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.     

Thermosolutal convection in a Maxwellian viscoelastic fluid in porous medium

The thermosolutal convection in a layer of Maxwellian viscoelastic fluid heated and soluted from below in porous medium is considered. The effects of uniform magnetic field and uniform rotation on the thermosolutal convection are also considered. For stationary convection, the Maxwellian viscoelastic fluid behaves like a Newtonian fluid. The sufficient conditions for the nonexistence of overstability are obtained. The critical Rayleigh number is found to increase with the increase in magnetic field, rotation and stable solute gradient.     

圆截面直流道中微粒黏弹性聚焦机理研究

微粒黏弹性聚焦技术近年来受到了广泛的研究重视, 但影响粒子聚焦特性的关键参数调控机理仍不清楚. 基于此目的, 本文量化研究了圆截面直流道中非牛顿流体诱导微粒黏弹性聚焦的行为, 给出了流速和流道长度对粒子聚焦特性的调控机理. 具体而言: 首先, 对比分析不同黏度牛顿流体(水和22 wt%甘油水溶液)和非牛顿流体(8 wt%聚乙烯吡咯烷酮水溶液)中粒子横向迁移行为, 发现非牛顿流体中粒子将在弹性力主导下聚焦至流道中心区域, 而牛顿流体中粒子则在惯性升力主导下迁移形成Segré-Silberberg圆环. 其次, 量化分析粒子尺寸和驱动流速对黏弹性聚焦效果的影响, 发现随着流速的增加, 粒子聚焦效果逐渐变好并最终趋于稳定, 且大粒子较小粒子具有更好的聚焦效果. 最后, 研究粒子沿流道长度的动态聚焦过程, 推导并验证了粒子聚焦所需安全流道长度的数学模型, 发现大粒子聚焦所需安全流道长度显著短于小粒子. 上述研究结果对于提升粒子黏弹性聚焦机理和过程的理解, 实现微粒聚焦特性的灵活控制具有非常重要的意义.     

Dynamic rheological properties of viscoelastic magnetic fluids in uniform magnetic fields

The dynamic rheological properties of viscoelastic magnetic fluids in externally applied uniform magnetic fields are investigated by a laboratory-made cone-plate rheometer in this study. In particular, the effects of the magnetic field on the viscoelastic properties (the complex dynamic modulus) of the viscoelastic magnetic fluids are studied. In the investigation, three viscoelastic magnetic fluids are made by mixing a magnetic fluid and a viscoelastic fluid with different mass ratios. As a supplementation to the experimental investigation, a theoretical analysis is also presented. The present study shows that the viscosity and elasticity of the viscoelastic magnetic fluids are significantly influenced by the magnetic field and the concentrations of the magnetic particles in the test fluids. Theoretical analysis qualitatively explains the present findings.     

Correlation of Two Coupled Particles in Viscoelastic Medium

Considering the viscoelastic memory effect, we study the correlated motion of two hydrodynamically coupled colloidal particles, each of which confined in a harmonic potential well, in a Kelvin-type and Maxwell-type viscoelastic medium. We find that viscoelastic relaxation plays a significant role in modifying the correlation, particularly the cross correlation. We also find that both the real and imaginary parts of the response function are significantly different from the viscous medium case. In particular there is a phase shift between the vanishing imaginary part and the maximal real part of the response function in a viscoelastic medium. In addition imaginary part of the cross correlation response function exhibits a net energy loss (gain) behavior when the elasticity parameter of the medium is larger (smaller) than the critical value for Kelvin (Maxwell) viscoelastic fluid. Some implication of our results and their connection with previous works are discussed.     

Correlation of Two Coupled Particles in Viscoelastic Medium

Considering the viscoelastic memory effect, we study the correlated motion of two hydrodynamically coupled colloidal particles, each of which confined in a harmonic potential well, in a Kelvin-type and Maxwell-type viscoelastic medium. We find that viscoelastic relaxation plays a significant role in modifying the correlation, particularly the cross correlation. We also find that both the real and imaginary parts of the response function are significantly different from the viscous medium case. In particular there is a phase shift between the vanishing imaginary part and the maximal real part of the response function in a viscoelastic medium. In addition imaginary part of the cross correlation response function exhibits a net energy loss （gain） behavior when the elasticity parameter of the medium is larger （smaller） than the critical value for Kelvin （Maxwell） viscoelastic fluid. Some implication of our results and their connection with previous works are discussed.     

