In-Silico Conceptualisation of Continuous Millifluidic Separators for Magnetic Nanoparticles

Magnetic nanoparticles are researched intensively not only for biomedical applications, but also for industrial applications including wastewater treatment and catalytic processes. Although these particles have been shown to have interesting surface properties in their bare form, their magnetisation remains a key feature, as it allows for magnetic separation. This makes them a promising carrier for precious materials and enables recovery via magnetic fields that can be turned on and off on demand, rather than using complex (nano)filtration strategies. However, designing a magnetic separator is by no means trivial, as the magnetic field and its gradient, the separator dimensions, the particle properties (such as size and susceptibility), and the throughput must be coordinated. This is showcased here for a simple continuous electromagnetic separator design requiring no expensive materials or equipment and facilitating continuous operation. The continuous electromagnetic separator chosen was based on a current-carrying wire in the centre of a capillary, which generated a radially symmetric magnetic field that could be described using cylindrical coordinates. The electromagnetic separator design was tested in-silico using a Lagrangian particle-tracking model accounting for hydrodynamics, magnetophoresis, as well as particle diffusion. This computational approach enabled the determination of separation efficiencies for varying particle sizes, magnetic field strengths, separator geometries, and flow rates, which provided insights into the complex interplay between these design parameters. In addition, the model identified the separator design allowing for the highest separation efficiency and determined the retention potential in both single and multiple separators in series. The work demonstrated that throughputs of ~1/4 L/h could be achieved for 250-500 nm iron oxide nanoparticle solutions, using less than 10 separator units in series.