Abstract: We present a numerical model that describes the microfluidic generation and manipulation of ferrofluid droplets under an external magnetic field. We developed a numerical Computational Fluid Dynamics (CFD) analysis for predicting and optimizing continuous flow generation and processing of ferrofluid droplets with and without the presence of a permanent magnet. More specifically, we explore the dynamics of oil-based ferrofluid droplets within an aqueous continuous phase under an external inhomogeneous magnetic field. The developed model determines the effect of the magnetic field on the droplet generation, which is carried out in a flow-focusing geometry, and its sorting in T-junction channels. Three-channel depths (25 um, 30 um, and 40 um) were investigated to study droplet deformation under magnetic forces. Among the three, the 30 um channel depth showed the most consistent droplet production for the studied range of flow rates. Ferrofluids with different loadings of magnetic nanoparticles were used to observe the behavior for different ratios of magnetic and hydrodynamic forces. Our results show that the effect of these factors on droplet size and generation rate can be tuned and optimized to produce consistent droplet generation and sorting. This approach involves fully coupled magnetic-fluid mechanics models and can predict critical details of the process including droplet size, shape, trajectory, dispensing rate, and the perturbation of the fluid co-flow for different flow rates. The model enables better understanding of the physical phenomena involved in continuous droplet processing and allows efficient parametric analysis and optimization.

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