The effect of mixing particles of different size on the electrorheological response under steady shear flow

 The effect of mixing particles of different sizes on the electrorheological response of suspensions under steady shear flow was investigated. Two sizes, 15 μm and 50 μm, of monodisperse spherical sulfonated poly(styrene-co-divinylbenzene) particles were used. Several electrorheological fluids were made containing different proportions of small and large particles dispersed in silicone oil, but with constant overall particulate concentration. It was found that the mixed size system produced the highest electrorheological response under the shear rates used (10 s⁻¹ to 500 s⁻¹), which is the opposite trend to previous studies of bimodal systems with larger size ratios. Received: 21 December 2000 Accepted: 29 March 2001     

Micro/nano-structured montmorillonite/titania particles with high electrorheological activity

A low-cost electrorheological (ER) material made of micro/nano-structured montmorillonite/titania particles was prepared by a one-pot solvothermal method. The micro/nano-structured particles were characterized by X-ray diffraction, Fourier transform infrared spectra, and scanning electron microscopy. It was found that the nanorod-like titania assembled on the surface of montmorillonite, the diameters of the nanorods were about 30 nm, and the lengths were about 300 nm. The electrorheological property of the micro/nano-structured particles in silicone oil was measured under dc electric fields. It was found that the micro/nano-structured montmorillonite/titania ER fluid exhibited much stronger electrorheological effect compared to pure montmorillonite and pure titania nanorod ER fluids, while its leaking current density was significantly lower than that of montmorillonite ER fluid. The stronger electrorheological effect might be attributed to the larger interfacial polarization and interparticle friction, which originated from the unique structure and morphology of micro/nano-structured particles, compared to pure montmorillonite and pure titania nanorods.     

A microstructural investigation of the nonlinear response of electrorheological suspensions

In the preceding paper, Part 1, the transition from linear to nonlinear behavior for electrorheological (ER) suspensions under start-up of steady shear flow was found to first arise from the slight rearrangement of unstable structures. In this paper, we investigate the transition to nonlinear behavior for ER suspensions under oscillatory shear flow, focusing on the role of the rearrangement of unstable structures, and employing experimental and simulation results. Again, we find that nonlinear deformation first arises from these rearrangements, as opposed to the gross rearrangement or rupture of particulate chains. The Fourier transform of the simulated time-dependent shear stress is employed to quantify the dependence of the critical strain on the deformation frequency and electric field strength. The predicted behavior is consistent with experimental trends. Methods for verifying the predictions are discussed, as well as possible avenues for exploiting this information in improved operating strategies and improved ER fluids.     

Batchelor’s theory extended to elongated cylindrical or ellipsoidal particles

Extensions to Batchelor’s theory have been derived to take into account different shaped particles while relating extensional viscosity enhancement to three parameters — shape, volume fraction and particle aspect ratio. The extended theory now allows calculation of the extensional viscosity enhancement, at a given volume fraction of particles, for either ellipsoidal or cylindrical particles. The formula improves the predictive capability of Batchelor’s theory when compared with measurements found in the literature for different rod-like polymer solutions.     

Attachment of solid elongated particles on the surface of a stationary gas bubble

Froth flotation is a separation process which plays a major role in the mining industry. It is essentially employed to recover a vast array of different valuable commodities such as rare earth minerals essential to the manufacture of high-tech products. Owing to its simplicity, the process is also widely used for the de-inking of recycled paper fibres and for the removal of pollutants from waste water. The flotation process essentially relies on the attachment of solid particles on the surface of gas bubbles immersed in water. The present study seeks to investigate the effect of the particle shape on the attachment mechanism. Using an in-house optical micro-bubble sensor the approach, the sliding and the adhesion of micron milled glass fibres on the surface of a stationary air bubble immersed in stagnant water is thoroughly investigated. The translational and rotational velocities were measured for fibres of various aspect ratios. The results are compared with a theoretical model and with experimental data obtained with spherical glass beads. It is found that the fibre orientation during the sliding motion largely depends on the collision area. Upon collision near the upstream pole of the gas bubble the major axis of the fibre aligns with the local bubble surface (tangential fibre alignment). If collision occurs at least 30° further downstream only head of the fibre is in contact with the gas–liquid interface (radial fibre alignment).     

