Brownian dynamics simulations with spin Brownian motion on the negative magneto-rheological effect of a rod-like hematite particle suspension

We have investigated the behaviour of a suspension of magnetic rod-like hematite particles in a simple shear flow with the addition of an applied magnetic field. A significant feature of the present hematite particle suspension is the fact that the magnetic moment of the hematite particle lies normal to the particle-axis direction. From simulations, we have attempted to clarify the dependence of the negative magneto-rheological effect on the particle aggregation and orientational distribution of particles. The present Brownian dynamics method has a significant advantage in that it takes into account the spin rotational Brownian motion about the particle axis in addition to the ordinary translational and rotational Brownian motion. The net viscosity is decomposed into three components and discussed at a deeper level and in detail: these three viscosity components arise from (1) the torque due to the magnetic particle–field interaction, (2) the torque and (3) the force due to the interaction between particles. It is found that a slight change in the orientational distribution has a significant influence on the negative magneto-rheological effect. In a relatively dense suspension, the viscosity components arising from an applied magnetic field and the interaction between particles come to change rapidly for a certain strength of the magnetic particle–particle interaction, which is due to the onset of the formation of raft-like clusters.     

Influence of the spin Brownian motion on the negative magneto-rheological effect in a rod-like haematite particle suspension

We have shown the basic equation of the orientational distribution function of prolate spheroidal haematite particles with rotational Brownian motion in a simple shear flow under an applied magnetic field. The equation has been solved numerically in order to investigate the influence of the spin Brownian motion on the orientational distribution, the negative magneto-rheological effect and the characteristics of magnetisation. With respect to the orientational distribution, the present results are in good agreement with those of the theory without that motion, which shows that the spin Brownian motion does not significantly influence the orientational distribution. In contrast, the influence of the spin Brownian motion appears more significantly in the negative viscosity: the negative viscosity effect decreases in comparison with that of the previous theory without the spin Brownian motion. Moreover, a more significant negative magneto-rheological effect is obtained for a larger particle aspect ratio. Since the magnetisation has a strong relationship with the orientation of the magnetic moment, the effect of the spin Brownian motion appears more significantly in this characteristic.     

Influences of magnetic particle–particle interactions on orientational distributions and rheological properties for a colloidal dispersion composed of rod-like particle with a magnetic moment normal to the particle axis

We have investigated mainly the influences of magnetic particle–particle interactions on the orientational distribution and viscosity of a semi-dense dispersion, which is composed of rod-like particles with a magnetic moment magnetized normal to the particle axis. In addition, the influences of the magnetic field strength, shear rate, and random forces on the orientational distribution and rheological properties have been clarified. The mean field approximation has been applied to take into account magnetic interactions between rod-like particles. The basic equation of the orientational distribution function has been derived from the balance of torques and solved by the numerical analysis method. The results obtained here are summarized as follows. For a strong magnetic field, the rotational motion of the rod-like particle is restricted in a plane normal to the shearing plane since the magnetic moment of the particle is restricted in the magnetic field direction. Under circumstances of a very strong magnetic interaction between particles, the magnetic moment is strongly restricted in the magnetic field direction, so that the particle has a tendency to incline in the flow direction with the magnetic moment pointing to the magnetic field direction. For a strong shear flow, a directional characteristic of rod-like particles is enhanced, and this leads to a more significant one-peak-type distribution of the orientational distribution function. Magnetic interactions between particles do not contribute to the increase in the viscosity because the mean-field vector has only a component along the magnetic field direction.     

