Structure parameter of electrorheological fluids in shear flow

A structure parameter, Sn = η(c)γ/τ(E), is proposed to represent the increase of effective viscosity due to the introduction of particles into a viscous liquid and to analyze the shear behavior of electrorheological (ER) fluids. Sn can divide the shear curves of ER fluids, τ/E(2) versus Sn, into three regimes, with two critical values Sn(c) of about 10(-4) and 10(-2), respectively. The two critical Sn(c) are applicable to ER fluids with different particle volume fractions φ in a wide range of shear rate γ and electric field E. When Sn < 10(-4), the shear behavior of ER fluids is mainly dominated by E and by shear rate when Sn > 10(-2). The electric current of ER fluids under E varied with shear stress in the same or the opposite trend in different shear rate ranges. Sn(c) also separates the conductivity variation of ER fluids into three regimes, corresponding to different structure evolutions. The change of Sn with particle volume fraction and E has also been discussed. The shear thickening in ER fluids can be characterized by Sn(c)(L) and Sn(c)(H) with a critical value about 10(-6). As an analogy to friction, the correspondence between τ/E(2) and friction coefficient, Sn and bearing numbers, as well as the similarity between the shear curve of ER fluids and the Stribeck curve of friction, indicate a possible friction origin in ER effect.     

Phase behavior of a simple dipolar fluid under shear flow in an electric field

Nonequilibrium molecular dynamics simulations are performed on a dense simple dipolar fluid under a planar Couette shear flow. Shear generates heat, which is removed by thermostatting terms added to the equations of motion of the fluid particles. The spatial structure of simple fluids at high shear rates is known to depend strongly on the thermostatting mechanism chosen. Kinetic thermostats are either biased or unbiased: biased thermostats neglect the existence of secondary flows that appear at high shear rates superimposed upon the linear velocity profile of the fluid. Simulations that employ a biased thermostat produce a string phase where particles align in strings with hexagonal symmetry along the direction of the flow. This phase is known to be a simulation artifact of biased thermostatting, and has not been observed by experiments on colloidal suspensions under shear flow. In this paper, we investigate the possibility of using a suitably directed electric field, which is coupled to the dipole moments of the fluid particles, to stabilize the string phase. We explore several thermostatting mechanisms where either the kinetic or configurational fluid degrees of freedom are thermostated. Some of these mechanisms do not yield a string phase, but rather a shear-thickening phase; in this case, we find the influence of the dipolar interactions and external field on the packing structure, and in turn their influence on the shear viscosity at the onset of this shear-thickening regime.     

Transient response of an electrorheological fluid under square-wave electric field excitation

The transient process of an electrorheological (ER) fluid based on zeolite and silicone oil sheared between two parallel plates to which a square-wave electric field is applied has been experimentally studied. The transient shear stress response to the strain or time is tested. The characteristic constants of time under different applied electric fields and shear rates have been determined. The response time is found to be proportional to shear rate with an exponent of about -0.75 in the tested shear rate range, which agrees with the theoretical predictions made by others. But it only shows a small dependence on the strength of the applied electric field. The results show that the transient process of ER fluids is related to the structure formation in the shearing. When the required shear strain is reached, the shear stress rises to a stable value under constant electric field. Although the electric field strength greatly affects the yield strength, it shows little effect on the stress response time. Also, experiments showed the electric field-induced shear stress decreased with an increase of shear rate.     

Influence of an electric field on the non-Newtonian response of a hybrid-aligned nematic cell under shear flow

The authors study shear flow in hybrid-aligned nematic cells under the action of an applied electric field by solving numerically a hydrodynamic model. The authors apply this model to a flow-aligning nematic liquid crystal (4'-n-pentyl-4-cyanobiphenyl) and obtain the director's configuration and the velocity profile at the stationary state. The authors calculate the local and apparent viscosities of the system and found that the competition between the shear flow and the electric field gives rise to an interesting non-Newtonian response with regions of shear thickening and thinning. The results also show an important electrorheological effect ranging from a value a bit larger than the Miesowicz viscosity etab [Nature (London) 17, 261 (1935)] for small electric fields and large shear flows to etac for large electric fields and small shear flows. The analysis of the first normal stress difference shows that for small negative shear rates, the force between the plates of the cell is attractive, while it is repulsive for all other values of shear rates. However, under the application of the electric field, one can modify the extent of the region of attraction. Finally, the authors have calculated the dragging forces on the plates of the cell and found that it is easier to shear in one direction than in the other.     

