The small shear rate response of electrorheological suspensions. I. Simulation in the point–dipole limit

On the absence of collective motion in a bulk suspension of spontaneously rotating dielectric particles

A suspension of dielectric particles rotating spontaneously when subjected to a DC electric field in two dimensions next to a no-slip electrode has proven to be an ideal model for active matter [Bricard et al., Nature, 2013, 503, 95-98]. In this system, an electrohydrodynamic (EHD) instability called Quincke rotation was exploited to create self-propelling particles which aligned with each other due to EHD interactions, giving rise to collective motion on large length scales. It is natural to question whether a suspension of such particles in three dimensions will also display collective motion and spontaneously flow like bacterial suspensions do. Using molecular dynamics type simulations, we show that dielectrophoretic forces responsible for chaining in the direction of the applied electric field in conventional electrorheological fluids and the counter-rotation of neighboring particles in these chains prevent collective motion in suspensions undergoing spontaneous particle rotations. Our simulations discover that the fundamental microstructural unit of a suspension under Quincke rotation is a pair of counter-rotating spheres aligned in the direction of the electric field. We perform a linear stability analysis that explains this observation.

Role of Phase-Dependent Dielectric Properties of Alumina Nanoparticles in Electromagnetic-Assisted Enhanced Oil Recovery

The utilization of metal-oxide nanoparticles in enhanced oil recovery (EOR) has generated considerable research interest to increase the oil recovery. Among these nanoparticles, alumina nanoparticles (Al₂O₃-NPs) have proved promising in improving the oil recovery mechanism due to their prominent thermal properties. However, more significantly, these nanoparticles, coupled with electromagnetic (EM) waves, can be polarized to reduce water/oil mobility ratio and create disturbances at the oil/nanofluid interface, so that oil can be released from the reservoir rock surfaces and travelled easily to the production well. Moreover, alumina exists in various transition phases (γ, δ, θ, κ, β, η, χ), providing not only different sizes and morphologies but phase-dependent dielectric behavior at the applied EM frequencies. In this research, the oil recovery mechanism under EM fields of varying frequencies was investigated, which involved parameters such as mobility ratio, interfacial tension (IFT) and wettability. The displacement tests were conducted in water-wet sandpacks at 95 °C, by employing crude oil from Tapis. Alumina nanofluids (Al₂O₃-NFs) of four different phases (α, κ, θ and γ) and particle sizes (25–94.3 nm) were prepared by dispersing 0.01 wt. % NPs in brine (3 wt. % NaCl) together with SDBS as a dispersant. Three sequential injection scenarios were performed in each flooding scheme: (i) preflushes brine as a secondary flooding, (ii) conventional nano/EM-assisted nanofluid flooding, and (iii) postflushes brine to flush NPs. Compared to conventional nanofluid flooding (3.03–11.46% original oil in place/OOIP) as incremental oil recovery, EM-assisted nanofluid flooding provided an increase in oil recovery by approximately 4.12–12.90% of OOIP for different phases of alumina. It was established from these results that the recovery from EM-assisted nanofluid flooding is itself dependent on frequency, which is associated with good dielectric behavior of NPs to formulate the oil recovery mechanism including (i) mobility ratio improvement due to an electrorheological (ER) effect, (ii) interfacial disturbances by the oil droplet deformation, and (iii) wettability alteration by increased surface-free energy.

Graphene Oxide and Its Inorganic Composites: Fabrication and Electrorheological Response

Composite particles associated with graphene oxide (GO) and inorganic materials provide the synergistic properties of an appropriate electrical conductivity of GO with the good dielectric characteristics of inorganic materials, making them attractive candidates for electrorheological (ER) materials. This review paper focuses on the fabrication mechanisms of GO/inorganic composites and their ER response when suspended in a non-conducting medium, including steady shear flow curves, dynamic yield stress, On-Off tests, and dynamic oscillation analysis. Furthermore, the morphologies of these composites, dielectric properties, and sedimentation of the ER fluids are covered.

Smart and Functional Conducting Polymers: Application to Electrorheological Fluids

Electro-responsive smart electrorheological (ER) fluids consist of electrically polarizing organic or inorganic particles and insulating oils in general. In this study, we focus on various conducting polymers of polyaniline and its derivatives and copolymers, along with polypyrrole and poly(ionic liquid), which are adopted as smart and functional materials in ER fluids. Their ER characteristics, including viscoelastic behaviors of shear stress, yield stress, and dynamic moduli, and dielectric properties are expounded and appraised using polarizability measurement, flow curve testing, inductance-capacitance-resistance meter testing, and several rheological equations of state. Furthermore, their potential industrial applications are also covered.

