The effect of normal electric field on the evolution of immiscible Rayleigh-Taylor instability

Manipulation of the Rayleigh-Taylor instability using an external electric field has been the subject of many studies. However, most of these studies are focused on early stages of the evolution. In this work, the long-term evolution of the instability is investigated, focusing on the forces acting on the interface between the two fluids. To this end, numerical simulations are carried out at various electric permittivity and conductivity ratios as well as electric field intensities using Smoothed Particle Hydrodynamics method. The electric field is applied in parallel to gravity to maintain unstable evolution. The results show that increasing top-to-bottom permittivity ratio increases the rising velocity of the bubble while hindering the spike descent. The opposite trend is observed for increasing top-to-bottom conductivity ratio. These effects are amplified at larger electric field intensities, resulting in narrower structures as the response to the excitation is non-uniform along the interface.     

激波管实验研究非均匀流场R-M不稳定性

利用激波管装置及马赫数为1.27的弱入射激波实验研究了SF6非均匀流场的R-M不稳定性。Air/SF6初始正弦界面由厚度为0.5μm的薄膜相隔得到,由阴影方法记录界面演化过程。实验结果表明:由于不稳定性,重流体(SF6)向轻流体(Air)演化成"尖钉"结构,而轻流体演化为"气泡"结构;由于界面切向速度差的Kelvin-Helmholtz不稳定性,"尖钉"头部翻转成蘑菇头形状;由于流场密度分布不均,低密度区流场扰动增长较快,扰动振幅发展的实验结果与PPM数值计算的结果较吻合。     

3D phase field modeling of electrohydrodynamic multiphase flows

A 3D phase field model is developed to investigate the electrohydrodynamic (EHD) two phase flows. The explicit finite difference method, enhanced by parallel computing, is employed to solve the coupled nonlinear governing equations for the electric field, the fluid flow field and free surface deformation. Numerical tests indicate that an appropriate interpolation of densities within the interface is critical in ensuring numerical stability for highly stratified flows. The 3D phase field model compares well with the Taylor theory for the deformation of a single dielectric droplet in an electric field. Computed results show that the deformation of a leaky dielectric droplet in an electric field undergoes various stages before it reaches the final oblate shape. This is caused by the free charge relaxation near the fluid–fluid interface. The coalescence of four droplets in an electric field illustrates a truly 3D deformation behavior and a complex evolving fluid flow field associated with the participating droplets. The coalescence is a result of combined actions produced by the global electric force, the circulatory flows generated by the local electrohydrodynamic stress and the electrically-induced deformation. The 3D phase field model is also applied in modeling of an electrohydrodynamic patterning process for manufacturing nanoscaled structures, in which complex 3D flow structures develop as the electrically-induced deformation evolves.     

The EHD-driven fluid flow and deformation of a liquid jet by a transverse electric field

The aim of this study is to investigate the effect of a uniform transverse electric field on the steady-state behavior of a liquid cylinder surrounded by another liquid of infinite extent. The governing electrohydrodynamic equations are solved 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 electrical and hydrodynamic stresses acting on the interface separating the two fluids is presented, and an expression is found for the interface deformation for small distortions from a circular shape. The electrical stresses acting on the interface of two leaky-dielectric liquids are compared with those acting on an interface separating a perfect dielectric or infinitely conducting core fluid cylinder from a surrounding perfect dielectric fluid. A comparison is made between the results of this study and those of a similar study for fluids with permeable interfaces and the classical results for liquid drops.     

Features of deformation of poroelastic media with low structural strength

Many natural and technological processes are associated with deformation and fracture of saturated or being saturated poroelastic media. Among such processes one can mention fluid soaking through a dam, fluid inflow to the cracks of hydraulic fracture, polishing using porous materials and special fluids, flow in catalytic pellets. All these processes are accompanied by deformation and fracture of a matrix with fluid flow. The effects at the interface porous body–fluid are essential for the processes.The specific features of deformation of poroelastic media with low structural strength are considered in this paper. The compressibility of the matrix skeleton is larger as compared to the compressibility of the saturating fluid in such media.It is shown that the oozing of the fluid at the surface of the poroelastic medium occurs in the consolidated flow regime under the action of `fluid piston' like loads if the structural strength of the medium is low. This result is obtained for both plane (deformation of a layer or halfinfinite medium) and centrally symmetric (deformation of a sphere) problems.     

