On the viscosity-modifying method for activating the Brownian motion of magnetic particles in lattice Boltzmann simulations

In order to apply the lattice Boltzmann method to a flow problem of magnetic suspensions, we have investigated the feasibility of the viscosity-modifying method that is expected to be a technique for sophisticating the activating method of the particle Brownian motion based on fluctuation hydrodynamics. We have addressed a magnetic suspension in thermodynamic equilibrium to clarify the influences of various factors such as the roughness of a lattice system and the volumetric fraction of magnetic particles on the scaling coefficient of viscosity. From the snapshots and pair correlation functions of magnetic particles, it is seen that the viscosity-modifying method can show good agreement with the results of Monte Carlo method in both quantitative and qualitative aspects. This good agreement is almost independent of the roughness of a lattice system if a relatively fine lattice system is used. The scaling coefficient of viscosity is almost constant and independent of the strengths of magnetic particle–field and particle–particle interactions, and also is almost constant for the variation of the volumetric fraction and the number of particles for a given lattice system unless a coarse lattice system is used. We may conclude from these results that the lattice Boltzmann method with the viscosity-modifying procedure is quite a possible technique for simulating a flow problem of magnetic particles under a non-uniform applied magnetic field.

► The viscosity-modifying method is investigated for activating the Brownian motion.
► Magnetic suspensions are addressed to clarify the feasibility of this method.
► The validity of the results is clarified by comparing with Monte Carlo results.
► The present method is a possible technique for simulating suspension flow problems.