Cellulose-Based Smart Fluids under Applied Electric Fields

Cellulose particles, their derivatives and composites have special environmentally benign features and are abundant in nature with their various applications. This review paper introduces the essential properties of several types of cellulose and their derivatives obtained from various source materials, and their use in electro-responsive electrorheological (ER) suspensions, which are smart fluid systems that are actively responsive under applied electric fields, while, at zero electric field, ER fluids retain a liquid-like state. Given the actively controllable characteristics of cellulose-based smart ER fluids under an applied electric field regarding their rheological and dielectric properties, they can potentially be applied for various industrial devices including dampers and haptic devices.

Describing magnetorheology under a colloidal glass approach

The equilibrium structure and dynamics of magnetorheological (MR) fluids are studied in this work by simulations, where particles are modeled as dipoles with a quasihard spherical core. Upon increasing the interaction strength, controlled experimentally by the magnetic field, elongated clusters grow and, for intense fields, thick columns form, aligned with the field. The dynamics of the system is monitored by the mean-squared displacement and density correlation functions, which show an increasing slowing down with the attraction strength. The correlation function shows a two-step decay, with a separation between microscopic and long time dynamics, a typical hallmark of undercooled fluids. We have therefore analyzed the dynamics of this MR fluid using the typical concepts for undercooled fluids. Thus, the second decay of the density correlation function is fitted with a stretched exponential, and the wave-vector dependence of the fitting parameters studied. Both the amplitude and the time scale oscillate in phase with the structure factor. Our results support the idea that the magnetorheological effect is in fact the manifestation of a colloidal system approaching an attractive glass transition (or gel transition).

Highly stable nanofluid based on polyhedral oligomeric silsesquioxane-decorated graphene oxide nanosheets and its enhanced electro-responsive behavior

Graphene oxide (GO) shows potential as an anisotropic nanofiller or a dispersed phase of electro-responsive electrorheological (ER) nanofluid due to its small size and high aspect ratio. But it is difficult to disperse GO in non-polar oil due to the hydrophilic nature of GO and thus the resulting fluid is often subject to dispersion instability and low ER effect. These disadvantages largely limit the real application of GO-based ER nanofluid. In this paper, we develop the polyhedral oligomeric silsesquioxane (POSS)-decorated GO (POSS-GO) nanosheets and demonstrate that decorating with POSS overcomes the dispersion instability of GO in silicone oil and enhances the ER effect. The morphology and structure of samples are characterized by atomic force microscopy, Fourier transform infrared spectroscopy, thermogravimetric analysis, and x-ray photoelectronic spectroscopy. The results show that the POSS-GO nanosheets are ultrathin with ∼3 nm thickness and have good compatibility with silicone oil and, as a result, the nanofluid of POSS-GO nanosheets in silicone oil shows high dispersion stability. After standing for one year at room temperature, no sedimentation occurs. Under an external electric field, the ER efficiency of the POSS-GO nanofluid is ten times as high as that of the pure GO fluid. This enhanced electro-responsive behavior is related to the fact that decorating with POSS partly reduces the GO and compresses the dielectrophoretic effect of the negatively charged pure GO fluid.

Electrorheological response of inorganic-coated multi-wall carbon nanotubes with core-shell nanostructure

The effect of coating thickness and sequence on the multi-wall carbon nanotube (MWCNT) surface on electrorheological (ER) activity is investigated. Silica-coated MWCNTs with different shell thicknesses and inorganic-coated MWCNTs with different shell sequences are fabricated using the sol-gel process. The morphology and elemental analyses of the core-shell structured MWCNTs were performed and the effect of coating thickness and coating materials on the MWCNT surface on ER and dielectric properties of inorganic-coated MWCNT suspensions have been analyzed from the measurement results of shear stress, viscosity, current density and permeability. The electrical conductivity of silica-coated MWCNTs decreases with an increase of the shell thickness. However, the dynamic yield stress and viscoelastic properties under an external electric field increased when the shell thickness reached 20 nm and then decreased with the thickness up to 40 nm. However, the titania-coated MWCNT suspension with a shell thickness of 40 nm showed the highest dynamic yield stress compared to the other core-shell structured MWCNT suspension at the same volume fraction. It has been found that the material of the outermost shell plays an important role in the ER performance. It has been concluded that the electrical conductivity and the permittivity of the MWCNTs can be controlled by adjusting the coating thickness and sequence of inorganic materials.

