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.     

Electrorheology of dielectric liquids

Dielectric liquids that show striking electrorheological (ER) effects are formulated by controlling the conductivity. Although the viscosity is increased on the application of a d.c. field, the flow of electrified fluids is Newtonian in the plain electrodes with smooth surfaces. When the liquids are sandwiched between the electrodes with flocked fabrics, the viscosity behavior is converted from Newtonian to shear-thinning flow. In electric fields, the convective flow is induced over the system due to the electrohydrodynamic(EHD) effect. The interactions between EHD convection and external shear give rise to the additional energy dissipation and in turn the increase in viscosity. The ER effects of simple liquids are very attractive in application to new fluid devices.     

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     

Effect of additives and measurement procedure on the electrorheology of hematite/silicone oil suspensions

The effects of measuring procedures and activating additives on the electrorheological (ER) behaviour of hematite/silicone oil suspensions are analysed. The structures built up in the presence of an electric field without shear are stronger than those produced with both electric and shear fields simultaneously applied. Such differences are measurable when the field strength is not high enough to dominate over hydrodynamic interactions. Regarding the effect of additives, the ER response is enhanced by water until a certain maximum amount, beyond which the effect decreases. The increase in water concentration also leads to higher values of the electric current. Similar results are observed when Brij 30 is used. However, this surfactant only raises the yield stress at low fields. Contrary to water, the surfactant forms droplets in solution, instead of adsorbing on the hematite surface. At sufficiently high field strengths, the droplets can coalesce, enclosing the hematite particles and thus reducing the overall ER effect.     

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.     

Dynamic responses of electrorheological fluid in steady pressure flow

The dynamic responses of the electrorheological fluid in steady pressure flow to stepwise electric fields are investigated experimentally. First of all, the transient responses of the ER fluid under various electric field strengths and flow velocities are obtained from the pressure behaviors in the flow channel with two parallel-plate electrodes. The response times are exponentially decreased with the increase of the flow velocity and the decrease of the electric field strength. Next, the relationship between the dynamic pressure behaviors of the ER fluid and the cluster structure formation processes of the ER particles is investigated using the flow visualization technique. Through the comparison study, it is verified that the dynamic responses of the ER fluid in the flow mode are mainly caused by the cluster densification process in the competition of the electric field-induced particle attraction and the hydrodynamic force, unlike those in the shear mode determined by the particle aggregation process.     

Dependence of the instantaneous response of impedance probes on the local distribution of the void fraction in a pipe

ln a vertical pipe of circular cross-section the instantaneous response of an impedance probe which has its electrodes mounted flush in the tube wall to avoid disturbing the two-phase flow, depends on the void-fraction distribution. Different probe geometries (different widths and numbers of electrodes) and different a.c. supplies were studied to minimize the influence of this parameter. With single-phase a.c. supply the electrodes of intermediate width yield the best results. An increase from two to four electrodes, does not entail any improvement, whatever the kind of electrode connection. With a six-phase a.c. supply, such that a rotating electric field is obtained within six electrodes, the results are better than those obtained with two electrodes of intermediate width supplied with single-phase current.     

Peculiar features in the rheological behavior of electrorheological suspensions

Studies have been made of concentrated (up to 60%) diatomite suspensions in transformer oil, the structure and theological properties of which depend on an applied electric field. Studies have been conducted of steady-state and transient regimes of straining involving continuous and periodic shear. The structure in such suspensions is formed in the presence of an electric field of 10^–3 –10² duration. The suspensions under continuous stationary strain behave as non-Newtonian fluids with a yield stress dependent on electric intensity. Under periodic deformation conditions the test suspensions exhibit elasticity which abruptly diminishes with increasing deformation amplitude.     

An experimental study of electrorheological fluid flow through a packed bed of glass beads

This paper shows that pressure drop-flow rate performance of an electrorheological (ER) fluid flowing through a packed bed of glass beads is consistent with a modified Ergun equation for yield stress flow through a packed bed. ER fluids are of scientific and engineering interest due to the sensitivity of their rheological properties on the applied electric field. As far as we know ER fluids have not been studied for flows through porous media. In this work a silica particle–silicone oil suspension is pumped through a rectangular packed bed of glass beads with applied electric fields. The silica particles are observed to form fibrous structures parallel to the electric field that stretch between the beads and extend between the electrodes. The pressure drop-flow rate performance agrees well with the expected performance calculated from a modified Ergun equation for a yield stress fluid flow through the packed bed with the viscosity and yield stress as functions of the applied electric field.     

