(209d) Lattice Boltzmann Simulation of a Two-Dimensional Poiseuille Flow of a Magnetic Suspension Between the Two Parallel Walls

In magnetic suspensions such as ferrofluids and magneto-rheological fluids, the magnetic particles show complex behavior under the influence of an applied magnetic field as well as a flow field. In the case of  a magnetic suspension in thermodynamic equilibrium, the Monte Carlo method is a highly effective and powerful tool, but not applicable to flow problems in thermodynamic non-equilibrium. The lattice Boltzmann method is a  hopeful method based on the concept of the virtual fluid particle for a flow problem of particle suspensions. This simulation technique has a great advantage that it can simulate the particle behavior and the flow field simultaneously in a non-equilibrium situation. However, in the case of a magnetic suspension,  the magnetic particles are coated with a soft steric layer such as a surfactant layer and an electric double layer, so that studies need to be conducted in order to clarify the availability of the lattice Boltzmann method for such dispersions. The previous work has clearly shown that the method of activating the Brownian motion of magnetic particles based on fluctuation hydrodynamics functions reasonably in terms of the introduction of the velocity-scaling method; the aggregate structures are in good agreement with those of Monte Carlo simulation. This conclusion has been obtained for a magnetic suspension in thermodynamic equilibrium, but the velocity-scaling method has a serious difficulty in application to a flow problem under a non-uniform applied magnetic field that is very important from an engineering point of view.  
    In the present study we have discussed the lattice Boltzmann method based on the fluctuation hydrodynamics which is applicable to a flow problem of a particle suspension in conjunction with taking into account the Brownian motion of dispersed particles. This simulation method has been applied to a two-dimensional Poiseuille flow of a magnetic suspension between the two parallel walls in order to investigate the behavior of magnetic particles under the situation of a non-uniform applied magnetic field. In this stimulation, the multi-body hydrodynamic interactions among particles and the translational and rotational Brownian motion of particles are taken into consideration. The viscosity-modifying technique is clarified to be quite available for generating the particle Brownian motion at a physically reasonable level: the snapshots and the pair correlation function are in good agreement with those of the Monte Carlo simulation. When magnetic particles flow between the two parallel walls in a non-uniform applied magnetic field, 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.  If the body force due to the particle-field interaction is more dominant, the magnetic particles are captured around the magnetic poles to form chain-like clusters from the anchored particles around the magnetic poles. If the magnetic interaction between particles is more dominant, loop-like or chain-like clusters move in the downstream direction without being tcaptured around the magnetic poles. If the random motion is more dominant, the magnetic particles simply flow in the downstream direction without aggregation of particles and attachment around the magnetic poles.