic device with an electronic chip platform consisting of integrated copper electrodes that carry currents to generate programmable magnetic field gradients locally. Alternating currents are applied to the electrodes in quadrature (using a 90° phase change from the neighboring electrode) to create a periodic magnetic field pattern that travels along the length of the microchannel. Our previous work evaluated magnetic and non-magnetic particles in a static magnetic field within the same channel geometry. This work is a phase 2 study that expands on the previous work and analyzes the dynamics of magnetic and non-magnetic entities characterized by material magnetic susceptibility in a transient magnetic field. This is an improvement over our previous work. The model, which is described in more detail in the methods section, combines a Eulerian-Lagrangian and two-way particle-fluid coupling CFD analysis with closed-form magnetic field analysis that is used to predict magnetic separation considering dominant magnetic and hydrodynamic forces similar to our previous works in magnetic drug targeting. The model was also validated with an experimental low frequency stationary flow study on separating non-magnetic latex fluorescent particles in a water based ferrofluid. The results from the experimental study and the developed model demonstrates that the proposed device may potentially be used as an effective platform for microparticle and cellular manipulation and sorting. The developed multi-physics model could potentially be used as a design optimization tool for traveling wave ferro-microfluidic devices.