A device to regulate rotational speed using a rotating regulator with electrorheological fluid

The authors propose a device consisting of a rotating regulator within an electrorheological fluid (ERF), in which the rotational speed of the rotating body can be regulated by supplying an electric field. This new type of device with ERF is relevant to engineering applications and can play a role in braking as well as in rotation regulation. The ERF used here consists of a colloidal suspension of smectite particles in a solvent. The experimental conditions are fixed in a range of comparatively small rotational speed. The authors clarified the hydrodynamic and electrical effects of the shape of the rotating disk, the kind of solvent contained in the ERF, the temperature, the electrode gap and the electric field strength on the steady characteristics of the torque, the electric current density and the electric power to a rotational speed. From the torque and rotational speed data, empirical equations were derived using nondimensional parameters for the purpose of convenient engineering design. The authors also clarified the correlation between the hydrodynamic and steady electric characteristics of the device and the transient characteristics of torque, the electric current and the rotational speed.     

Maximum size of bubbles during nucleate boiling in an electric field

By taking account of the electric field effects on the shape of bubbles. Fritz's analysis on maximum bubble volume during boiling was extended to the boiling process in the presence of a uniform electric field. It was found that the maximum bubble volume decreases with increase in electric field strength and the dielectric constant of the boiling liquid. The decrease of bubble departure size with increase in electric field strength was confirmed by experimental observations.     

Plasma flow accompanied by blowing and pumping of plasma across electrodes

The article discusses plane stationary slowly varying flows of a nonviscous plasma with good conductivity in a channel in a transverse magnetic field; the flows are accompanied by blowing in and pumping plasma across solid metallic electrodes. The Hall effect is taken into consideration. It is shown that the potential jump near the anode, which appears in an accelerated plasma flow in an ordinary channel with solid electrodes, can be eliminated in flows accompanied by blowing in (pumping) of plasma. It is also shown that flows are possible in which the velocity, density, and the transverse electric field increase in the direction of the accelerator cathode.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 26–34, November–December, 1970.     

Viscoelasticity of a dielectric fluid in nonuniform electric fields generated by electrodes with flocked fabrics

The rheological behavior of a dielectric fluid is studied in nonuniform electric fields which are generated by an electrode covered with flocked fabrics. Although no electrorheological (ER) effects are observed in uniform fields between metal electrodes with smooth surfaces, striking increases in viscosity and elastic response are induced by the electrode with flocked fabrics. The presence of flocked fabrics does not have a significant effect on the fluid rheology without electric fields. The ER behavior and current density are influenced by the fiber length even at a constant field strength. When a very small amount of fine particles is introduced in the electrified fluid without shear, we can see the rapid and large-scale motion of particles between the tips of fibers and plate electrode. In high DC fields, the Coulomb force acting on a free charge often gives rise to the secondary motion of fluid. The local motion of fluid in high electric fields is refereed to as electrohydrodynamic (EHD) convection. The additional energy may be required to change the periodic patterns of EHD convection by forced shear. Therefore, the ER effect demonstrated by the modification of electrode with flocked fabrics can be attributed to a combined effect of EHD convection and external shear. Received: 10 March 1998 Accepted: 1 June 1998     

Electrorheological properties of PDMS/carbon black suspensions under shear flow

Suspensions of polydimethylsiloxane (PDMS) containing low amounts (1 wt.% or less) of a highly conducting carbon black (CB) filler are rendered conductive and exhibit electrorheological (ER) responses under shear flow when exposed to an externally applied AC electric field. The presence of columnar structures, consisting of CB particles aligned in the direction of the electric field is evidenced through optical microscopy experiments. The appearance of yielding behavior and positive ER response, manifested by an increase in the viscosity of the suspensions, depend strongly on the filler loading, strength of the electric field, magnitude of the shear field, and viscosity of the medium. The responses are stronger at low filler loadings, below the percolation threshold, and at very low shear rates, where the microstructure of the dispersed phase remains intact. At higher shear rates, corresponding to Mason numbers (Mn) above 1, the structure is disrupted and thus does not contribute to the observed shear stress. The rheological characterization is accompanied with admittance measurements, to demonstrate that the induced polarization forces between particles lead to the formation of electrically conductive structures within the polymer matrix. A critical comparison with the qualitative predictions based on the theory of induced dipole–dipole interactions shows that the theory is valid for these dilute systems.     

电流变阻尼器动力特性的研究

电流变液是一种可控流体，它在电场的作用下可从牛顿流体变为屈服剪应力较高的粘塑性体，且这种变化连续，可逆，迅速。本文在简要介绍了电流变阻尼器的原理和特点后，就电流变阻尼器的动力特性，如流量和阻尼力等，建立模型，将流体流动分为剪切流动和压差流动两种情况进行了讨论，并进行迭加，使流量和阻尼计算公式得到修正和完善，最后对阻尼力进行简化，提出压差流动占绝对优势，完全可以反映电流变阻尼器的阻尼特性，为进一步实现对阻尼器的控制提供了理论基础。     

