The separation of biopharmaceutical products from production media continues to be a challenging task. High gradient magnetic Separation (HGMS) is a promising downstream processing technique as it integrates many batch operations into a single unit operation. However, so far, most HGMS processes are discontinuous and there is no commercially available one that can satisfy the specific needs of biopharmaceutical processing. We propose to exploit the interactions of functionalized magnetic particles with magnetic field gradients, forced convective flows and large centrifugal forces to facilitate the recovery of biopharmaceuticals from the media in which they are manufactured. We are developing various numerical tools, including, a particle trajectory model to track the particle movement and its capture onto magnetizable wires, a dynamic particle buildup growth model to study the dynamic process of particle accumulation and its effects on surrounding flow and magnetic fields, and a discrete element method (DEM) package to investigate the behavior of the particle sludge under a centrifugal field. Experiments were carried out to verify the validity of our models. We performed dimensional analysis and defined various dimensionless numbers in order to make the methods and results to be scalable. A small scale single-wire flow channel was made to test the dynamic buildup growth model. And a real magneto-centrifugal contactor was used to study the bulk movement of particle buildup under centrifugal force and compared with DEM simulation results. The models developed here will be used for the design, evaluation, and optimization of continuous magneto-centrifugal contactors that are suitable for biopharmaceutical downstream processing.