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     

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.     

Electrorheology of dilute suspensions induced by hydrodynamic instability

The viscosity behavior in electric fields was measured for dilute suspensions of p-[perfluoro(2-isopropyl-1,3-dimethyl-1-butenyl)oxy]benzoic acid particles (PFNA) in silicone oils. The application of electric fields causes a viscosity increase in a wide range of shear rates. Since the electrorheological (ER) effect is much stronger at low shear rates, the flow becomes shear-thinning. However, contrary to conventional ER suspensions which are reversibly converted between Newtonian fluids and Bingham solids, the PFNA suspensions are fluids even in electric fields. When the particle concentration is increased to 5 wt.%, the ER effect reaches saturation. Further increase does not contribute to additional viscosity enhancement. These results cannot be explained through the chain formation mechanism established for conventional systems. After the ER experiments, the bob surface of the rheometer is covered with several stripes of aggregated particles. Although the strength of electric and shear fields is constant in the rheometer, the periodic structure may be formed in the flow of electrified suspensions. When a dielectric liquid is subjected to high electric fields, the secondary motion of liquid can be induced by the Coulomb force acting on free charge. The electrohydrodynamic (EHD) convection is responsible for the periodic distribution of particles concentration. The ER effect of PFNA suspensions may be generated by a combined effect of EHD convection and external shear.     

The effect of volume relaxation on elastohydrodynamic lubrication

In elastohydrodynamic lubrication (EHD) three important non-Newtonian effects arise. These are volume viscoelasticity, shear viscoelasticity, and the variation of viscosity with shear rate. All these effects tend to decrease the shear stress or traction.In this paper the effect of volume relaxation of EHD is examined using experimental viscosity data obtained in a simple viscometric flow. It is shown that the viscosity of a fluid during EHD is unlikely to reach its equilibrium value. Approximations to the viscosity as a function of time lead to the conclusion that volume and shear viscoelasticity have effects which are of the same order of magnitude and will be difficult to separate except by an exact knowledge of the shear rate and pressure profiles.     

Electrorheologial properties of hematite/silicone oil suspensions under DC fields

Electrorheological (ER) fluids composed of α-Fe₂O₃ (hematite) particles suspended in silicone oil are studied in this work. The rheological response has been characterized as a function of field strength, shear rate and volume fraction. Rheological tests under DC electric fields elucidated the influence of the electric field strength, E, and volume fraction, ϕ, on the field-dependent yield stress, τ_y. It was found that this quantity scales with E and ϕ with a linear and parabolic dependence, respectively. The viscosities of electrified suspensions were found to increase by several orders of magnitude as compared to the unelectrified suspension at low shear rates, although at high-shear rates hydrodynamic effects become dominant and no effects of the electric field on the viscosity are observed. The work is completed with the analysis of microscopic observations of the structure acquired by the ER fluid upon application of a constant electric field. Electrohydrodynamic convection is found to be the origin of the ER response rather than the commonly admitted particle fibrillation. This fact can provide an explanation to the relationship between yield stress and electric field strength as well as the pattern of periodic structures observed in the measurement geometries.     

电场作用下气泡上升行为特性的数值计算研究

利用电场控制气泡形态及运动,强化气液相间传热传质是电流体动力学的重要研究内容之一. 然而目前多数研究集中在非电场下的气泡动力学上,对于电场下的气泡行为特性及电场的作用机制仍需开展深入研究. 本研究对电场作用下单个气泡在流体中上升过程的动力学行为进行了数值模拟研究. 在建立二维模型的基础上求解电场方程与Navier-Stokes方程,并采用水平集方法捕捉了上升气泡的位置及形状. 模拟结果的准确性与有效性通过与前人实验和数值结果进行对比得到了验证. 通过改变雷诺数、邦德数和电邦德数等不同参数研究了电场下液体黏度、表面张力和电场力对气泡运动变形的影响. 计算结果表明,电场对气泡的动态特性有显著影响. 非电场情况下液体黏度和表面张力较大时气泡基本维持球状,反之气泡发生变形并逐步达到稳定状态. 此外,电场作用使气泡在初始上升阶段发生剧烈形变,随着不断上升,气泡形变程度不断减小,且气泡的上升速度和长径比均出现振荡. 垂直电场使气泡的上升速度有较大的提高,且随着电邦德数的增大,难以达到相对稳定的状态.      

