Comparative study on the dynamics of rotating paramagnetic particles simulated by particle dynamics, Stokesian dynamics and lattice Boltzmann methods

Paramagnetic particles, when subjected to external unidirectional rotating magnetic fields, form chains which rotate along with the magnetic field. In this paper three simulation methods, namely particle dynamics (PD), Stokesian dynamics (SD) and Lattice Boltzmann (LB) methods, have been used to study the dynamics of these rotating chains. SD simulations with two different levels of approximations-additivity of forces (AF) and additivity of velocities (AV) - for hydrodynamic interactions have been carried out. The effect of hydrodynamic interactions between paramagnetic particles under the effect of a rotating magnetic field is analyzed by comparing the LB & SD simulations, which include hydrodynamic interactions, with PD simulations in which hydrodynamic interactions are neglected. It has been found that for macroscopically observable properties like average chain length as a function of Mason number (Ma), reasonable agreement is found between all the three methods. For microscopic properties like the force distribution on each particle along the chain, inclusion of hydrodynamic interaction becomes important to understand the underlying physics of chain formation. This has been validated by the fact that when the phase angle is calculated as a function of Ma using PD and SD simulations, PD simulations showed higher values compared to SD simulations at lower Ma. A comparison with experimental data showed SD method to be more accurate at low Ma. Further comparison between the two approximations of SD simulations revealed that the AF method reproduces hydrodynamic interactions more accurately.