Effect of volume fraction on chains of superparamagnetic colloids at equilibrium

Abstract

For a few decades, the influence of a magnetic field on the aggregation process of superparamagnetic colloids has been well known on short time scale. However, the accurate study of the equilibrium state is still challenging on some aspects. On the numerical aspect, current simulations have only access to a restricted set of experimental conditions due to the computational cost of long range interactions in many body systems. In the present paper, we numerically explore a new range of parameters thanks to sped up numerical simulations validated by a recent experimental and numerical study. We first show that our simulations reproduce results from previous study in well-established conditions. Then we show that unexpectedly long chains are observed for higher volume fractions and intermediate fields. We also present theoretical developments taking into account the interaction between the chains which are able to reproduce the data that we obtained with our simulations. We finally confirm this model thanks to experimental data.

Chain Formation and Phase Separation in Ferrofluids: The Influence on Viscous Properties

“…Because the size of the particles in ferrofluids is much smaller than the wavelength of visible light, the separate particles and branched structures consisting of the chain segments cannot be detected using optical observations. However, they have been detected using electronic microscopy (see, for example, [ 16 , 17 , 18 ]) and have been visualized in many computer simulations (for example, [ 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 ] and an overview in [ 5 ]).…”

“…There seems to be no doubt that the bulk condensation in the systems of purely dipole–dipole interacting particles can take place under the action of a strong enough magnetic field with the magnetic moments of all particles being well oriented. Indeed, the field-induced bulk structures have been detected not only in laboratory experiments [ 17 , 20 , 30 , 31 , 32 , 33 , 34 , 36 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 ], where the details of the interparticle interaction were not completely known, but also in computer simulations [ 18 , 99 , 100 , 101 ] with dipole–dipole interacting particles. Moreover, these transitions have been directly observed many times in experiments with magnetorheological suspensions that consist of micron-sized magnetizable particles (for an overview, see [ 102 ]).…”

Application of Magnetic Nano-Immobilized Enzyme in Soybean Oil Degumming: Numerical Simulation in a Liquid-Solid MFB

“…e magnetic interactions between nanomagnetic enzyme particles are presented in Supplementary Figure 3, where r denotes the distance between particles enzyme A and B and B 0 is the intensity of the applied uniform magnetic field. m a and m b are the magnetic moment of nanoparticles A and B, respectively [27]. F r represents the radial component and F θ represents the orthoradial component of the interparticle magnetic force F mi applied by particle A on particle B. e two components F r and F θ are obtained by projecting the F mi force in the polar base (r, θ).…”

De l’évaporation des colloïdes magnétiques

“…It was initially believed that only the interactions between single particles in a given aggregate, chain or ribbon, had to be taken into account to describe the equilibrium of the system [63,69]. However, recent numerical simulations, supported by experiments, showed that, at high volume fraction, the long-range interaction between various chains, which is repulsive, also has to be taken into account [89]. It has been demonstrated that a "two-levels" mean eld theory could reproduce the behavior of such system.…”

“…It has been demonstrated that a "two-levels" mean eld theory could reproduce the behavior of such system. This theory denes one mean interaction for the particles inside a given aggregate, and another mean interaction for the repulsion between dierent aggregates [89].…”