Mathematical Modeling and Analysis of a Magnetic Nanoparticle-Enhanced Mixing in a Microfluidic System Using Time-Dependent Magnetic Field

An innovative time-dependent magnetically actuated mixing process based on magnetic nanoparticles (MNPs) for enhancing the mixing performance of a microfluidic system is presented in this paper. Finite-element technique that combines time-dependent magnetic field with mass transfer of species is employed for quantifying the effect of convection, diffusion, and magnetic field on the mixing performance. It is shown that it is possible to generate periodic magnetic forces that can make the MNPs oscillate in different directions. This oscillation of MNPs causes agitation in the surrounding fluid thus improving the mixing in the microfluidic system. Effects of MNP size, inlet velocity of the fluid entering the system, and switching frequency of magnetic field are investigated. Mixing efficiency analysis result shows that in order to have an effective MNP-based mixing, an optimum switching frequency is required that not only depends on applied magnetic field but also on convective flow velocity, channel's dimension, and nanoparticle size. It is also observed that if the switching frequency is much higher or lower than the optimum switching frequency, then MNPs add limited disturbance to the fluid flow and do not significantly enhances the mixing. Moreover, the optimum switching frequency and the inlet flow velocity is also scalable. Furthermore, when MNP actuated mixing is compared with passive mixing strategies, it is found to be more efficient. The simulation performed in this paper using the multiphysics model provides an excellent estimate of the potential to use time-dependent magnetic actuation technique for efficiently mixing or tagging MNPs with target biomolecules on-chip for further analysis. The model will also be very useful in investigating a wide range of design parameters for designing and fabricating efficient integrated lab-on-a-chip devices for point-of-care applications.