Effect of streamwise and spanwise electric fields on transient growth in a two-fluid channel flow

A linear model of a two-fluid channel flow under streamwise/spanwise electric field is built. Both the fluids are assumed to be incompressible, viscous and perfectly dielectric. The effect of the streamwise and spanwise electric fields on transient behavior of small three-dimensional disturbances is studied. The numerical result shows that the streamwise electric field suppresses transient growth of the disturbance with spanwise uniform wave number. The spanwise electric field diminishes transient growth of the disturbance with streamwise uniform wave number. Two peaks of optimal growth are detected in the wave number plane. The peak at relatively large spanwise wave number is dominated by the lift-up mechanism and little influenced by electric field. Differently, the peak at relatively small wave number is associated with the characteristic of the interface and possibly influenced by electric field. The effect of the Weber number, the Reynolds number and the relative electrical permittivity on optimal growth is studied as well. A scaling law is obtained for relatively small Weber numbers and relatively large Reynolds numbers.     

Modulation instability of electrohydrodynamic waves on liquid jet

An analytical study of slow modulation has been made of cylindrical interface between two inviscid streaming fluids, in the presence of a relaxation of electrical charges at the interface, and stressed by an axial electric field. A new technique based on the perturbation theory, to derive the non-linear evolution equations has been introduced. These equations are combined to yield a non-linear Ginzburg–Landau equation and a non-linear modified Schrödinger equation describing the evolution of wave packets. The linear analysis showed that the streaming has a destabilizing effect and the electric field has stabilizing influence associated with parameters condition involving the electric conductivity and permittivity of the fluids. While the non-linear approach indicated that the streaming may become unstable for sufficiently high velocities, with a new condition on the material properties, involving weak electric relaxation times in both fluids.     

二层流体中波动问题的Hamilton正则方程

研究了两种常密度不可压缩理想流体组成的垂直分层的二流体系统的无旋等熵流动,考虑了上层流体与空气及两层流体间的表面张力。流动区域在水平方向无限伸展,上层流体有限深度,下层流体无限深。利用自由面及分界面相对于静止时平衡位置的偏移以及两层流体的速度势构造了Hamilton函数。为导出Hamilton正则方程引用了Euler描述下的流体运动的变分原理。自由面的位移是Hamilton意义下的正则变量,其对偶变量是上层流体在自由面上取值的速度势与密度的乘积。另一个正则变量是分界面的位移,其对偶变量是下层流体的密度与下层流体速度势在分界面上所取值的乘积减去上层流体密度与上层流体速度势在分界面上所取值的相应乘积。导出的Hamilton结构对分析分层流动中表面波与内波的相互作用是重要的。     

Jet pinch-off and drop formation in immiscible liquid–liquid systems

The behavior of glycerin–water jets flowing into immiscible ambients of Dow Corning 200 fluid was investigated using laser induced fluorescence (LIF). Undistorted images were obtained by matching the index of refraction of the fluids. A sinusoidal perturbation was superposed on the flow to phase lock the drop formation. The forcing frequency dramatically affected the size, spacing, and number of drops that formed within a forcing cycle and the angle between drops and the jet interface just before pinch-off. Two fluid combinations were studied with similar density ratios, but viscosity ratios differing by a factor of 20. The viscosity ratio affected the jet stability as well as pinch-off angles and drop size. Received: 28 January 1999/Accepted: 20 January 2000     

MHD Couette two-fluid flow and heat transfer in presence of uniform inclined magnetic field