磁流体粘度的实验研究

采用毛细法粘度计测量了水基Fe磁流体的粘度,分析了磁性粒子份额、表面活性剂含量以及外加磁场强度和方向对粘度的影响。实验结果表明,磁流体粘度随着磁性粒子和表面活性剂浓度的增加而增加;随着外加磁场强度的增大而增大,对于相同的磁流体,在外加磁场方向垂直于流动方向时的粘度大于外加磁场方向平行于流动方向时的粘度;表面活性剂含量的增大将减弱外加磁场对磁流体粘度的影响。     

Stability of stratified fluid in porous medium in the presence of suspended particles and variable magnetic field

General equations governing the stability of stratified fluid in a stratified porous medium in the presence of suspended particles and variable horizontal magnetic field, separately, have been derived. Assuming stratifications in density, viscosity, suspended particles number density, medium porosity, medium permeability and a magnetic field of exponential form the dispersion relations have been obtained. Systems have been found to be stable for stable stratifications and unstable for unstable stratifications. A system which was unstable in the absence of magnetic field can be completely stabilized by a magnetic field for a certain wave-number range. The behaviour of growth rates with respect to fluid viscosity, medium permeability, suspended particles number density and magnetic field has been examined analytically.     

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     

Probing structural relaxation in complex fluids by critical fluctuations

Complex fluids, such as polymer solutions and blends, colloids, and gels, are of growing interest in fundamental and applied soft-condensed-matter science. A common feature of all such systems is the presence of a mesoscopic structural length scale intermediate between the atomic and macroscopic scales. This mesoscopic structure of complex fluids is often fragile and sensitive to external perturbations. Complex fluids are frequently viscoelastic (showing a combination of viscous and elastic behavior), with their dynamic response depending on the time and length scales. Recently, noninvasive methods to infer the rheological response of complex fluids have gained popularity through the technique of microrheology, where the diffusion of probe spheres in a viscoelastic fluid is monitored with the aid of light scattering or microscopy. Here, we propose an alternative to traditional microrheology that does not require doping of probe particles in the fluid (which can sometimes drastically alter the molecular environment). Instead, our proposed method makes use of the phenomenon of “avoided crossing” between modes associated with the structural relaxation and critical fluctuations that are spontaneously generated in the system.     

Bifurcation analysis and amplitude equations for viscoelastic convective fluids

Summary The possible bifurcations of a convective instability in viscoelastic fluid are studied. The viscoelastic behaviour is modelized by means of the Oldroyd type fluid whose parameters can be adjusted to suit a large class of polymeric fluids. We analyse in some detail bifurcations of codimension one (stationary or oscillatory convection) and codimension two for such kind of fluids. By a weak nonlinear analysis, the coefficients of the amplitude equations corresponding to the different bifurcations are also determined. It has been found that the nature of the convective solution depends crucially on both the viscoelastic parameters and the constitutive equation used to describe the fluid.     

Short-time inertial response of viscoelastic fluids: observation of vortex propagation

We probe the response of viscous and viscoelastic fluids on micrometer and microsecond length and time scales using two optically trapped beads. In this way we resolve the flow field, which exhibits clear effects of fluid inertia. Specifically, we resolve the short-time vortex flow and the corresponding evolution of this vortex, which propagates diffusively for simple liquids. For viscoelastic fluids, this propagation is shown to be faster than diffusive and the displacement correlations reflect the frequency-dependent shear modulus of the medium.     

EHD kelvin-helmholtz instability in viscous porous medium permeated with suspended particles

The electrohydrodynamic Kelvin-Helmholtz instability of the plane interface between two uniform, superposed viscous and streaming dielectric fluids permeated with suspended particles through porous medium is considered under the influence of a tangential electric field. In the absence of surface tension, it is found that perturbations transverse to the direction of streaming are unaffected by the presence of both streaming and the tangential electric field, if perturbations in the direction of streaming are ignored. For perturbations in all other directions there exists instability for a certain wavenumber range. In the presence of surface tension, it is found that the instability of this system is suppressed by the presence of the tangential electric field. Both the tangential electric field and the surface tension have stabilizing effects and they are able to suppress Kelvin-Helmholtz instability for small wavelength perturbations. The medium porosity reduces the stability range given in terms of a difference in streaming velocities and the electric field effect, while the suspended particles do not affect the above results.     

Cell-level canonical sampling by velocity scaling for multiparticle collision dynamics simulations

A local Maxwellian thermostat for the multiparticle collision dynamics algorithm is proposed. The algorithm is based on a scaling of the relative velocities of the fluid particles within a collision cell. The scaling factor is determined from the distribution of the kinetic energy within such a cell. Thereby the algorithm ensures that the distribution of the relative velocities is given by the Maxwell–Boltzmann distribution. The algorithm is particularly useful for non-equilibrium systems, where temperature has to be controlled locally. We perform various non-equilibrium simulations for fluids in shear and pressure-driven flow, which confirm the validity of the proposed simulation scheme. In addition, we determine the dynamic structure factors for fluids with and without thermostat, which exhibit significant differences due to suppression of the diffusive part of the energy transport of the isothermal system.     