The dielectric properties and flow of electrorheological fluids based on polymer-coated nanodispersed barium tetraacetate titanyl particles upon a dynamic shear in electric fields

The shear stress in flowing electrorheological fluids consisting of PMS-20 poly(dimethylsiloxane) filled with nanodispersed barium tetraacetate titanyl particles coated with polymers (polyethyleneimine, poly(ethylene glycol), and polyethyloxazoline) has been studied as depending on the strengths of direct- and alternating-current (f = 50 Hz) electric fields. Results of analyzing the dielectric spectra of electrorheological fluids in a frequency range of 25–10⁶ Hz have been presented. The values of the shear stress in the flowing fluids as depending on the nature of a polymer adsorbed on the particle surface decrease in a series corresponding to a reduction in the Maxwell–Wagner relaxation times of the suspensions. The current-voltage characteristics of the electrorheological fluids at high voltages (up to 5 kV) indicate the realization of the mechanism of currents limited by the space charge. The influence of an adsorbed polymer on the magnitude of the electrorheological effect is reduced to blocking polar groups on the particle surface and variations in the conductivity, effective dielectric permittivity, and loss tangents of filler materials. An increase in the contribution from these factors leads to a gradual decrease in the magnitude of the electrorheological effect.     

Structure changes of electrorheological fluids based on polyaniline particles with various hydrophilicities and time dependence of shear stress and conductivity during flow

Particles of polyaniline protonated with perfluorooctanesulfonic acid provided a material with hydrophobic surface. This property enabled its perfect dispersion in silicone oil due to its good compatibility with the hydrophobic medium. In contrast, in a suspension of hydrophilic polyaniline particles doped with sulfamic acid, strong interactions of particles prevailed, which led to the formation of entangled chains of aggregated particles in suspension. The difference in structural properties of suspensions exists already in the absence of electric field and significantly influences their electrorheological behavior after application of electric field. The formation of electrorheological structure has been monitored by recording time dependences of the shear stress and the electric current passing through the flowing suspensions.     

Near-wall velocities of particles suspended in shear flow and a streamwise electric field

Particles with a diameter of ∼0.5 µm in a dilute (volume fractions φ_∞ < 4 × 10⁻³) suspension assemble into highly elongated structures called “bands” under certain conditions in combined Poiseuille and electroosmotic flows in opposite directions through microchannels at particle-based Reynolds numbers Re_p < < 1. The particles are first concentrated near, then form “bands” within ∼6 µm of, the channel wall. The experiments described here examine the near-wall dynamics of individual “tracer” particles during the initial concentration, or accumulation, of particles, and the steady-state stage when the particles have formed relatively stable bands at different near-wall shear rates and electric field magnitudes. Surprisingly, the near-wall upstream particle velocities are found to be consistently greater in magnitude than the expected values based on the particles being convected by the superposition of both flows and subject to electrophoresis, which is in the same direction as the Poiseuille flow. However, the particle velocities scale linearly with the change in electric field magnitude, suggesting that the particle dynamics are dominated by linear electrokinetic phenomena. If this discrepancy with theory is only due to changes in particle electrophoresis, electrophoresis is significantly reduced to values as small as 20%–50% of the Smoluchowski relation, or well below previous model predictions, even for high particle potentials.     

Computer simulation of DNA orientation and deformation in a shear flow field

The structure and orientation of semiflexible chain molecules in a shear flow field were studied by Brownian dynamics simulation. Molecules in the size range 200 nm to 1 μm were modeled as chains of spherical subunits with parameters chosen to mimic the size and persistence length of B-DNA. The analysis of the steady-state orientation showed a rather broad and asymmetric distribution. The simulations also showed that the orientation of the largest main axis of the moment of inertia tensor is significantly higher compared to the orientation obtained from averaging over the individual bonds in the molecules, the latter procedure being the relevant case when comparing with, e.g., linear dichroism experiments.     

