Magnetic beads can be functionalized to capture and separate target pathogens from blood for extracorporeal detoxification. The beads can be magnetically separated from a blood stream and collected into a coflowing buffer solution using a two-phase liquid-liquid continuous-flow microfluidic device in the presence of an external field. However, device design and process optimization, i.e. high bead recovery with minimum blood loss or dilution remain a substantial technological challenge. We introduce a CFD-based Eulerian-Lagrangian computational model that enables the rational design and optimization of such systems. The model takes into account dominant magnetic and hydrodynamic forces on the beads as well as coupled bead-fluid interactions. Fluid flow (Navier-Stokes equations) and mass transfer (Fick's law) between the coflowing fluids are solved numerically, while the magnetic force on the beads is predicted using analytical methods. The model is demonstrated via application to a prototype device and used to predict key performance metrics; degree of bead separation, flow patterns, and mass transfer, i.e. blood diffusion to the buffer phase. The impact of different process variables and parameters - flow rates, bead and magnet dimensions and fluid viscosities - on both bead recovery and blood loss or dilution is quantified for the first time. The performance of the prototype device is characterized using fluorescence microscopy and the experimental results are found to match theoretical predictions within an absolute error of 15%. While the model is demonstrated here for analysis of a detoxification device, it can be readily adapted to a broad range of magnetically-enabled microfluidic applications, e.g. bioseparation, sorting and sensing.

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The advantages of miniaturized systems and the laminar flow regime that is present in microfluidic channels have opened a new range of applications in which the use of multiple streams with different reagents is exploited. However, further development of these microdevices needs deeper understanding on the phenomena involved in order to efficiently design such microsystems. In this work, we report the analysis of the solute mass transport performance in Y-Y-shaped microchannels as a function of the couple influence of both the flow patterns and mass transport kinetics. With this objective, the influence of the following operation variables has been analyzed, the ratio between the residence and diffusion times (γ) and the volumetric ratio between the fluid phases (α), that was determined for three different geometric configurations. The performance of the devices was presented as the solute separation factor in the donor fluid and the concentration factor in the receiving phase. Results showed that the ratio α greatly impacts the solute concentration value reported in both phases for the same γ value, which in turn influences the solute mass flow at the channel outlets. Both the flow patterns and the concentration gradients developed inside the systems were numerically studied by using Computational Fluid Dynamics (CFD) techniques and experimentally analyzed by fluorescence microscopy with fluorescein employed as model solute. This study represents a thorough analysis of the phenomena that determine the performance of the separation of solutes between homogeneous flowing fluids in microdevices where the fluid dynamics are coupled with mass transfer phenomena and facilitates its extension to the general case where separation is enhanced by chemical reactions.