Synthesis and electrorheological properties of polar molecule-dominated TiO 2 particles with high yield stress

Two types of amorphous TiO₂ particles with different particle sizes were synthesized by a simple sol–gel method and were characterized by X-ray diffraction analysis, field emission scanning electron microscopy, and Fourier transform infrared spectrometry. The electrorheological (ER) results show that the TiO₂/silicone oil suspensions exhibited a remarkable ER effect. The static shear stress can be up to 130 kPa (shear rate 0.2 s^− 1) under the DC electric field of 4 kV/mm at room temperature. The polar molecules present on the particles’ surface play a decisive role for the observed giant ER effect, which arises from the alignment of polar molecules in the gap between neighboring particles.     

Maximising the electrorheological effect for bidisperse nanofluids from the electrostatic force between two particles

A multipole re-expansion solution for two nonidentical dielectric spheres in a parallel electric field is used to determine the critical ratio of particle radii which leads to the strongest force of attraction between the spheres at various interstices and under varying dielectric properties. These critical ratios provide genuine optimal dimensions, in the sense that the force of attraction decreases for both increasing and decreasing ratios. Numerical results are compared with experimental results from the literature and discussed from the perspective of the impact on the design of electrorheological nanofluids.     

Suspension of layered particles: an optimum electrorheological fluid for d.c. applications

 A comparison is made between two types of solid particles used in electrorheological fluids: particles with homogeneous electrical properties versus layered particles with a semi-conducting core surrounded by an outer layer of lower conductivity. Rheological measurements of these suspensions under steady shear and d.c. electric field show that the layered particle system produces the same yield stress but with a substantially reduced electric current. X-ray spectroscopic analysis confirms that these particles have a thin layer of SiO_x on the outer surface which causes the reduction in conductivity. Measurement of the dielectric permittivity followed by analysis using the Maxwell-Wagner model of polarization indicates that the conductivity of the outer layer is about 0.62 times that of the core region. Received: 13 January 1999 Accepted: 26 July 1999     

The electrorheological property of a polyaniline-coated copolystyrene particle suspension

Polyaniline-coated copoly (styrene styrenesulphonate) (PSS) particles were prepared by oxidative polymerization of aniline hydrochloride using ammonium persulphate in the presence of anionic PSS particles. Polyanilinecoated PSS particles were found to be higher dispersibility than polyaniline itself in an organic solvent. A suspension of polyanilinecoated PSS particle in silicone oil was found to exhibit high performance at higher temperature without the necessity for water.     

Mathematical modeling of electrorheological materials

Received May 11, 2000 / Published online January 23, 2001     

Modulus-switching viscoelasticity of electrorheological networks

To form an electrorheological network (ERN), semiconducting nanoparticles were embedded in a polymer that was cross-linked to restrict particle motion. The microstructure ranged from random to aligned, depending on the degree of field-induced particle alignment during chemical network formation. We investigated in detail the softness effects of the matrix, having a relatively low storage modulus, on the dynamic rheological behavior of the ERN and analyzed its anisotropy. The anisotropy of the microstructure was probed rheologically with the modes of small-amplitude oscillatory shear (loading perpendicular to the field direction) and compression (loading in the field direction). The storage shear modulus was found to be a function of the applied electric field, particle volume fraction, and the pre-alignment electric field strength during the cross-linking reaction of the matrix, which governs the thickness of particle columns and intercolumn distance. Nonlinear behavior at small strain (below 0.1%) was conspicuous; this nonlinear viscoelasticity was accompanied by only a limited deformation of ordered connectivity. Throughout this study, we fabricated the ERN with the highly controllable modulus-switching effect acting in a shear-mode operation. Managing this anisotropy of an ERN by the electrical and chemical process is important in the design of smart materials that will provide improved stability and mechanical strength compared with fluid-type electrorheological materials and faster response time compared with that of conventional charged polymer gel.     

