Hydromagnetic instability of streaming fluids in porous medium

The instability of the plane interface between two uniform, superposed, electrically conducting and counter-streaming fluids through a porous medium is considered in the presence of a horizontal magnetic field. In the absence of surface tension, perturbations transverse to the direction of streaming are found to be unaffected by the presence of streaming if perturbations in the direction of streaming are ignored. For perturbations in all other directions there exists instability for a certain wavenumber range. The instability of this system is postponed by the presence of magnetic field. The magnetic field and surface tension are able to suppress this Kelvin-Helmholtz instability for small wavelength perturbations and the medium porosity reduces the stability range given in terms of a difference between the streaming velocities and the Alfvén velocity.This research forms a part of the research project awarded to the first author (R.C.S.) by the University Grants Commission.     

Capillary-gravity waves in the presence of infinite porous plates

Summary The wave motion generated by a porous plate immersed in a non-wetting liquid of infinite depth is investigated. The boundary value problem for the velocity potentials is solved using Taylor's assumption on the plate and a contact-line condition that accounts for the dynamic variation of the angle of contact and the vorticity there. The amplitude of the radiated waves and the energy dissipated are calculated both when the plate is oscillating horizontally and vertically with a prescribed velocity. Also the scattering of a harmonic wave incident normally to the plate is considered and the reflexion and transmission coefficients are obtained.     

Three-dimensional electrohydrodynamic temporal instability of a moving dielectric liquid sheet emanated into a gas medium

A linear electrohydrodynamic instability analysis is presented for an inviscid dielectric liquid sheet emanated into an inviscid dielectric gas medium in the presence of a horizontal electric field. The influence of Weber number, gas-to-liquid density ratio, and the applied electric field on the evolution of two-, and three-dimensional disturbances of symmetrical and antisymmetrical types is studied. It is found, for antisymmetrical waves, that two-dimensional disturbances always prevail over three-dimensional disturbances, regardless of Weber number or gas-to-liquid density ratio values, especially for long waves; while for short waves, both two- and three-dimensional disturbances grow at approximately the same rate. It is also found, for symmetrical waves, that two-dimensional disturbances always dominate the instability process at low Weber number, and when the Weber number is large, symmetrical three-dimensional disturbances become more unstable than two-dimensional ones for long waves. The effect of increasing the gas-to-liquid density ratio is to promote the dominance of long three-dimensional symmetrical waves over their two-dimensional counterpart. Finally, the equilibrium Weber number at which the growth rates of two- and three-dimensional modes are equal is discussed for both symmetrical- and antisymmetrical-disturbances cases.-1     

Hydromagnetic transverse instability of two highly viscous fluid-particle flows with finite ion Larmor radius corrections

A linear analysis of the combined effect of viscosity, finite ion Larmor radius and suspended particles on Kelvin-Helmholtz instability of two superposed incompressible fluids in the presence of a uniform magnetic field is carried out. The magnetic field is assumed to be transverse to the direction of streaming. A general dispersion relation for such a configuration has been obtained using appropriate boundary conditions. The stability analysis is discussed analytically, and the obtained results are numerically confirmed. Some special cases are recovered and corrected. The limiting cases of absence of suspended particles (or fluid velocities) and finite Larmor radius, absence of suspended particles are discussed in detail. In both cases, all other physical parameters are found to have stabilizing as well as destabilizing effects on the considered system. In the former case, the kinematic viscosity is found to has a stabilizing effect, while in the later case, the finite Larmor radius is found to has a stabilizing influence for a vortex sheet. It is shown also that both finite Larmor radius and kinematic viscosity stabilizations for interchange perturbations are similar to the stabilization effect due to a magnetic field for non-interchange perturbations. Received 13 January 2003 Published online 24 April 2003 RID="a" ID="a"Also at: Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt. e-mail: m.elsayed@uaeu.ac.ae     

Tracer dispersion in power law fluids flow through porous media: Evidence of a cross-over from a logarithmic to a power law behaviour

An analytical model is presented to describe the dispersion of tracers in a power-law fluid flowing through a statistically homogeneous and isotropic porous medium. The model is an extension of Saffman's approach to the case of non-Newtonian fluids. It is shown that an effective viscosity depending on the pressure gradient and on the characteristics of the fluid, must be introduced to satisfy Darcy's law. An analytical expression of the longitudinal dispersivity is given as a function of the Peclet number Pe and of the power-law index n that characterizes the dependence of the viscosity on the shear rate . As the flow velocity increases the dispersivity obeys an asymptotic power law: . This asymptotic regime is achieved at moderate Peclet numbers with strongly non-Newtonian fluids and on the contrary at very large values when n goes to 1 ( for n=0.9). This reflects the cross-over from a scaling behaviour for towards a logarithmic behaviour predicted for Newtonian fluids (n=1). Received: 22 July 1997 / Revised and Accepted: 2 July 1998     