Facile fabrication of Pickering emulsion polymerized polystyrene/laponite composite nanoparticles and their electrorheology

Polystyrene (PS)/laponite composite nanoparticles were fabricated using a surfactant-free Pickering emulsion polymerization method, in which emulsions of styrene dispersed in water were stabilized by hydrophilic laponite modified with cetyltrimethylammonium bromide. The PS/laponite nanoparticles, of which their surface was covered compactly by laponite clay platelets, were observed by scanning electron microscopy. Fourier-transform infrared spectroscopy, X-ray diffraction, and thermogravimetric analysis confirmed their chemical composition, crystallographic structure, and thermal properties and weight loss percentage of the laponite located on the surface of the PS particle, respectively. When an external electrical field was applied, the chain-like structure of the laponite coated nano-sized PS particle exhibiting electrorheological characteristics was observed by optical microscopy. The electrorheological performance of the bulk properties was also examined using a rotational rheometer equipped with a high voltage generator.

Simulation study on the trembling shear behavior of eletrorheological fluid

The trembling shear behavior of electrorheological (ER) fluids has been investigated by using a computer simulation method, and a shear-slide boundary model is proposed to understand this phenomenon. A thiourea-doped Ba-Ti-O ER fluid which shows a trembling shear behavior was first prepared and then systematically studied by both theoretical and experimental methods. The shear curves of ER fluids in the dynamic state were simulated with shear rates from 0.1 to 1000 s(-1) under different electric fields. The simulation results of the flow curves match the experimental results very well. The trembling shear curves are divided into four regions and each region can be explained by the proposed model.

Numerical simulation of microstructure formation of suspended particles in magnetorheological fluids

Microstructure formation of magnetic particles and nonmagnetic particles in magnetorheological (MR) fluids is investigated using the particle method simulation based on simplified Stokesian dynamics. Spherical nonmagnetic particles are rearranged in the field direction due to the formation of magnetic particles in chain-like clusters. Cluster formation of spherocylindrical magnetic particles forces spherical nonmagnetic particles to arrange in the direction of the field. In contrast, the spherocylindrical nonmagnetic particles, with an aspect ratio of two or three, are not sufficiently rearranged in the field direction by cluster formation of spherical magnetic particles. Even after cluster formation in the presence of a magnetic field, the uniformity of distribution of particles on the plane perpendicular to the field direction shows very little change. However, the deviation of uniformity in particle distribution is reduced when the volume fraction of magnetic particles is the same as that of nonmagnetic particles.

Electrorheological fluid dynamics

We use the Onsager principle to derive a two-phase continuum formulation for the hydrodynamics of the electrorheological (ER) fluid, consisting of dielectric microspheres dispersed in an insulating liquid. Predictions of the theory are in excellent agreement with the experiments. In particular, it is shown that whereas the usual configuration of applied electric field being perpendicular to the shearing direction can lead to shear thinning at high shear rates and thus the loss of ER effect, the interdigitated, alternating electrodes configuration can eliminate the shear-thinning effect.

Electrorheological fluids: structures and mechanisms

Electrorheology denotes the control of a colloid's flow properties through an electric field. We delineate the basic characteristics of electrorheological (ER) fluids, and show that the use of an effective dielectric constant concept can yield quantitative predictions. In particular, the ground state structure, the structural transition that occurs under crossed electric and magnetic fields, the high-field yield stress and its variation with particle size are all in good agreement with the experiments. The recently discovered giant electrorheological effect, owing its origin to molecular dipoles, is described and contrasted with the conventional ER effect that arises from induced polarization effects.

Dynamic effects on nonlinear alternating current responses in electrorheological fluids

By using a perturbation approach, we investigate dynamic effects on nonlinear alternating current (ac) responses in electrorheological (ER) fluids under an ac or direct current electric field. We show that the dynamic effect due to a shear flow, which exerts a torque on ER particles and thus leads to the rotation of the particles about their centers, plays a significant role in the responses. Our results can be well interpreted in the dielectric dispersion spectral representation, and they offer a convenient method to determine the relaxation time and rotation velocity of ER particles by measuring the nonlinear ac responses.