On aggregate structures in a rod-like haematite particle suspension by means of Brownian dynamics simulations

We have investigated aggregation phenomena in a suspension composed of rod-like haematite particles by means of Brownian dynamics simulations. The magnetic moment of the haematite particles lies normal to the particle axis direction and therefore the present Brownian dynamics method takes into account the spin rotational Brownian motion about the particle axis. We have investigated the influence of the magnetic particle–field and particle–particle interactions, the shear rate and the volumetric fraction of particles on the particle aggregation phenomena. Snapshots of aggregate structures are used for a qualitative discussion and the cluster size distribution, radial distribution function and the orientational correlation functions of the direction of particle axis and magnetic moment are the focus for a quantitative discussion. The significant formation of raft-like clusters is found to occur at a magnetic particle–particle interaction strength much larger than that required for a magnetic spherical particle suspension. This is because the rotational Brownian motion has a significant influence on the formation of clusters in a suspension of rod-like particles with a large aspect ratio. An applied magnetic field enhances the formation of raft-like clusters. A shear flow does not have a significant influence on the internal structure of the clusters, but influences the cluster size distribution of the raft-like clusters.     

Negative viscosity due to magnetic properties of a non-dilute suspension composed of ferromagnetic rod-like particles with magnetic moment normal to the particle axis

The negative viscosity of a colloidal dispersion composed of ferromagnetic rod-like particles, which have a magnetic moment normal to the particle axis, have been investigated. A simple shear flow problem has been treated to clarify the particle orientational distribution and rheological properties of such a semi-dense dispersion, under circumstances of an external magnetic field applied in the direction normal to the shear plane of a simple shear flow. The results obtained here are summarized as follows. For the cases of a very strong magnetic field and magnetic interactions between particles, the magnetic moment of the rod-like particles is significantly restricted in the magnetic field direction, so that the particle approximately aligns in the shear flow direction. Also, the particle can easily rotate around the axis of the cluster almost freely even in a simple shear flow. Characteristic orientational properties of the particle cause negative viscosity, as in the previous study for a dilute dispersion. However, magnetic particle-particle interactions have a function to make such negative viscosity decrease.     

Application of the Brownian dynamics method to a rod-like hematite particle dispersion

We have investigated various problems that arise in applying the Brownian dynamics method to a suspension composed of rod-like hematite particles, which have a magnetic moment normal to the particle axis direction. The accuracy and the deviation of simulation results from theoretical solutions have been discussed by comparison with the theoretical solutions that were obtained by solving the basic equations of the orientational distribution function. The characteristics of the negative viscosity are not observed to be dependent on a time interval unless a sufficiently short time interval is used. The present simulation results can satisfactorily reproduce the qualitative characteristics of the negative magneto-rheological effect that was predicted by the previous theoretical investigation. Good quantitative agreement is obtained in the range of small-applied magnetic fields, but agreement is not significantly good in the large magnetic field region. The deviation of the negative viscosity from the theoretical prediction cannot be improved by using a more accurate numerical algorithm such as moving from Euler to second-order or fourth-order Runge–Kutta. The results of the orientational distribution can well reproduce the characteristic features that the distribution has a gradual shape with low linear-like peak, which is in significant contrast to the sharp single-peak distribution of a ferromagnetic rod-like particle dispersion. The present orientational distributions are in significantly good agreement with those of the theoretical prediction in regard to the position and the height of a peak and the general shape of the overall profile. Good agreement of the present magnetisation curves with the theoretical prediction verifies that the spin rotational Brownian motion is activated at a physically reasonable level in the present simulations.     

Lattice Boltzmann simulation of the two-dimensional flow of a magnetic suspension between two parallel walls under a non-uniform magnetic field

We have developed a lattice Boltzmann method based on fluctuation hydrodynamics that is applicable to the flow problem of a particle suspension. In this method, we have introduced the viscosity-modifying method, rather than the velocity-scaling method, in which a modified viscosity is used for generating random forces in lattice Boltzmann simulations. The viscosity-modifying method is found to be applicable to the simulation of a magnetic particle suspension. We have applied this method to the two-dimensional Poiseuille flow of a magnetic suspension between two parallel walls in order to investigate the behavior of magnetic particles in a non-uniform applied magnetic field. From the results of the snapshots, the pair correlation function between the magnetic pole and the magnetic particles and the averaged local particle velocity and magnetization distributions, it was observed that the behavior of the magnetic particles changes significantly depending upon which factor dominates the phenomenon in the balance between the magnetic particle–particle interaction, the non-uniform applied magnetic field and the translational and rotational Brownian motion.     