NUMERICAL STUDY OF THE BEHAVIOR OF A BUBBLE ATTACHED TO A TIP IN A NONUNIFORM ELECTRIC FIELD

In order to investigate the effects of a nonuniform electric field on the behavior of a bubble, a numerical study on the shape of a bubble attached to a conducting tip on a supporting wall is performed. The equilibrium bubble shape is determined by solving the free boundary problem that consists of the governing equation for electric field and the normal stress condition at the bubble surface. A numerically generated composite orthogonal coordinate system is employed to solve the free boundary problem. A bubble on a tip is found to be extended in the direction parallel to the applied electric field. The elongation increases steeply with an increase of the electric field strength and the height of the tip. It is also observed that a highly elongated bubble has a shape with slender waist. The bubble shape obtained from numerical studies are qualitatively similar to the shapes observed in experiments. If the contact radius is maintained during bubble deformation, the contact angle and the aspect ratio increase with the increase of the electric field strength and the tip height. On the other hand, if the contact angle is fixed during bubble deformation, the contact radius decreases as the electric field strength increases. In order to estimate the effect of electric field on the bubble departure volume, the surface tension force and the downward electric force exerted on a bubble are also computed for a bubble of fixed volume under the fixed contact angle condition. The sum of the two forces is found to decrease with increasing strength of nonuniform electric field. This fact suggests that the bubble departure volume decreases in a nonuniform electric field.     

A dielectrophoretic study of the carbon nanotube chaining process and its dependence on the local electric fields

The chaining process of a system of interacting carbon nanotubes (CNTs) under an alternating current electric field is investigated at two regions of different electric field characteristics. For the region of uniform electric field (far from the electrodes), a two-dimensional multiparticle approach based on the dielectrophoretic (DEP) theory and classical mechanics is proposed to investigate the CNT rotational and translation motion. For this scenario, CNT rotation and alignment along the electric field direction occurs first, followed by the translation and chaining processes which were found to be highly dependent on the CNT-to-CNT initial configuration. On the other hand, the presence of high electric field gradients governs the CNT chaining at regions near the electrodes. DEP forces caused by such gradients were computed by finite element analysis and compared to the magnitude of the CNT-to-CNT interacting forces at zones of uniform electric fields. A critical distance of CNT-to-CNT separation was estimated, which determines if a CNT is attracted towards the electrode or if it is attracted by other CNTs away from the electrodes. Experimental evidence of CNTs dynamic motion under electric fields is presented to support the predicted trends.     

Manipulation of particles using dielectrophoresis

A numerical scheme based on the distributed Lagrange multiplier method (DLM) is used to study the motion of particles of electrorheological suspensions subjected to non-uniform electric fields. At small Reynolds number, the time taken by the particles to collect at the minimums or maximums of the electric field is primarily determined by a parameter defined to be the ratio of the dielectrophoretic and viscous forces. Simulations show that in non-uniform electric fields the collection time is also influenced by a parameter defined by the ratio of the electrostatic particle–particle interaction and dielectrophoretic forces. The collection time decreases as this parameter decreases because when this parameter is less than one, particles move to the regions of high or low electric field regions individually. However, when this parameter is greater than one, particles regroup into chains which then move toward the electric field maximums or minimums without breaking. It is also shown that when the real part of the Clausius–Mosotti factor (β) is negative the positions of the local minimums of the electric field, and thus also the locations where particles collect, can be modified by changing the electric potential boundary conditions.     

A new Finite Element Method for magneto-dynamical problems: two-dimensional results

A mixed Lagrange finite element technique is used to solve the Maxwell equations in the magneto-hydrodynamic (MHD) limit in an hybrid domain composed of vacuum and conducting regions. The originality of the approach is that no artificial boundary condition is enforced at the interface between the conducting and the insulating regions and the non-conducting medium is not approximated by a weakly conducting medium as is frequently done in the literature. As a first evaluation of the performance of the method, we study two-dimensional (2D) configurations, where the flow streamlines of the conducting fluid are planar, i.e., invariant in one direction, and either the magnetic field (“magnetic scalar” case) or the electric field (“electric scalar” case) is parallel to the invariant direction. Induction heating, eddy current generation, and magnetic field stretching are investigated showing the usefulness of finite element methods to solve magneto-dynamical problems with complex insulating boundaries.     

Heating of a medium as a result of Joule energy dissipation

It is well known that when a magnetic field is present and electric currents flow through a gas, terms over and above those present in the case of ordinary thermal conductivity appear in the heat flux density vector. If the gas is dense enough and the magnetic field not over large, then the anisotropy caused by the magnetic field may be neglected. However, for a sufficiently large electric current a term proportional to the temperature and to the current density vector remains in the heat flux density vector. This effect explains, for example, the asymmetry of heat fluxes in the electrodes of a continuously operated electromagnetic accelerator (1).We shall consider this situation in relation to the example of a fully ionized quasineutral gas with identical electron and ion temperatures.