Electrorheological properties of polyaniline suspensions: Field-induced liquid to solid transition and residual gel structure

Polyaniline (PANI) was synthesized via oxidative coupling polymerization in acid conditions and de-doped in solution of ammonia. The electrorheological (ER) properties of the PANI/silicone oil suspensions were investigated in oscillatory shear as functions of electric field strength, particle concentration, and host fluid viscosity. Consistent with literature, the PANI ER fluid exhibits viscoelastic behavior under the applied electric field and the ER response is strongly enhanced with increasing electric field strength and particle concentration. The dynamic moduli, G' and G'' increase dramatically, by 5 orders of magnitude, as the electric field strength is increased to 2 kV/mm. A viscoelastic liquid to solid transition occurs at a critical electric field strength, in the range Ec = 50-200 V/mm, whose value depends on particle concentration and host fluid viscosity. The fibrillar structure formed in the presence of the applied field has a static yield strength tau(y), whose value scales with electric field strength as tau(y) approximately E(1.88). When the field is switched off a residual structure remains, whose yield stress increases with the strength of the applied field and particle concentration. When the applied stress exceeds the yield stress of the residual structure, fast, fully reversible switching of the ER response is obtained.

Method to calculate electrical forces acting on a sphere in an electrorheological fluid

We describe a method to calculate the electrical force acting on a sphere in a suspension of dielectric spheres in a host with a different dielectric constant, under the assumption that a spatially uniform electric field is applied. The method uses a spectral representation for the total electrostatic energy of the composite. The force is expressed as a certain gradient of this energy, which can be expressed in a closed analytic form rather than evaluated as a numerical derivative. The method is applicable even when both the spheres and the host have frequency-dependent dielectric functions and nonzero conductivities, provided the system is in the quasistatic regime. In principle, it includes all multipolar contributions to the force, and it can be used to calculate multibody as well as pairwise forces. We also present several numerical examples, including host fluids with finite conductivities. The force between spheres approaches the dipole-dipole limit, as expected, at large separations, but departs drastically from that limit when the spheres are nearly in contact. The force may also change sign as a function of frequency when the host is a slightly conducting fluid.

Interparticle force in electrorheological solids: many-body dipole-induced dipole model

One often investigates electrorheological (ER) solids by using the point-dipole (PD) approximation, which, however, is known to err considerably for touching particles due to the existence of many-body (local-field) effects and multipolar interactions. Beyond the PD model, previous attempts have been restricted to either local-field effects only or multipolar interactions only, but not both. In the present work, we have developed a many-body dipole-induced dipole model for an ER solid the lattice structure of which can be changed due to the application of external fields, in an attempt to take into account both local-field effects and multipolar interactions. The results show that the multipolar interaction can indeed be dominant over the dipolar interaction, while the local-field effect may yield an important correction. Also, the results are well understood with the aid of spectral representation theory.

Electrorheological properties and microstructure of silica suspensions

We present experimental and theoretical results on the electrorheological response and microstructure of colloidal suspensions composed of silica nanoparticles dispersed in a silicon oil, as a function of electric field strength and silica water content. Using small-angle neutrons scattering experiments, we determined the evolution of the static structure factor of the suspensions when an electric field is applied. Experimental data were fitted with model calculations using the Percus-Yevick solution for Baxter's hard-sphere adhesive potential. The obtained stickiness parameter is directly related to the polarization interactions that depend on the water content of silica particles. The influence of the polarization interparticle potential on the rheology of the silica dispersions was investigated in a second time. A microscopic theory for the shear viscosity of adhesive hard-sphere suspensions was successfully used which describes the steady shear viscosity of suspension in terms of the fractal concept.

Bidisperse electrorheological fluids using hydrolyzed styrene-acrylonitrile copolymer particles: synergistic effect of mixed particle size

Monodisperse micron-sized styrene-acrylonitrile copolymer (SAN) particles with three different sizes (about 5, 10, and 15 microm) were prepared by a two-step seeded polymerization and used for a study of bidisperse electrorheological (ER) suspensions. The effect of the particle size and the size-mixing fraction on ER properties was studied with varying the size of these monodisperse copolymer particles. When the two particle sizes were mixed, the suspension generally showed a decrease in the shear yield stress, reaching a minimum value. However, a bidisperse ER suspension of large particles containing a small fraction of fine particles showed an interesting synergy effect of size mixing on ER response, giving enhanced yield stresses over the other size-mixing fractions. This synergistic ER suspension also showed a great increase in the viscoelastic property. The current density of suspensions was maximum at the synergistic bidisperse suspension. This synergy effect in a particular bidisperse suspension was investigated in view of the structure model consideration and was concluded to be due to a close packing and a peculiar structural ordering at an optimum size ratio and mixing fraction.