The influence of fluid properties on electrohydrodynamic heat transfer enhancement in liquids under viscous and electrically dominated flow conditions

Fluid property effects on electrohydrodynamic (EHD) heat transfer enhancement were investigated. Heat transfer, pressure drop, electrical power requirements, and the transition between the viscous dominated and electrically dominated flow regimes as a function of fluid properties were examined using three cooling oils having widely varying physical properties. Low viscosity and low electrical conductivity gave the greatest heat transfer enhancement for a given electrical power input. The required electrical power to achieve a specified heat transfer enhancement was greater for working fluids that had a small charge relaxation time, defined as the ratio of the electrical permittivity to the electrical conductivity. These results correlate well with available experimental and analytical data. A theoretical prediction of the effect of fluid properties and forced flow rate on the onset of EHD enhancement was experimentally verified. The onset of significant EHD heat transfer enhancement occurs most readily in low viscosity liquids at low Reynolds number flows for a given electrical power input.     

Numerical modelling of electrovortex and heat flows in dc electric arc furnace with cooling bottom electrode

The article is devoted to the numerical modelling of electrovortex and convection flows in DC electric arc furnace with the cooling bottom electrode. The shear stress on the fettle area are offered as criteria for the estimation of vortex flows influence on the increased wearing of fettle. It is shown that cooling down the bottom electrode to the melting metal temperature leads to decrease of shear stress on the fettle area by 15 %.     

Cellular structure in a natural convection loop and its chaotic behaviour: II. Theory

A theoretical study of thermal convection in a vertically oriented thin toroidal loop which is placed in a uniform negative vertical temperature gradient is reported. The Boussinesq approximation is employed, and the first-order perturbed fields from a steady conduction state are obtained in the form of a double Fourier series. The critical Rayleigh number for the onset of convection is determined and various types of steady convective patterns, including cellular structure, are examined. Four typical modes are superposed to express the time-dependent velocity and temperature fields, whose mode-amplitudes constitute an extended version of the Lorenz model. Numerical simulation shows a sequence of transitions from steady to periodic, quasi-periodic, and chaotic states as the Rayleigh number is increased. The present model successfully explains our experimental results.     

Numerical study on a vertical plate with variable viscosity and thermal conductivity

Free convection over an isothermal vertical plate immersed in a fluid with variable viscosity and thermal conductivity is studied in this paper. We consider the two-dimensional, laminar and unsteady boundary layer equations. Using the appropriate variables, the basic governing equations are transformed to non-dimensional governing equations. These equations are then solved numerically using a very efficient implicit finite difference scheme known as Crank–Nicolson scheme. The fluid considered in this study is of viscous incompressible fluid of temperature dependent viscosity and thermal conductivity. The effect of varying viscosity and thermal conductivity on velocity, temperature, shear stress and heat transfer rate are discussed. The velocity and temperature profiles are compared with previously published works and are found to be in good agreement.     

The electrohydrodynamics of superimposed fluids subjected to a nonuniform transverse electric field

This study aims to investigate electrohydrodynamics of two superimposed fluids that are confined between a pair of two-dimensional flat plates and are exposed to a sinusoidal electric field in zero gravity. The goal is to identify the parameters that affect the flow structure and interface deformation using a simple closed form solution. The governing electrohydrodynamic equations are solved analytically for Newtonian and immiscible fluids in the framework of leaky-dielectric theory and in the limit of small electric field and fluid inertia. A detailed analysis of the electric and flow fields is presented and it is shown that the electric field induces sinusoidal electrical stresses at the interface, which lead to periodic convection cells. The parameters affecting the sense of flow circulation and strength are investigated and it is shown that the former depends on the relative magnitude of the electric permittivity and conductivity ratios while the latter is controlled by the relative thicknesses of the fluid layers and the ratio of the electric conductivities and viscosities of the fluids. The maximum flow strength is achieved at a relative thickness that is set by the competition between the electric and hydrodynamic effects. For small deformation, the distortion of the interface is examined using a normal stress balance at the interface, and it is shown that the degree of interface deformation scales with the square of the amplitude of the electric potential nonuniformity, while its wavenumber is twice that of the imposed potential nonuniformity. Furthermore, a zero-deformation curve is found, which delineates the region in the permittivity-conductivity space according to the sense of interface deformation. The results show that for certain ranges of fluid layer thicknesses and permittivity ratios, the interface will remain flat, despite the action of the nonuiform field.     