Stability of cylindrical conducting fluids with heat and mass transfer in longitudinal periodic electric field

A novel system to study the effect of an axial periodic electric field on the stability of a system of cylinders of conducting fluids in the presence of heat and mass transfer is investigated. The stability of a cylindrical interface between the vapor and liquid phases of a fluid is studied when the vapor is hotter than the liquid and the two phases are enclosed between two cylindrical surfaces coaxial with the interface. The linear dispersion relation is found to be of damped Mathieu-type equation with real coefficients. The method of multiple time scales is used to obtain approximate solution and analyze the stability criteria for both the nonresonant and resonant cases. The stability of the system is also discussed analytically and numerically for such cases. It is found that both the heat and mass transfer coefficient and the dimensions of the system have destabilizing influences on the considered system, while azimuthal wavenumber is found to have a stabilizing effect. The dual role of the electric field frequency is also observed on the stability of the system depending on the electrical conductivities values. Finally the behaviour of the resonance points corresponding to the effects of each of the above physical parameters are determined, and a comparison between the obtained results with the corresponding results in the case of a constant applied electric field is achieved.     

The instability of streaming fluids with fine dust in porous medium

The instability of the plane interface between two uniform, superposed, and streaming fluids permeated with suspended particles through porous medium is considered. The effect of a uniform horizontal magnetic field on the problem is also studied. In the absence of surface tension, perturbations transverse to the direction of streaming are found to be unaffected by the presence of streaming if perturbations in the direction of streaming are ignored, whereas for perturbations in all other directions there exists instability for a certain wavenumber range. The instability of the system is postponed by the presence of magnetic field. The magnetic field and surface tension are able to suppress this Kelvin-Helmholtz instability for small wavelength perturbations and the medium porosity reduces the stability range given in terms of a difference in streaming velocities and the Alfvén velocity. The suspended particles do not affect the above results.     

Viscosity effects in foam drainage: Newtonian and non-newtonian foaming fluids

We have studied the drainage of foams made from Newtonian and non-Newtonian solutions of different viscosities. Forced-drainage experiments first show that the behavior of Newtonian solutions and of shear-thinning ones (foaming solutions containing either Carbopol or Xanthan) are identical, provided one considers the actual viscosity corresponding to the shear rate found inside the foam. Second, for these fluids, a drainage regime transition occurs as the bulk viscosity is increased, illustrating a coupling between surface and bulk flow in the channels between bubbles. The properties of this transition appear different from the ones observed in previous works in which the interfacial viscoelasticity was varied. Finally, we show that foams made of solutions containing long flexible PolyEthylene Oxide (PEO) molecules counter-intuitively drain faster than foams made with Newtonian solutions of the same viscosity. Complementary experiments made with fluids having all the same viscosity but different responses to elongational stresses (PEO-based Boger fluids) suggest an important role of the elastic properties of the PEO solutions on the faster drainage.     

Rayleigh-taylor instability of viscoelastic fluids with suspended particles in porous medium in hydromagnetics

The instability of the plane interface between two viscoelastic (Oldroydian) superposed conducting fluids permeated with suspended particles in porous medium is studied when the whole system is immersed in a uniform magnetic field. The dispersion relation for the Oldroydian viscoelastic fluid is obtained which also yields dispersion relations for Maxwellian and Newtonian fluids in special cases, in the presence of suspended particles in porous medium in hydromagnelics. The system is found to be stable for potentially stable case. The presence of magnetic field stabilizes certain wave number band whereas the system was unstable for all wave numbers in the absence of magnetic field, for the potentially unstable configuration. The growth rates increase (for certain wave numbers) and decrease (for other wave numbers) with the increase in stress relaxation time, strain retardation time, suspended particles number density and medium permeability.     