Brownian dynamics simulations of a cubic haematite particle suspension with a more effective treatment of steric layer interactions

We have proposed a new repulsive layer model for describing the interaction between steric layers of coated cubic particles. This approach is an effective technique applicable to particle-based simulations such as a Brownian dynamics simulation of a suspension composed of cubic particles. 3D Brownian dynamics simulations employing this repulsive interaction model have been performed in order to investigate the equilibrium aggregate structures of a suspension composed of cubic haematite particles. It has been verified that Brownian dynamics employing the present steric interaction model are in good agreement with Monte Carlo results with respect to particle aggregate structures and particle orientational characteristics. From the viewpoint of developing a surface modification technology, we have also investigated a regime change in the aggregate structure of cubic particle in a quasi-2D system by means of Brownian dynamics simulations. If the magnetic particle–particle interaction strength is relatively strong, in zero applied magnetic field the particles aggregate in an offset face-to-face configuration. As the magnetic field strength is increased, the offset face-to-face structure is transformed into a more direct face-to-face contact configuration that extends throughout the whole simulation region.     

Quasi-2D Monte Carlo simulations of a colloidal dispersion composed of magnetic plate-like particles with magnetic moment normal to the particle axis

We have investigated aggregation phenomena of a colloidal dispersion composed of magnetic plate-like particles by means of Monte Carlo simulations. Such plate-like particles have been modelled as disk-like particles with magnetic moment normal to the particle axis at the particle centre, with the section shape of a spherocylinder. The main objective of the present study is to clarify the influences of the magnetic field strength and magnetic interactions between particles on particle aggregation phenomena. We have concentrated our attention on a quasi-2D system from an application point of view such as the development of surface quality changing technology using such magnetic plate-like particles. A magnetic field is applied along the direction perpendicular to the plane of the monolayer. Internal structures of particle aggregates are discussed quantitatively in terms of radial distribution and orientational pair correlation functions. For the case of strong magnetic interactions between particles, particles form long column-like clusters with their magnetic moments alternating in direction between the neighbouring particles. These tendencies appear under circumstances of a weak applied magnetic field. However, as the magnetic field strength increases, particles incline towards the magnetic field direction, so that particles do not form such clusters.     

Negative magneto-rheological effect of a dispersion composed of spindle-like hematite particles

We have experimentally investigated the negative magneto-rheological effect that is theoretically predicted to appear in a dispersion composed of spindle-like hematite (α-Fe₂O₃) particles. The spindle-like hematite particles were synthesized by aging a solution of FeCl₃ and KH₂PO₄ for 72?h at 373?K. The particle size distribution was determined by digital image analysis from electronic microscope observation of the particles. In the present study we considered a glycerol–water-based dispersion in order to clarify the influence of the shear rate and the magnetic field strength on the negative magneto-rheological effect. Measurement of the viscosity was carried out using a rotational-type rheometer in an external magnetic field generated by Helmholtz coils. The main results obtained can be summarized as follows. The viscosity of a hematite/glycerol–water dispersion relative to that with no applied magnetic field decreases with increasing magnetic field strength: that is, we observed the negative viscosity effect that has previously been predicted from theoretical considerations. Moreover, the negative magneto-rheological effect is observed to decrease with increasing shear rate, which also agrees qualitatively with the theoretical prediction.     

Quasi-2D Monte Carlo simulations of phase transitions and internal aggregate structures in a highly dense suspension composed of magnetic plate-like particles

The phase transitions and the internal aggregate structures of a highly dense suspension composed of magnetic plate-like particles with a magnetic moment normal to the particle axis have been investigated by means of the Monte Carlo method. The present study considered a quasi-2D system in order to clarify the influences of the volumetric fraction of particles and the magnetic field strength on particle aggregations and phase transitions. The internal structures of particle aggregates have been discussed quantitatively in terms of pair correlation functions, orientational pair correlation functions, nematic and polar order parameters. The main results obtained here are summarized as follows. When the influence of the magnetic interaction between particles is of the same order of that of the perpendicular magnetic field strength, the particles form column-like clusters, and the internal structure of the suspension shows solid-like structures. For the case of a strong applied magnetic field, the internal structure is transformed from solid-like structures into isotropic ones. However, as the volumetric fraction increases, the particles form brick wall-like structures under the situation of a strong applied magnetic field, and the internal structure exhibits solid-like ones. The brick wall-like structures also appear for a relatively weak magnetic field applied along the in-plane direction despite a slightly smaller volumetric fraction compared with the case of the perpendicular applied magnetic field.     