Acoustic radiation from a fluid-filled, subsurface vascular tube with internal turbulent flow due to a constriction

The vibration of a thin-walled cylindrical, compliant viscoelastic tube with internal turbulent flow due to an axisymmetric constriction is studied theoretically and experimentally. Vibration of the tube is considered with internal fluid coupling only, and with coupling to internal-flowing fluid and external stagnant fluid or external tissue-like viscoelastic material. The theoretical analysis includes the adaptation of a model for turbulence in the internal fluid and its vibratory excitation of and interaction with the tube wall and surrounding viscoelastic medium. Analytical predictions are compared with experimental measurements conducted on a flow model system using laser Doppler vibrometry to measure tube vibration and the vibration of the surrounding viscoelastic medium. Fluid pressure within the tube was measured with miniature hydrophones. Discrepancies between theory and experiment, as well as the coupled nature of the fluid-structure interaction, are described. This study is relevant to and may lead to further insight into the patency and mechanisms of vascular failure, as well as diagnostic techniques utilizing noninvasive acoustic measurements.     

Theory of Brownian motion in a Jeffreys fluid

We have constructed a kinetic theory of Brownian motion in a rheologically complex medium—a Jeffreys fluid that is characterized by a combination of two viscosity mechanisms: ordinary and delayed. This model is shown to be much better suited for the interpretation of experiments on the microrheology of viscoelastic media than the standard Maxwell model. In particular, no oscillations of the mean-square particle displacement arise in a Jeffreys fluid, which is a nonremovable artifact of the theory of Brownian motion in a Maxwell fluid. The developed approach can to be used also consider the diffusion of particles in other complex fluids whose rheology is described by phenomenological schemes.     

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.     

Non-Steady Wall-Bounded Flows of Viscoelastic Fluids Under Periodic Forcing

The problem of oscillating flows inside pipes under periodic forcing of viscoelastic fluids is addressed here. Starting from the linear Oldroyd-B model, a generalized Darcy’s law is obtained in the frequency domain and an explicit expression for the dependence of the dynamic permeability on the fluid parameters and forcing frequency is derived. Previous results in both viscoelastic and Newtonian fluids are here shown to be particular cases of our results. On the basis of our calculations, a possible explanation for the observed damping of local dynamic response as the forcing frequency increases is given. Good fitting with recent experimental studies of wave propagation in viscoelastic media is here exhibited. Sound wave propagation in viscoelastic media flowing inside straight pipes is investigated. In particular, we obtain the local dynamic response for weakly compressible flows.     

Degeneration of flow pattern in acousto-elastic flow through sharp-edge microchannels

Acoustic streaming (AS) is the steady time-averaged flow generated by acoustic field, which has been widely used in enhancing mixing and particle manipulation. Current researches on acoustic streaming mainly focus on Newtonian fluids, while many biological and chemical solutions exhibit non-Newtonian properties. The acoustic streaming in viscoelastic fluids has been studied experimentally for the first time in this paper. We found that the addition of polyethylene oxide (PEO) polymer to the Newtonian fluid significantly altered the flow characteristics in the microchannel. The resulting acousto-elastic flow showed two modes: positive mode and negative mode. Specifically, the viscoelastic fluids under acousto-elastic flow exhibit mixing hysteresis features at low flow rates, and degeneration of flow pattern at high flow rates. Through quantitative analysis, the degeneration of flow pattern is further summarized as time fluctuation and spatial disturbance range reduction. The positive mode in acousto-elastic flow can be used for the mixing enhancement of viscoelastic fluids in the micromixer, while the negative mode provides a potential method for particle/cell manipulation in viscoelastic body fluids such as saliva by suppressing unstable flow.     

Recent advances in the simulation of particle-laden flows

A substantial number of algorithms exists for the simulation of moving particles suspended in fluids. However, finding the best method to address a particular physical problem is often highly non-trivial and depends on the properties of the particles and the involved fluid(s) together. In this report, we provide a short overview on a number of existing simulation methods and provide two state of the art examples in more detail. In both cases, the particles are described using a Discrete Element Method (DEM). The DEM solver is usually coupled to a fluid-solver, which can be classified as grid-based or mesh-free (one example for each is given). Fluid solvers feature different resolutions relative to the particle size and separation. First, a multicomponent lattice Boltzmann algorithm (mesh-based and with rather fine resolution) is presented to study the behavior of particle stabilized fluid interfaces and second, a Smoothed Particle Hydrodynamics implementation (mesh-free, meso-scale resolution, similar to the particle size) is introduced to highlight a new player in the field, which is expected to be particularly suited for flows including free surfaces.