The MHD Couette flow of two immiscible fluids in a parallel plate channel in the presence of an applied electric and inclined magnetic field is investigated in the paper. One of the fluids is assumed to be electrically conducting, while the other fluid and the channel plates are assumed to be electrically insulating. Separate solutions with appropriate boundary conditions for each fluid are obtained and these solutions are matched at the interface using suitable matching conditions. The partial differential equations governing the flow and heat transfer are transformed to ordinary differential equations and closed-form solutions are obtained in both fluid regions of the channel. The results for various values of the Hartmann number, the angle of magnetic field inclination, the loading parameter and the ratio of the heights of the fluids are presented graphically to show their effect on the flow and heat transfer characteristics.     

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.     

Simulation of forming processes by FEM with a Bingham fluid model

We model the forming process as a fluid flow. A finite element program, FIDAP, which analyses flow problems, was used to calculate velocity and strain rates at points throughout the material during the deformation process. This allows predictions to be made on the shape and quality of the resulting part. The stress-strain relation we used models the plastic flow of metals (Bingham fluids). The FEM approximation of such a fluid is tested by comparing results for a simple analytical example. In forming processes provision must be made for friction between dye and workpiece, and the program was modified accordingly. Two classical ring forming simulations are compared to published results.     

Some properties of multi-fluid stokes flows

The solution of Stokes' equations for a rotating axisymmetric body which possesses reflection symmetry about a planar interface between two infinite immiscible quiescent viscous fluids is shown to be independent of the viscosities of the fluids and identical with the solution when the fluids have the same viscosity. The result is generalized to a rotating axisymmetric system of bodies which possesses reflection symmetry about each interface of a plane stratified system of fluids. An analogous result for two-fluid systems with a nonplanar static interface is also derived. The effect on torque reduction produced by the presence of a second fluid layer adjacent to a rotating axisymmetric body is considered and explicit calculations are given for the case of a sphere. A proof of uniqueness for unbounded multi-fluid Stokes' flow is given and the asymptotic far field structure of the velocity field is determined for axisymmetric flow caused by the rotation of axisymmetric bodies.     

A finite strain model of stress, diffusion, plastic flow, and electrochemical reactions in a lithium-ion half-cell

We formulate the continuum field equations and constitutive equations that govern deformation, stress, and electric current flow in a Li-ion half-cell. The model considers mass transport through the system, deformation and stress in the anode and cathode, electrostatic fields, as well as the electrochemical reactions at the electrode/electrolyte interfaces. It extends existing analyses by accounting for the effects of finite strains and plastic flow in the electrodes, and by exploring in detail the role of stress in the electrochemical reactions at the electrode-electrolyte interfaces. In particular, we find that that stress directly influences the rest potential at the interface, so that a term involving stress must be added to the Nernst equation if the stress in the solid is significant. The model is used to predict the variation of stress and electric potential in a model 1-D half-cell, consisting of a thin film of Si on a rigid substrate, a fluid electrolyte layer, and a solid Li cathode. The predicted cycles of stress and potential are shown to be in good agreement with experimental observations.     

An SPH multi‐fluid model based on quasi buoyancy for interface stabilization up to high density ratios and realistic wave speed ratios

