Efficient numerical modelling of magnetophoresis in millifluidic systems

Continuous flow magnetophoresis represents a common technique for actively separating particles within a fluid. For separation systems design, accurately predicting particle behaviour helps to characterise system performance, typically measured by the separation efficiency (SE). While finite element method (FEM) simulations offer high accuracy, they demand extensive computational resources. Alternatively, results can be achieved more quickly with simplified numerical models that use analytical descriptions of fluid flow, magnetic fields, and particle movement. In this research, we model a millifluidic system that separates magnetic particles using magnetophoresis. Therefore, we (1) develop a simple numerical model that can simulate continuous flow magnetophoresis for rectangular channels in two and three dimensions, (2) introduce a novel and simple approach to calculate the SE, and (3) quantify the effects of model assumptions in flow profile and dimensions on SE. Our method for estimating SE considers particle flux variation across the channel's cross-section due to the flow profile. The results are compared to an FEM model developed in COMSOL. The obtained three-dimensional simulation model computes results in seconds, around 180 times faster than the FEM approach, while deviating less than 2% from the FEM results. A comparison of the different two-dimensional and three-dimensional models underscores the significant influence of the flow profile and the SE calculation method on the result. The two dimensional models generally overestimate the SE of up to 15% due to their lower peak flow velocity. However, using a constant flow velocity leads to good agreement for high SE due to the overlap of differences in flow profile and SE calculation.