Active colloidal suspensions exhibit polar order under gravity

Recently, the steady sedimentation profile of a dilute suspension of chemically powered colloids was studied experimentally [J. Palacci et al., Phys. Rev. Lett. 105, 088304 (2010)]. It was found that the sedimentation length increases quadratically with the swimming speed of the active Brownian particles. Here we investigate theoretically the sedimentation of self-propelled particles undergoing translational and rotational diffusion. We find that the measured increase of the sedimentation length is coupled to a partial alignment of the suspension with the mean swimming direction oriented against the gravitational field. We suggest realistic parameter values to observe this polar order. Furthermore, we find that the dynamics of the active suspension can be derived from a generalized free energy functional.     

Importance of depletion interactions for structure and dynamics of ferrofluids

The influence of attractive depletion forces on the structure and dynamics of ferrofluids is studied by computer simulations. In the presence of a magnetic field, we find that sufficiently strong depletion forces lead to an assembly of particle chains into columnar structures with hexagonal ordering inside the columns. In a planar shear flow, this ordering is destroyed, leading to strong shear thinning behavior. A pronounced anisotropy of the shear viscosity is observed. The viscosity is found to be largest when the magnetic field is oriented in the gradient direction of the flow.     

Effects of magnetic field on shape evolution of Fe–Co particles in a Cu matrix

The effects of magnetic field on the shape evolution of ferromagnetic fcc Fe–Co particles in Cu–0.83 at.% Fe–1.37 at.% Co alloy single crystals were examined using magnetic anisotropy measurements. The Cu–Fe–Co single crystals were aged at 993 K for 2 h to 24 h under a magnetic field of 10 T parallel to either the [001] or [011] direction. The magnetic anisotropy was examined by measuring magnetic torque around the (100) plane. It was found that the fcc Fe–Co particles are elongated in the direction parallel to the magnetic field. Furthermore, the elongation along [001] is more remarkable than that along [011]. The results are explained quantitatively by considering the minimization of the sum of the interface energy, elastic strain energy and magnetostatic energy of spheroidal particles.     

Carbon nanotube/polyaniline nanocomposites and their electrorheological characteristics under an applied electric field

A conducting polyaniline (PANI) was synthesized via an oxidative dispersion polymerization technique, using poly(vinyl alcohol) (PVA) as a polymeric stabilizer, in the presence of multi-walled carbon nanotubes (MWNT) purified in acidic solution, and dispersion stability of the MWNT in an aqueous solution of PVA was studied for different PVA concentrations. Their morphology was confirmed by a scanning electron microscope. Its electrorheological (ER) characteristics were also investigated by dispersing the PANI/MWNT composite particles in an insulating silicone oil. Its ER properties were examined using a rotational rheometer under varying applied DC electric field strengths, in which the ER fluid is generally composed of a suspension of conducting particles dispersed in an insulating fluid, which shows a rapid and reversible change in shear viscosity with an applied electric field. Synthesized PANI/MWNT composite particles are observed to enhance interparticular interactions, since the degree of polarization of PANI/MWNT composite particle increases with applied electric field strengths. The shear stresses of the PANI/MWNT nanocomposite based ER fluid increase with the electric field strength for a broad range of shear rates.     

Consistent theory of turbulent transport in two-dimensional magnetohydrodynamics

A theory of turbulent transport is presented in two-dimensional magnetohydrodynamics with background shear and magnetic fields. We provide theoretical predictions for the transport of magnetic flux, momentum, and particles and turbulent intensities, which show stronger reduction compared with the hydrodynamic case, with different dependences on shearing rate, magnetic field, and values of viscosity, Ohmic diffusion, and particle diffusivity. In particular, particle transport is more severely suppressed than momentum transport, effectively leading to a more efficient momentum transport. The role of magnetic fields in quenching transport without altering the amplitude of flow velocity and in inhibiting the generation of shear flows is elucidated. Implications of the results are discussed.     