Numerical simulation of deformation behavior of droplet in gas under the electric field and flow field coupling

The water droplets in the process of electrostatic coalescence are important when studying electrohydrodynamics. In the present study, the electric field and flow field are coupled through the phase field method based on the Cahn–Hilliard formulation. A numerical simulation model of single droplet deformation under the coupling field was established. It simulated the deformation behavior of the movement of a droplet in the continuous phase and took the impact of droplet deformation into consideration which is affected by two-phase flow velocity, electric field strength, the droplet diameter, and the interfacial tension. The results indicated that under the single action of the flow field, when the flow velocity was lower, the droplet diameter was greater as was the droplet deformation degree. When the flow velocity was increased, the droplet deformation degree of a small-diameter droplet was at its maximum size, the large-diameter droplet had a smaller deformation degree, and the middle-diameter droplet was at a minimum deformation degree. When the flow velocity was further increased, the droplet diameter was smaller, and the droplet deformation degree was greater. Under the coupled effect of the electric field and flow field, the two-phase flow velocity and the electric field strength were greater, and the degree of droplet deformation was greater. While the droplet diameter and interfacial tension were smaller, the degree of droplet deformation was greater. Droplet deformation degree increased along with the two-phase flow velocity. The research results provided a theoretical basis for gas–liquid separation with electrostatic coalescence technology.     

Numerical simulation of droplet coalescence behavior in gas phase under the coupling of electric field and flow field

The coalescence behavior of droplets in an electric field belongs to the important research contents of electrohydrodynamics. Based on the phase field method of the Cahn–Hilliard equation, the electric field and the flow field are coupled to establish the numerical model of twin droplet coalescence in a coupled field. The effects of flow rate, electric field strength, droplet diameter, and interfacial tension on the coalescence behavior of droplets during the coalescence process were investigated. The results show that the dynamic behavior of the droplets is divided into coalescence, after coalescence rupture, and no coalescence under the coupling of electric field and flow field. The proper increase of the electric field strength will accelerate the coalescence of the droplets, and the high electric field strength causes the droplets to burst after coalescence. Excessive flow rates make droplets less prone to coalescence. Under the coupling field, the larger the droplet interface tension, the smaller the droplet diameter, the smaller the flow rate, and the shorter the droplet coalescence time. The results provide a theoretical basis for the application of electrostatic coalescence in gas–liquid separation technology.     

Force acting on the microparticles in electrorheological solids under the application of a nonuniform ac electric field

Under the application of electric fields, the structure of electrorheological (ER) solids can be changed from the body-centered tetragonal lattice to other lattices. We have derived the dipole factor for the lattice by taking into account the local-field effect through the Ewald–Kornfeld formulation, and expressed it in the spectral representation exactly. It is found that when the ER solid is subject to a nonuniform ac electric field, the force acting on the microparticle can be affected by the structure transformation, and local-field effect as well as field frequency. Our results are very well understood in the spectral representation theory.     

Preparation and electrorheological characteristic of Y-doped BaTiO3 suspension under dc electric field

The electrorheological (ER) effects of BaTiO₃ or other perovskite materials with high dielectric constant are presumed to be large. However, their weak ER activity is very puzzling. In this study, we choose cubic BaTiO₃ and first achieve its ER enhancement under dc electric field by modifying its intrinsic structure with doping rare earth Y ions, which are synthesized by means of sol-gel technique. DSC-TG, FT-IR, XRD, ICP and XPS techniques are used to characterize thermal, structure and component change of materials. It is demonstrated that Y³⁺ substitutes for Ba²⁺, which causes lattice-distorting defects. Rheological experiments show that Y-doped BaTiO₃ suspension has notable ER effect and clear fibrillation structure under dc electric field, while the pure cubic BaTiO₃ suspension suffers from electrophoretic effects and its ER effect is very weak. The ER effect of typical Y-doped BaTiO₃ ER suspension is ten times that of pure BaTiO₃ ER suspension. Based on the electrical measurements, the enhancement of ER activity of BaTiO₃ may be attributed to the increase of conductivity due to Y-doping. The enhancement in ER activity of cubic BaTiO₃ under dc electric field by doping rare earth Y ions is helpful to further understand the perovskite-based ER materials with high dielectric constant but low ER activity.     

Numerical simulation of bubble dynamics in a micro-channel under a nonuniform electric field

A numerical method is used to simulate the motion and coalescence of air bubbles in a micro-channel under a nonuniform electric field. The channel is equipped with arrays of electrodes embedded in its wall and voltages are applied on the electrodes to generate a specified electric field gradient in the longitudinal direction. In the study, the Navier-Stokes equations are solved by using the level set method handling the deformable/moving interfaces between the bubbles and the ambient liquid. Both the polarization Coulomb force and the dielectrophoresis force are considered as the force source of the Navier-Stokes equations by solving the Maxwell's equations. The flow field equations and the electric field equations are coupled and solved by using the finite element method. The electric field characteristics and the dynamic behavior of a bubble are analyzed by studying the distributions of the electric field and the force, the deformation and the moving velocity of the air bubble. The result suggests that the model of dispersed drops suspended in the immiscible dielectric liquid and driven by a nonuniform electric field is an effective method for the transportation and coalescence of micro-drops.     