Critical role of flow-modified permittivity in electrorheology: model and computer simulation

We propose a model that takes into account the effect of flow-modified permittivity (FMP) on electrorheology (ER). Our computer simulation shows that for Mason numbers less than 0.1, ER effects are mainly attributable to the deformation of chain structures, in agreement with earlier theoretical and simulation work. At larger Mason numbers, where chain structures have been destroyed by shear flows, we show that an FMP-induced misalignment between the particle dipole moments and the applied electric field plays a crucial role in producing ER effects. We also identify conditions under which negative ER effects are seen at large Mason numbers.

Electrorheological suspensions

The objective of this article is to give a review of electrorheological (ER) suspensions whose rheological properties can abruptly change under an external electric field. Attention is given to the physical backgrounds behind ER phenomena reported recently. The criteria on how to design a high performance ER fluid and mechanisms explaining how an ER suspension displays the ER effect are focused upon. We begin with a brief historic introduction, ER materials, followed by positive ER effect, negative ER effect and photo-ER effect discussions. The physical parameters that can substantially affect the ER effect are discussed thereafter, and physical processes occurring in ER suspensions under an electric field are reviewed. The mechanisms of the ER effect proposed before are summarized. A future outlook on the ER material development and ER fluid applications is given.

Relaxation of surface charge on rotating dielectric spheres: Implications on dynamic electrorheological effects

We have examined the effect of an oscillatory rotation of a polarized dielectric particle. The rotational motion leads to a redistribution of the polarization charge on the surface of the particle. We show that the time-averaged steady-state dipole moment is along the field direction, but its magnitude is reduced by a factor that depends on the angular velocity of rotation. As a result, the rotational motion of the particle reduces the electrorheological effect. We further assume that the relaxation of the polarized charge is arised from a finite conductivity of the particle or host medium. We calculate the relaxation time based on the Maxwell-Wagner theory, suitably generalized to include the rotational motion. Analytic expressions for the reduction factor and the relaxation time are given and their dependence on the angular velocity of rotation will be discussed.

Computer simulations of electrorheological fluids in the dipole-induced dipole model

We have employed the multiple image method to compute the interparticle force for a polydisperse electrorheological (ER) fluid in which the suspended particles can have various sizes and different permittivities. The point-dipole (PD) approximation, being routinely adopted in the computer simulation of ER fluids, is known to err considerably when the particles approach and finally touch due to multipolar interactions. The PD approximation becomes even worse when the dielectric contrast between the particles and the host medium is large. From the results, we show that the dipole-induced-dipole (DID) model yields very good agreements with the multiple image results for a wide range of dielectric contrasts and polydispersity. As an illustration, we have employed the DID model to simulate the athermal aggregation of particles in ER fluids, both in uniaxial and rotating fields. We find that the aggregation time is significantly reduced. The DID model partially accounts for the multipolar interaction and is simple to use in the computer simulation of ER fluids.

Electrorheological Response and Structure Growth of Colloidal Silica Suspensions

The electrorheological response and structure growth of colloidal silica suspension was studied with in situ measurements of the shear stress, electric conductivity, and dielectric permittivity of the suspension. The measurements were carried out under steady and sweep shears after the application of an electric field of alternative current (100 Hz) using silica particles with a diameter of 630 nm and a water content of 4.5 wt%. The measurements of the conductivity enabled the detection of structure growth formed by particle aggregation and clarified that the development of the particle aggregation enlarged the dielectric permittivity and the shear stress. Hysteretic behavior observed in the electrorheological response was explained by considering structure growth of the particle aggregation. The correlation equation for the shear stress and the dielectric permittivity obtained in our previous work (1) was found to be applicable to the present results. Copyright 2001 Academic Press.

Dynamic electrorheological effects and interparticle force between a pair of rotating spheres

We consider a two-particle system in which a particle is held fixed, and the other one rotates around the axis perpendicular to the line joining the particles' centers. The rotating particle leads to a displacement of its polarization charge on the surface. Our results show that the rotational motion of the particles generally reduces the force between the particles. The dependence of interparticle force on the angular velocity of rotation will be discussed.

Force between two spherical inclusions in a nonlinear host medium

In an attempt to investigate the effect of nonlinear characteristics on particle interactions, a self-consistent mean-field theory in combination with a multiple image method has been employed to compute the interparticle force. Taking the nonlinearity of the host medium into account, the interparticle force exhibits a nonmonotonic behavior as the applied electric field is increased. We show that the interparticle force increases initially at low fields, goes through a maximum at an optimal electric field, then decreases with increasing field, and vanishes at a critical electric field at which the effective dielectric contrast between the host and the inclusions becomes zero. The influence of a larger volume fraction of inclusions on the interparticle force is also investigated.