Measuring magnetic force field distributions in microfluidic devices: Experimental and numerical approaches

Precisely and accurately determining the magnetic force and its spatial distribution in microfluidic devices is challenging. Typically, magnetic microfluidic devices are designed in a way to both maximize the force within the separation region and to minimize the necessity for knowing such details—such as designing magnetic geometries that create regions of nearly constant magnetic force or that dictate the behavior of the magnetic force to be highly predictable in a specified region. In this work, we present a method to determine the spatial distribution of the magnetic force field in a magnetic microfluidic device by particle tracking magnetophoresis. Polystyrene microparticles were suspended in a paramagnetic fluid, gadolinium, and this suspension was exposed to various magnetic field geometries. Polystyrene particle motion was tracked using a microscope and images processed using Fiji (ImageJ). From a sample with a large spatial distribution of particle tracks, the magnetic force field distribution was calculated. The force field distribution was fitted to nonlinear spatial distribution models. These experimental models are compared to and supported by 3D simulations of the magnetic force field in COMSOL.