A phenomenological model of electrorheological fluids

The fundamental assumption of the paper is that the extra stress tensor of an electrorheological fluid is an isotropic tensor valued function of the rate of strain tensor D and the vector n (which characterizes the orientation and length N of the fibers formed by application of an electric field). The resulting constitutive equation for is supplemented by the solution of the previously studied time evolution equation for n. Plastic behavior for the shear and normal stresses is predicted. Anticipating that the action of increasing shear rate is i) to orient the fibers more and more in the direction of flow and ii) simultaneously to break up the fibers leads to the conclusion that for the same behavior is encountered as without an electric field. Using realistically possible approximation formulas for the dependence of and N on leads to the Bingham behavior for and power law behavior for large shear rates.

Structural changes of silica particles in elongated rubber by two-dimensional small-angle X-ray scattering and extended reverse Monte Carlo analysis

Two-dimensional pattern reverse Monte Carlo method is applied to investigate structural changes of silica particle filler in uniaxially elongat ed rubber. We calculated three-dimensional confor mations of spherical silica particles using a series of two-dimensional patterns of structure factors during elongation. The structure factors we used are inter polated from experimentally observed structure factors for the elongation ratio ε?=?0.0, 0.5, 1.0, and 1.5. To make a continuous motion of particles, we set the elongation ratio with small interval Δε?=?0.001. It is found that the structural change of the particles seem to be reliable at least for small ε regions because spurious motions like the Brownian motions are not observed.     

Layered model of electrorheological fluid under flow

We present a theoretical model of the behavior of a concentrated electrorheological fluid (ERF) which explicitly takes into account the effects of conductivity. The increase in shear viscosity under an electric field is due to a layered structure between the electrodes, made up of the remnants of particle chains adhering to the electrodes by electrostatic image forces, and a freely flowing liquid layer where all the shear flow is concentrated. This layered model can explain the variation of electric current with shear rate, as well as the rheological response of a dynamic yield stress proportional to the square of the applied electric field.     

On constitutive equations for electrorheological materials

Constitutive equations for electrorheological (ER) fluids have been based on experimental results for steady shearing flows and constant electric fields. The fluids have been modeled as being rigid until a yield stress is reached. Additional stress is then proportional to the shear rate. Recent experimental results indicate that ER materials have a regime of solid-like response when deformed from a rest state. They behave in a viscoelastic-like manner under sinusoidal shearing and exhibit time-dependent response under sudden changes in shear rate or electric field. In this work, a constitutive theory for ER materials is presented which accounts for these recent experimental observations. The stress is given by a functional of the deformation gradient history and the electric field vector. Using the methods of continuum mechanics, a general three-dimensional constitutive equation is obtained. A sample constitutive equation is introduced which is then used to determine the response of an ER material for different shear histories. The calculated shear response is shown to be qualitatively similar to that observed experimentally.     

Detonation of elongated charges with cavities

Channel effects have been investigated in elongated charges of cast Composition B with cavities of various shapes. The existence of a transient regime has been established and the velocities of the channel shock waves in the regime have been measured. The parameters of the jets formed in tubular charges are estimated.The authors are grateful to V. M. Titov for systematically discussing the results and to V. P. Urushkin for assisting with the organization of the experiments.     

Dielectric analysis of TiO2-based electrorheological suspensions

Dielectric behaviors of titanium dioxide (TiO₂)-based electrorheological (ER) suspensions with different particle concentrations and TiO₂ polymorphs were investigated in the frequency range of 40 Hz to 110 MHz. Two relaxations in kilohertz and megahertz frequency range were attributed to interface polarization between TiO₂ and silicone oil and ion pair polarization between dissociated counterions and fixed charges on TiO₂ surfaces, respectively. Dipolar coefficient D, which is related to the construction or structure of the colloid, changes after critical volume fraction $\phi _{\rm c} \approx $ 0.05, indicating that chain-like or network structures are formed by particles. Based on percolation model, the values of critical exponent suggest that particles may form two-dimensional percolation network. Furthermore, the effective dielectric mismatch parameter, $\beta _{\rm eff}$ , was calculated based on the obtained phase parameters. We found that rutile should have better ER activity than anatase. The main reason for weak ER activity of pure TiO₂ ER suspensions may due to poor conductivity properties of TiO₂ crystals.