Experimental study and CFD simulation of rotational eccentric cylinder in a magnetorheological fluid

In this study, a magnetorheological (MR) fluid is prepared using carbonyl iron filings and low viscosity lubricating oil. The effects of magnetic field and weight percentage of particles on the viscosity of the MR fluid have been measured using a rotational viscometer. The yield stress under an applied magnetic field was also obtained experimentally. In the absence of an applied magnetic field, the MR fluid behaves as a Newtonian fluid. When the magnetic field is applied, the MR fluid behaves like Bingham plastics with a magnetic field dependent yield stress. Afterward, the results compared with those of CFD simulation of two eccentric cylinders in the MR fluid. Results show that the influences of MR effects, caused by the applied magnetic field, on the model characteristics are significant and not negligible. The viscosity is enhanced by increasing of the magnetic field, eccentricity ratio and weight percentage of suspensions. The MR effects and increasing of weight percentage and eccentricity ratio also provide an enhancement in the yield stresses and required total torque for rotation of inner cylinder. Also the simulation results indicate a good representation of the experiment by the model.     

Transient magnetoviscosity of dilute ferrofluids

The magnetic field induced change in the viscosity of a ferrofluid, commonly known as the magnetoviscous effect and parameterized through the magnetoviscosity, is one of the most interesting and practically relevant aspects of ferrofluid phenomena. Although the steady state behavior of ferrofluids under conditions of applied constant magnetic fields has received considerable attention, comparatively little attention has been given to the transient response of the magnetoviscosity to changes in the applied magnetic field or rate of shear deformation. Such transient response can provide further insight into the dynamics of ferrofluids and find practical application in the design of devices that take advantage of the magnetoviscous effect and inevitably must deal with changes in the applied magnetic field and deformation. In this contribution Brownian dynamics simulations and a simple model based on the ferrohydrodynamics equations are applied to explore the dependence of the transient magnetoviscosity for two cases: (I) a ferrofluid in a constant shear flow wherein the magnetic field is suddenly turned on, and (II) a ferrofluid in a constant magnetic field wherein the shear flow is suddenly started. Both simulations and analysis show that the transient approach to a steady state magnetoviscosity can be either monotonic or oscillatory depending on the relative magnitudes of the applied magnetic field and shear rate.     

Angular dependence of nucleation field of a prolate spheroid

A simple upper bound for the nucleation field of a spheroidal particle in a magnetic field applied at an arbitrary angle with the particle symmetry axis has been given. The bound is supposed to be good enough for particles of a soft magnetic type with a moderate aspect ratio.     

Application of the dissipative particle dynamics method to magnetic colloidal dispersions

The validity of the application of the dissipative particle dynamics (DPD) method to ferromagnetic colloidal dispersions has been investigated by conducting DPD simulations for a two–dimensional system. First, the interaction between dissipative and magnetic particles has been idealized as some model potentials, and DPD simulations have been carried out using such model potentials for a two magnetic particle system. In these simulations, attention has been focused on the collision time for the two particles approaching each other and touching from an initially separated position, and such collision time has been evaluated for various cases of mass and diameter of dissipative particles and model parameters, which are included in defining the equation of motion of dissipative particles. Next, a multi–particle system of magnetic particles has been treated, and particle aggregates have been evaluated, together with the pair correlation function along an applied magnetic field direction. Such characteristics of aggregate structures have been compared with the results of Monte Carlo and Brownian dynamics simulations in order to clarify the validity of the application of the DPD method to particle dispersion systems. The present simulation results have clearly shown that DPD simulations with the model interaction potential presented here give rise to physically reasonable aggregate structures under circumstances of strong magnetic particle–particle interactions as well as a strong external magnetic field, since these aggregate structures are in good agreement with those of Monte Carlo and Brownian dynamics simulations.