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.     

Weakly nonlinear EHD stability of slightly viscous jet

A weakly nonlinear approach is utilized here to study the electrohydrodynamic (EHD) instability of an incompressible viscous liquid jet stressed by an axial electric field. The linear motion equations is solved in the light of nonlinear boundary conditions. The viscosity is assumed to be small. The study takes into account both the shear and radial components of the stresses at the interface. In the linear theory, we discuss the breakup phenomena of liquid jets. Also, it is found that, the electrical shearing stresses have no effect at the linear marginal state, while the linear cutoff wavenumber depends on the electrical shearing stresses. A nonlinear perturbation method is introduced. This method can be described our problem precisely. The nonlinear stability is compared with the linear stability condition in the weak viscosity case. It is found that, the weak viscosity has effect on the nonlinear stability condition, in contrast with the linear analysis, whereas the nonlinear cutoff wavenumber doesn't depend on the weak viscosity in both the linear and nonlinear theory.     

The onset of convection in a nanofluid saturated porous layer using Darcy model with cross diffusion

Linear and nonlinear stability analysis for the onset of convection in a horizontal layer of a porous medium saturated by a nanofluid is studied. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The modified Darcy equation that includes the time derivative term is used to model the momentum equation. In conjunction with the Brownian motion, the nanoparticle fraction becomes stratified, hence the viscosity and the conductivity are stratified. The nanofluid is assumed to be diluted and this enables the porous medium to be treated as a weakly heterogeneous medium with variation, in the vertical direction, of conductivity and viscosity. The critical Rayleigh number, wave number for stationary and oscillatory mode and frequency of oscillations are obtained analytically using linear theory and the non-linear analysis is made with minimal representation of the truncated Fourier series analysis involving only two terms. The effect of various parameters on the stationary and oscillatory convection is shown pictorially. We also study the effect of time on transient Nusselt number and Sherwood number which is found to be oscillatory when time is small. However, when time becomes very large both the transient Nusselt value and Sherwood value approaches to their steady state values.     

Time-dependent plane Poiseuille flow of a Johnson–Segalman fluid

We numerically solve the time-dependent planar Poiseuille flow of a Johnson–Segalman fluid with added Newtonian viscosity. We consider the case where the shear stress/shear rate curve exhibits a maximum and a minimum at steady state. Beyond a critical volumetric flow rate, there exist infinite piecewise smooth solutions, in addition to the standard smooth one for the velocity. The corresponding stress components are characterized by jump discontinuities, the number of which may be more than one. Beyond a second critical volumetric flow rate, no smooth solutions exist. In agreement with linear stability analysis, the numerical calculations show that the steady-state solutions are unstable only if a part of the velocity profile corresponds to the negative-slope regime of the standard steady-state shear stress/shear rate curve. The time-dependent solutions are always bounded and converge to different stable steady states, depending on the initial perturbation. The asymptotic steady-state velocity solution obtained in start-up flow is smooth for volumetric flow rates less than the second critical value and piecewise smooth with only one kink otherwise. No selection mechanism was observed either for the final shear stress at the wall or for the location of the kink. No periodic solutions have been found for values of the dimensionless solvent viscosity as low as 0.01.     

