Numerical insights into magnetic particle enrichment and separation in an integrated droplet microfluidic system

•Magnetic particle manipulation inside droplets was accurately modeled.•An integrated droplets microfluidic system was proposed.•An accurate and comprehensive multiphysics model was developed.•Particles’ trajectories were precisely predicted using static and dynamic approaches.•Separation efficiency of concentrated magnetic particles were calculated. Particle concentration and manipulation inside droplets hold great potential in expanding lab-in-a-droplet applications ranging from biological to chemical assays. Herein, we present a numerical model that provides sufficient insights into magnetic particle enrichment in an integrated microfluidic system considering the most possible interactions and forces. The proposed system comprises three distinct interconnected modules: droplet generator, spacer, and splitter with a permanent magnet placed under the splitting zone. Two approaches are developed to predict the particle trajectories inside the droplet, namely, magnetohydrophoretic streamline (static) and multi-particle tracing (dynamic). It is found that although the presence of an external magnetic force may help to improve the separation/enrichment of the magnetic particles in such microfluidic systems, however, the location of the magnet must be carefully determined to avoid the inverse effect of the magnetic field on the separation/enrichment efficiency. Moreover, the full particle enrichment is obtained at a maximum magnetic force to drag force ratio of >0.8% and a magnetophoretic velocity to the mean fluid velocity ratio of >6% for both 2.83 µm and 4.4 µm magnetic beads. The presented accurate numerical model, together with its unique features of low computational cost and broad applicability, such as separating particles with different properties, can further broaden utility in droplet microfluidics. [Display omitted]