On the accurate large-scale simulation of ferrofluids

Abstract

Fig. 1. Our approach can accurately reproduce the observation that real ferrofluid is literally climbing up a steel helix placed above a strong electromagnet. This figure shows the final results of our simulation of this scenario rendered from different viewpoints. We present an approach to the accurate and efficient large-scale simulation of the complex dynamics of ferrofluids based on physical principles. Ferrofluids are liquids containing magnetic particles that react to an external magnetic field without solidifying. In this contribution, we employ smooth magnets to simulate ferrofluids in contrast to previous methods based on the finite element method or point magnets. We solve the magnetization using the analytical solution of the smooth magnets' field, and derive the bounded magnetic force formulas addressing particle penetration. We integrate the magnetic field and force evaluations into the fast multipole method allowing for efficient large-scale simulations of ferrofluids. The presented simulations are well reproducible since our approach can be easily incorporated into a framework implementing a Fast Multipole Method and a Smoothed Particle Hydrodynamics fluid solver with surface tension. We provide a detailed analysis of our approach and validate our results against real wet lab experiments. This work can potentially open the door for a deeper understanding of ferrofluids and for the identification of new areas of applications of these materials.

Reconfigurable multifunctional ferrofluid droplet robots

“…Here, μ 0 = 4π • 10 −7 H=m denotes the magnetic permeability of vacuum, and H(r) is a summation of both the externally applied and internally produced magnetic fields H ext and H ferro (M). The magnetization of ferrofluids is given by M = χ(H ext + H ferro (M)) due to the paramagnetic property, where χ is the volume susceptibility of the ferrofluid (31). When smartly programming H ext (B ext is equivalently used in later sections) by using either electromagnets (30) or permanent magnets (29) as illustrated in Fig.…”

The magnetic switch manufacturing by using ferrofluid and ferrofluid doped copper nanoparticles

“…The selective spectral behavior of suspended nanoparticles of magnetite (Fe 3 O 4 ) NPs and cobaltferrite (CoFe 2 O 4 ) coated with starch, was observed through switching on/off of the external magnetic field [11]. In 2019, Huang et al, found that simulation of ferrofluids is similar to the simulation of the complex dynamics of ferrous, as the magnetic particles of ferrofluids react with an external magnetic field [12]. During this work design and implementation of magnetic switch based on ferrofluid and ferrofluid doped with copper nanoparticals is presented.…”

Lattice-Boltzmann and Eulerian Hybrid for Solid Burning Simulation

“…In general, fluids simulation methods have been developed based on a Navier-Stokes solver. After Stam [5] introduced an unconditionally stable solver for incompressible fluid, non-Newtonian fluid [6][7][8] as well as a lot of Newtonian fluid [9][10][11][12][13][14], including fire or flame simulation [15][16][17][18][19][20], were introduced. Fedkiw et al [21] introduced a simple buoyancy force model coupled with change of temperatures to simulate heated gas and adopted a vorticity confinement model to create interesting swirling effects of smoke.…”