A continuum model for magnetic particle flows in microfluidics applicable from dilute to packed suspensions

The manipulation of magnetic microparticles has always been pivotal in the development of microfluidic devices, as it encompasses a broad range of applications, such as drug delivery, bioanalysis, on-chip diagnostics, and more recently organ-on-chip development. However, predicting the behavior and trajectory of these particles remains a recurring and partly unresolved question. Magnetic particle-laden flows can display intricate collective behaviors, such as packed plugs, column-shaped aggregates, or fluidization, which are difficult to predict. In this study, we introduce a finite-element model to simulate highly dense flows of magnetic microparticles. Our method relies on an interpenetrating continuum approach, where both the liquid and particle phases are described by the Navier-Stokes equations, in which the magnetic force, interphase friction, and interparticle forces were included. We demonstrate its applicability across the entire range of particle packing densities and compare the results with experimental data from real microfluidic application cases. The model successfully replicates complex behaviors, such as particle aggregation, plug formation and fluidization. This approach has potential to accelerate microfluidic device development by reducing the need for costly and time-consuming experimental optimization.