One-dimensional steady magnetogasdynamic flow in oblique fields and the structure of shock waves

Summary An exact solution in closed form, in terms of elliptic functions, is obtained for the one-dimensional steady flow of a polytropic gas with finite constant electrical conductivity which is influenced by an oblique magnetic field and a transverse electric field in the absence of viscosity, thermal conductivity and all other non-electrical dissipative mechanisms. The solution is presented in terms of elementary functions and the many possible flow patterns are discussed in detail in the case when, at some position, the transverse momentum equals the transverse Maxwell stress; a case which is appropriate to the structure of switch-on and switch-off shock waves.The research reported in this paper was supported in part by the United States Air Force under Grant No. AF-EOAR-65-58 and monitored by the European Office, Office of Aerospace Research.     

Direct modeling of flow of FENE fluids

Direct simulations of macromolecular fluids are carried out for flows between parallel plates and in expanding and contracting channels. The macromolecules are modeled as FENE dumbbells with soft disks or Lennard-Jones dumbbell-dumbbell interactions. The results are presented in terms of profiles and contour plots of velocity, pressure, temperature, density, and flow fields. In addition the data for potential energy, shear stress, and the normal components of the stress tensor are collected. In general, an excellent agreement is found between the simulated profiles and the well-known flow structures, such as flow separation and formation of viscous eddies, indicating that micro-hydrodynamics is a viable tool in linking macroscopic phenomena with the underlying physical mechanisms. The simulations are performed in the Newtonian regime, for medium-size systems comprising up to 3888 dumbbells. This number is sufficiently large to control boundary and particle number effects. The flow is induced by gravity. The traditional stochastic (thermal) and periodic boundary conditions are employed. Also, diffusive boundary conditions, which could include a stagnant fluid layer and repulsive potential walls, are developed. The scaling problems, which are related to the application of a large external force in a microscopic system (of the size of the order 100 Å), result in extreme pressure and temperature gradients. In addition, the viscosity and thermal conductivity coefficients obtained from velocity and temperature profiles of the channel flow are presented. These results are confirmed independently from modeling of Couette flow by the SLLOD equations of motion and from the Evans algorithm for thermal conductivity.     

Flow of couple stress fluid with variable thermal conductivity

The steady flow and heat transfer of a couple stress fluid due to an inclined stretching cylinder are analyzed. The thermal conductivity is assumed to be temperature dependent. The governing equations for the flow and heat transfer are transformed into ordinary differential equations. Series solutions of the resulting problem are computed. The effects of various interested parameters, e.g., the couple stress parameter, the angle of inclination, the mixed convection parameter, the Prandtl number, the Reynolds number, the radiation parameter, and the variable thermal conductivity parameter, are illustrated. The skin friction coefficient and the local Nusselt number are computed and analyzed. It is observed that the heat transfer rate at the surface increases while the velocity and the shear stress decrease when the couple stress parameter and the Reynolds number increase. The temperature increases when the Reynolds number increases.     

Steady MHD Couette flow with temperature-dependent physical properties

The influence of variation in physical variables on the steady magnetohydrodynamic (MHD) Couette flow with heat transfer is studied. An external uniform magnetic field is applied perpendicular to the parallel plates and the fluid is acted upon by a constant pressure gradient. The viscosity and the thermal as well as electric conductivities are assumed to be temperature dependent. The two plates are kept at two constant but different temperatures, and the viscous and Joule dissipations are considered in the energy equation. A numerical solution for the governing nonlinear coupled equations of motion and the energy equation is obtained. The effect of the temperature-dependent viscosity, thermal conductivity, and electrical conductivity on both the velocity and temperature distributions is examined. H.A. Attia - On leave from: Dept. of Eng. Mathematics and physics, El-Fayoum University, El-Fayoum, Egypt     

Forced and mixed convection boundary layer flow along a flat plate with variable viscosity and variable Prandtl number: new results

The steady laminar boundary layer flow along a flat plate is studied taking into account the variation of fluid viscosity and fluid Prandtl number with temperature. In the forced convection case the plate moves with constant velocity and its temperature varies in power law with x. In the mixed convection case the plate temperature is constant and the fluid moves upwards due to an external free stream and due to buoyancy forces. The results are obtained with the direct numerical solution of the boundary layer equations. The study concerns the wall heat transfer, the wall shear stress and velocity and temperature profiles across the boundary layer. The results of the present work are different from those existing in the literature, which have been obtained with the assumption of constant Pr number.