Three-dimensional and analytical modeling of microfluidic particle transport in magnetic fluids

We present an analytical model that can predict the three-dimensional (3D) transport of non-magnetic particles in magnetic fluids inside a microfluidic channel coupled with permanent magnets. The magnets produce a spatially non-uniform magnetic field that gives rise to a magnetic buoyancy force on the particles. Resulting 3D trajectories of the particles are obtained by (1) calculating the 3D magnetic buoyancy force exerted on the particles via an analytical distribution of magnetic fields as well as their gradients, together with a nonlinear magnetization model of the magnetic fluids, (2) deriving the 3D hydrodynamic viscous drag force on the particles with an analytical velocity profile of a low Reynolds number ferrohydrodynamic flow in the channel including wall effect'' and magnetoviscous effect of the magnetic fluids, and (3) constituting and solving the governing equations of motion for the particles using the analytical expressions of magnetic buoyancy force and hydrodynamic viscous drag force. We use such a model to study the particles' trajectories in the channel and investigate the magnitude of their deflections at different flow rates, with different properties of magnetic fluids and different geometrical parameters of the system.