Borehole guided waves in a non-Newtonian (Maxwell) fluid-saturated porous medium

<正>The property of acoustic guided waves generated in a fluid-filled borehole surrounded by a non-Newtonian (Maxwell) fluid-saturated porous formation with a permeable wall is investigated.The influence of non-Newtonian effects on acoustic guided waves such as Stoneley waves,pseudo-Rayleigh waves,flexural waves,and screw waves propagations in a fluid-filled borehole is demonstrated based on the generalized Biot-Tsiklauri model by calculating their velocity dispersion and attenuation coefficients.The corresponding acoustic waveforms illustrate their properties in time domain.The results are also compared with those based on generalized Biot's theory.The results show that the influence of non-Newtonian effect on acoustic guided wave,especially on the attenuation coefficient of guided wave propagation in borehole is noticeable.     

多孔介质中含溶解反应的互溶驱替过程格子Boltzmann研究

采用格子Boltzmann方法研究了孔隙尺度下多孔介质内含流固溶解反应的互溶驱替过程,重点研究了被驱替流体与驱替流体黏性差异较大的情况下,溶解反应引起的多孔介质内部结构变化对驱替过程的影响;定量分析了不同达姆科勒数及佩克莱数下多孔介质孔隙率和驱替过程驱替效率随时间的演变.研究结果表明:达姆科勒数较大时,溶解反应的发生会在多孔介质内部生成虫洞,导致一部分被驱替流体不能被波及,驱替流体沿虫洞离开多孔介质,造成驱替效率的减少.在此基础上,随着达姆科勒数的增大,孔隙率变化越大,生成的虫洞越宽,最终驱替效率变大,但仍小于无溶解反应时的驱替效率;随着佩克莱数的增大,指进增长速度越快,孔隙率变化越小,驱替效率越小.     

含少量气泡流体饱和孔隙介质中的弹性波

考虑孔隙流体中含有少量气泡,且气泡在声波作用下线性振动,研究声波在这种孔隙介质中的传播特性.本文先由流体质量守恒方程和孔隙度微分与流体压力微分的关系推导出了含有气泡形式的渗流连续性方程;在处理渗流连续性方程中的气体体积分数时间导数时,应用Commander气泡线性振动理论导出气体体积分数时间导数与流体压强时间导数的关系,进而得到了修正的Biot形式的渗流连续性方程;最后结合Biot动力学方程求得了含气泡形式的位移场方程,便可得到两类纵波及一类横波的声学特性.通过对快、慢纵波的频散、衰减及两类波引起的流体位移与固体位移关系的考察,发现少量气泡的存在对快纵波和慢纵波的传播特性影响较大.     

Nonlinear Rayleigh–Taylor instability of two superposed magnetic fluids under parallel rotation and a normal magnetic field

The Rayleigh–Taylor instability (RTI) of a ferrofluid has been the subject of recent research, because of its implications on the stability of stellar and planetary interiors. This paper analyzes the effects of rotation and magnetic field on nonlinear RTI of two superposed ferrofluids. It is considered that the system is subjected to uniform parallel rotation and normal magnetic field. Surface tension acts at the interface. The method of multiple scales is utilized to obtain the solutions and dispersion relations are obtained for the nonlinear problem of RTI of magnetic fluids. Finally the stability of the problem is discussed.     

Numerical studies of gravity destabilized percolation in 2D porous media

Two dimensional simulations of percolation are realized on square networks of pore throats with a random capillary pressure distribution. We analyse the influence of a destabilizing gravity field (g) and of the standard deviation of the distribution of the capillary pressure thresholds (W_t). The fragmentation process is not taken into account in this study. For an increase of g or/and when W_t decreases, two transitions are analyzed with three different regimes displacement patterns: Invasion percolation, invasion percolation in a gradient, and invasion in a pure gradient. The transitions are controlled both by the ratio g/W_t and by the sample size (L). A scaling law between the saturation at the percolation threshold and g/W_t allows delineating the three regimes in agreement with theoretical argument of the percolation in a gradient.     

Mixed convection boundary layer flow over a vertical surface embedded in a thermally stratified porous medium

The mixed convection boundary layer flow through a stable stratified porous medium bounded by a vertical surface is investigated. The external velocity and the surface temperature are assumed to vary as xm, where x is measured from the leading edge of the vertical surface and m is a constant. Numerical solutions for the governing Darcy and energy equations are obtained. The results indicate that the thermal stratification significantly affects the surface shear stress as well as the surface heat transfer, besides delays the boundary layer separation.     

