Lattice Boltzmann Simulation of a Two-Dimensional Flow of a Magnetic Suspension between the Two Parallel Walls under a Non-Uniform Magnetic Field

Abstract

First we have developed the Lattice Boltzmann method based on the fluctuation hydrodynamics which is applicable to a flow problem of a particle suspension. In this method, we have introduced the viscosity-modifying method, instead of the velocity-scaling method, in which the modified viscosity is used for generating the random forces in the lattice Boltzmann simulation. This viscosity-modifying method has been seen to be available for a magnetic particle suspension. Then we have applied this method to a two-dimensional Poiseuille flow of a magnetic suspension between the two parallel walls in order to investigate the behavior of magnetic particles in a non-uniform applied magnetic field situation. From the results of the snapshots, the pair correlation function between the magnetic pole and the magnetic particles and the averaged local particle velocity and magnetization distributions, it is seen that the behavior of magnetic particles drastically changes due to which factor dominates the phenomenon much more significantly among the magnetic particle-particle interaction, the non-uniform applied magnetic field strength and the translational and rotational Brownian motion.