On the Hybrid-Type Method of Brownian Dynamics and Lattice Boltzmann for Activating the Brownian Motion of Magnetic Particles

Abstract

We have discussed the feasibility of a method for activating the Brownian motion of dispersed particles in the lattice Boltzmann method. The method to be treated in the present study is a technique based on the Brownian dynamics method, in which the random forces in the Brownian dynamics are added to the equations of motion of magnetic particles. In order to activate the Brownian motion at a physically reasonable level, a viscosity-modifying method is introduced in adjusting the random displacements of the particles. The viscosity-modifying method is verified by comparing the present results with those of the Monte Carlo simulations. The main results obtained here are summarized as follows. The aggregate structures of magnetic particles are in good agreement with the results of the Monte Carlo method. Moreover, the pair correlation functions agree well with the Monte Carlo results quantitatively. The scaling coefficient of viscosity is seen to be constant and independent of the strengths of magnetic particle-field and particle-particle interactions. Also, it is independent of the volumetric fraction and the number of particles, if lattice system’s roughness is constant. We may conclude from these results that the hybrid-type method of lattice Boltzmann and Brownian dynamics combined with the viscosity-modifying procedure can be expected to be a hopeful technique for simulating a flow problem of magnetic particles under a non-uniform applied magnetic field.