MHD flow of nanofluids over an exponentially stretching sheet in a porous medium with convective boundary conditions

This article concentrates on the steady magnetohydrodynamic(MHD) flow of viscous nanofluid. The flow is caused by a permeable exponentially stretching surface. An incompressible fluid fills the porous space. A comparative study is made for the nanoparticles namely Copper(Cu), Silver(Ag), Alumina(Al2O3) and Titanium Oxide(TiO2). Water is treated as a base fluid. Convective type boundary conditions are employed in modeling the heat transfer process. The non-linear partial differential equations governing the flow are reduced to an ordinary differential equation by similarity transformations. The obtained equations are then solved for the development of series solutions. Convergence of the obtained series solutions is explicitly discussed. The effects of different parameters on the velocity and temperature profiles are shown and analyzed through graphs.     

Ageing of random porous media following fluid deterministic displacement, freezing, thawing

This paper introduces and investigates a simple model of random porous media degradation via several fluid displacing, freezing, and thawing cycles. The fluid transport is based on the deterministic method. The result shows that the topology and the geometry of porous media have a strong effect on displacement processes. The cluster size of the viscous fingering (VF) pattern in the percolation cluster increases with the increase of iteration parameter n. When iteration parameter , the VF pattern does not change with n. When and , the peak value of the distribution increases as n increases; is the normalized distribution of throat sizes after different displacement-damage but before the freezing. The distribution of throat size N(r) after displacement but before freezing damage, shows that the major change, after successive cycles, happens at r>0.9. The peak value of the distribution reaches a maximum when and r=1, where is the normalized distribution of the size of invaded throats for different iterations. This result is different from invasion percolation. The distribution of velocities normal to the interface of VF in the percolation cluster is also studied. When , the scaling function distribution is very sharp. The sweep efficiency E increases along with the increasing of iteration parameter n and decreases with the network size L. And E has a minimum as L increases to the maximum size of the lattice. The VF pattern in the percolation cluster has one frozen zone and one active zone. Received 30 March 1999 and Received in final form 8 August 1999     

Effects of rotation and magnetic field on the nonlinear peristaltic flow of a second-order fluid in an asymmetric channel through a porous medium

In this paper, the effects of both rotation and magnetic field of the peristaltic transport of a second-order fluid through a porous medium in a channel are studied analytically and computed numerically. The material is represented by the constitutive equations for a second-order fluid. Closed-form solutions under the consideration of long wavelength and low Reynolds number is presented. The analytical expressions for the pressure gradient, pressure rise, friction force, stream function, shear stress, and velocity are obtained in the physical domain. The effects of the non-dimensional wave amplitude, porosity, magnetic field, rotation, and the dimensionless time-mean flow in the wave frame are analyzed theoretically and computed numerically. Numerical results are given and illustrated graphically in each case considered. Comparison was made with the results obtained in the presence and absence of rotation, magnetic field, and porosity. The results indicate that the effects of the non-dimensional wave amplitude, porosity, magnetic field, rotation, and the dimensionless time-mean flow are very pronounced in the phenomena.     

Numerical study for the electrified instability of viscoelastic cylindrical dielectric fluid film surrounded by a conducting gas

The linear electrohydrodynamic cylindrical instability of annular Walters B^′${\mathrm{B}}^{\prime }$ viscoelastic dielectric fluid layer surrounded by a conducting gas in the presence of radial electric field is investigated. The obtained dispersion relation is found to be complicated and cannot be treated theoretically easily. Two limiting cases of interest are investigated, when the inertia is dominant, and when both the kinematic viscosity and viscoelasticity are high, and the corresponding new stability conditions are obtained for both cases. We solve the eigenvalue problem numerically using the continuation method which gives better results than the classical non-linear solvers such as Newton and Secant methods. It is found that the applied radial electric field has a dual role on the stability of the considered system, depending of the chosen wavenumbers range. Both the kinematic viscoelasticity and liquid depth are found to have stabilizing effects, while both the kinematic viscosity and surface tension have destabilizing effects on the considered system. The stability or instability breaks down for critical wavenumber values at which the growth rate vanishes. The behaviors of both the maximum growth rate and the corresponding dominant wavenumber are discussed in detail corresponding to the effect of all physical parameters. Finally a comparison between the results obtained here for Walters B^′${\mathrm{B}}^{\prime }$ viscoelastic fluids, and those obtained here too if the fluid is replaced by a Rivlin–Ericksen viscoelastic one is achieved. The limiting cases of absence of electric field and/or kinematic viscoelasticity are also investigated in detail.     

模拟静电场实验中导电介质的选择

通过比较3种静电场描绘仪器的实验结果,分析误差产生的原因,指出选择导电介质应注意的问题。