Nematic-isotropic interfaces under shear: a molecular-dynamics simulation

We present a large-scale molecular-dynamics study of nematic-paranematic interfaces under shear. We use a model of soft repulsive ellipsoidal particles with well-known equilibrium properties, and consider interfaces which are oriented normal to the direction of the shear gradient (common stress case). The director at the interface is oriented parallel to the interface (planar). A fixed average shear rate is imposed with moving periodic boundary conditions, and the heat is dissipated with a profile-unbiased thermostat. First, we study the properties of the interface at one particular shear rate in detail. The local interfacial profiles and the capillary wave fluctuations of the interfaces are calculated and compared with those of the corresponding equilibrium interface. Under shear, the interfacial width broadens and the capillary wave amplitudes at large wavelengths increase. The strain is distributed inhomogeneously in the system (shear banding), the local shear rate in the nematic region being distinctly higher than in the paranematic region. Surprisingly, we also observe (symmetry-breaking) flow in the vorticity direction, with opposite direction in the nematic and the paranematic state. Finally, we investigate the stability of the interface for other shear rates and construct a nonequilibrium phase diagram.     

Structure and dynamics of concentration fluctuations in a polymer blend solution under shear flow

The technique of small-angle light scattering (SALS) has been employed to investigate the time-dependent behavior of a single-phase, semidilute solution of polystyrene and polybutadiene in dioctyl phthalate under shear flow. Concentration fluctuations in the polymer blend solution are found to grow with time in the direction of flow, and their orientation angles evolve from 45° from the flow direction toward 0°, with the steady-state value being dependent on shear rate. SALS patterns are simulated using a modified Cahn-Hilliard-Cook model, with an additional collective restoring force to account for polymer elasticity. Predictions from this modified model for the orientation angles of the concentration fluctuations are in excellent agreement with the experimental results. Our model also predicts that the quiescent structure factor has a Gaussian form and that the steady-state orientation of the scattering patterns is dependent on shear rate. These predictions are also in good agreement with our experimental observations. © 1994 John Wiley & Sons, Inc.     

A study of rubber flow in a mold during the tire shaping process using experiment and computer simulation

Automobile tires consist of more than ten layers, including tread, belt, carcass, sidewall, etc. The outermost layer, known as the tread, plays an important role during driving as it comes in direct contact with the road. This tread has grooves with complicated shapes, which are formed by a mold during the shaping process. When the tread rubber does not fill the mold properly, tire quality deteriorates crucially. As such, it is important to observe the flow of the tread rubber during the shaping process. To determine the flow of tread rubber in the mold, we conducted an experiment and computer simulation with white rubber strips inserted into specific areas of the tread. The white rubber strips showed detailed flow behavior of the tread rubber visually in the mold during the shaping process. No significant flows were observed for rubber in the central area of each block of the mold, but more changes were found near the edges of each block. The strips of rubber below the grooves exhibited more significant changes as they were pressed down by the protruding area of the mold. Moreover, there was no flow of rubber between blocks in the mold. This implies the profile design of the extruded tread should match the mold profile and the volume of each block. The experiment and simulation had similar results, and the observations of rubber flow in the mold using simulation proved to be highly useful.     

The behavior of fluids near solutes: a density functional theory and computer simulation study

The density distribution of solvent near a solute particle is studied using density functional theory and Monte Carlo simulation. The fluid atoms interact with each other via a hard sphere plus Yukawa potential, and interact with the solute via a hard sphere potential. For small solute sizes, the solvent displays liquidlike ordering near the particle. When the solute become larger, a drying transition is observed at state points near the coexistence conditions of the solvent. These predictions are similar to those of a recent theory for the hydrophobic effect by Lum, Chandler, and Weeks [J. Phys. Chem. 103, 4570 (1999)], although a comparison with simulations shows that the theory of this work is quantitatively more accurate. The connection between density functional methods and the LCW approach is also established.