We introduce a smoothed particle hydrodynamics (SPH) concept for the stabilization of the interface between 2 fluids. It is demonstrated that the change in the pressure gradient across the interface leads to a force imbalance. This force imbalance is attributed to the particle approximation implicit to SPH. To stabilize the interface, a pressure gradient correction is proposed. In this approach, the multi‐fluid pressure gradients are related to the (gravitational and fluid) accelerations. This leads to a quasi‐buoyancy correction for hydrostatic (stratified) flows, which is extended to nonhydrostatic flows. The result is a simple density correction that involves no parameters or coefficients. This correction is included as an extra term in the SPH momentum equation. The new concept for the stabilization of the interface is explored in 5 case studies and compared with other multi‐fluid models. The first case is the stagnant flow in a tank: The interface remains stable up to density ratios of 1:1000 (typical for water and air), in combination with artificial wave speed ratios up to 1:4. The second and third cases are the Rayleigh‐Taylor instability and the rising bubble, where a reasonable agreement between SPH and level‐set models is achieved. The fourth case is an air flow across a water surface up to density ratios of 1:100, artificial wave speed ratios of 1:4, and high air velocities. The fifth case is about the propagation of internal gravity waves up to density ratios of 1:100 and artificial wave speed ratios of 1:4. It is demonstrated that the quasi‐buoyancy model may be used to stabilize the interface between 2 fluids up to high density ratios, with real (low) viscosities and more realistic wave speed ratios than achieved by other weakly compressible SPH multi‐fluid models. Real wave speed ratios can be achieved as long as the fluid velocities are not very high. Although the wave speeds may be artificial in many cases, correct and realistic wave speed ratios are essential in the modelling of heat transfer between 2 fluids (eg, in engineering applications such as gas turbines).     

Electric fields in the rheology of disperse systems

In the present survey, the influence of electric fields on the structure and rheological properties of disperse systems as well as the effect of deformations on their electrical characteristics are discussed. The properties of these systems are considered in terms of the dielectric permittivity and electrification potential. The considerable thickness of the double electric layer around the disperse phase particles, which is characteristic of disperse systems with nonpolar hydrocarbon dispersion media, provides the possibility for strong electric fields to produce an electric nonuniformity on the surface of the disperse phase particles. The formation of hydrate layers on the particles creates the possibility of polarization of the disperse phase. In plastic disperse systems such as greases, a strong orientation effect is observed, which contributes to the creation of frozen flow patterns when the flow is suddenly stopped. The survey is concluded with a consideration of the process of formation of chain structures in the direction of the lines of force of the electric field whose orientation is normal to the direction of flow, which can lead to complete stoppage of the flow.     

Hydromagnetic flow near an accelerated plate in the presence of a magnetic field

Summary Hydromagnetic flow of a viscous incompressible fluid due to uniformly accelerated motion of an infinite flat plate in the presence of a magnetic field fixed relative to the plate, is discussed. It is assumed that the induced magnetic field is negligible compared to the imposed magnetic field. It is observed under these conditions that the velocity at any point and at any instant decreases when the strength of the magnetic field is increased.     

Two-layer flow of magnetic fluids

The plane two-layer flow of viscous incompressible fluids with differentmagnetic properties between two horizontal rigid planes in a nonuniform traveling magnetic field is investigated. An arbitrary nonuniform periodic traveling magnetic field generates wavelike changes in the interface between the media and fluid flows with nonzero flow rates. From the given magnetic field the interface shape and the velocities, pressures and mean flow rates of the fluids are calculated. The cases of a cosine magnetic force and of the magnetic field created by ferromagnetic cylinders moving in a uniform magnetic field are considered. The effect of various parameters on the mean flow rates of the fluids is investigated.     

Dynamic behaviour of a bubble near an elastic infinite interface

This paper presents a study to describe the behaviour of a non-equilibrium bubble in a fluid (Fluid 1) that is in contact with another fluid (Fluid 2). Fluid 2 is assumed to incorporate some elastic properties, which are modelled through a pressure term at the fluid–fluid interface. The Laplace equation is assumed to be valid in both fluids and the boundary integral method is employed to simulate the dynamics of the bubble and the fluid–fluid interface. Interesting characteristic phenomena concerning bubble oscillations and the deformation of the fluid–fluid interface are studied for a range of parameters (distance from the fluid–fluid interface, density ratios of the two fluids and elastic properties of Fluid 2). Some of the phenomena observed are jet formation in the bubble, bubble splitting, a ring bubble separating from the main bubble, mushroom-shaped bubbles and the dynamic elevation of the elastic interface. Most of these phenomena are only observed when Fluid 2 possesses some elastic properties (besides the usual formation of a high speed liquid jet). Comparisons with experimental observations confirm the validity of our simulations.     

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.