Embedded electromagnetically sensitive particle motion in functionalized fluids

Abstract

The primary objective of this paper is to characterize the motion of small electromagnetically sensitive particles which are embedded in a flowing neutral fluid. There are a variety of industrial applications for electromagnetic particle-laden fluids, such as fluid-based actuators, coatings and functionalized inks, to name a few. This work compares the relative strengths of the forces induced by electromagnetic fields and fluid drag, and their composite effects on particle motion. Both analytical and numerical investigations are undertaken. After an analysis of a single isolated particle, a three-dimensional model problem comprised of a Representative Volume Element of flowing particle-laden fluid, under the action of external electromagnetic fields, is studied. A computational staggering scheme is developed to solve the coupled system utilizing a fully implicit Finite-Difference discretization of the Navier–Stokes equations for the fluid and a direct particle-dynamics description is used for the particles. For large numbers of embedded particles, because of the extreme computational difficulty of interface-conforming fine-mesh spatial discretizations for the fluid, simplifying assumptions for the coupling are made based on semi-analytical computation of drag-coefficients, allowing for the use of coarser meshes. Even after these simplifications, the particle-fluid system is strongly-coupled. The strongly-coupled system is implicitly solved, iteratively, within each time-step using a recursive staggering scheme, which employs temporal adaptivity to control the coupling error. The approach allows researchers to rapidly compute such systems with moderate laptop/desktop resources. Numerical examples are provided to illustrate the model and the numerical solution scheme, and limitations and extensions of the model are discussed.