Static yield stress of ferrofluid-based magnetorheological fluids

In this work, the yield stress of ferrofluid-based magnetorheological fluids (F-MRF) was investigated. The fluids are composed of a ferrofluid as the liquid carrier and micro-sized iron particles as magnetic particles. The physical and magnetorheological properties of the F-MRF have been investigated and compared with a commercial mineral oil-based MR fluid. With the addition of a ferrofluid, the anti-sedimentation property of the commercial MR fluids could be significantly improved. The static yield stress of the F-MRF samples with four different weight fractions (ϕ) of micro-sized iron particles were measured using three different testing modes under various magnetic fields. The effects of weight fraction, magnetic strength, and test mode on the yielding stress have been systematically studied. Finally, a scaling relation, , was proposed for the yield stress modeling of the F-MRF system.     

Rheometry on magnetorheological (MR) fluids

Test fixtures of a commercial concentric cylinder rheometer (Physica Rheolab MC 20) were modified to enable measurements under magnetic inductions up to 0.5 Tesla in a shear rate range of 0.1 up to 1000 s ^–1 and temperatures 0° to 150°C. In the 2 x90°-cups only two 90° sectors of the stationary part of the double concentric cylinder arrangement are submitted to the magnetic field which is created outside the test tools by an electromagnet. A prototype of a 360°-cup contains the electromagnet within the cup and avoids the correction necessary for the sector geometry. Measurements are shown for a carbonyl iron MR fluid and two nano MR fluids. An encouraging comparison of the viscosity function and MR effect (shear stress changes due to the field) measured by using the various cups is presented. The detailed investigation of the magnetic field distribution in the tools yields a distinct radial field gradient and also stray fields that make the quantification of the effective field in the gap difficult. The change of the field when the gap is filled with MR fluid is addressed. MR effects up to 13 000 Pa have been found, the limited torque range of the rheometer making it necessary to use relatively small gap dimensions which introduce errors due to edge effects. Shear rates up to 40000 s^–1 as typical for the application in dampers were investigated by a piston-driven capillary rheometer making use of a thermostated rectangular slit with superimposed magnetic field. A satisfactory agreement of the magnetorheological data with the concentric cylinder results is found in the overlapping shear rate range.     

Stagnation-point flow of upper-convected Maxwell fluids

Two-dimensional stagnation-point flow of viscoelastic fluids is studied theoretically assuming that the fluid obeys the upper-convected Maxwell (UCM) model. Boundary-layer theory is used to simplify the equations of motion which are further reduced to a single non-linear third-order ODE using the concept of stream function coupled with the technique of the similarity solution. The equation so obtained was solved using Chebyshev pseudo-spectral collocation-point method. Based on the results obtained in the present work, it is concluded that the well-established but controversial prediction that in stagnation-point flows of viscoelastic fluids the velocity inside the boundary layer may exceed that outside the layer may just be an artifact of the rheological model used in previous studies (namely, the second-grade model). No such peculiarity is predicted to exist for the Maxwell model. For a UCM fluid, a thickening of the boundary layer and a drop in wall skin friction coefficient is predicted to occur the higher the elasticity number. These predictions are in direct contradiction with those reported in the literature for a second-grade fluid.     

A three-dimensional non-linear constitutive law for magnetorheological fluids, with applications

In this paper we first summarize the magnetic and mechanical balance equations for magnetorheological fluids undergoing steady motion in the presence of a magnetic field. A general three-dimensional non-linear constitutive law for such a fluid is given for the case in which the magnetic induction vector is used as the independent magnetic variable. The equations are needed for the analysis of boundary-value problems involving fluids with dispersed micron-sized ferrous particles subjected to a time-independent magnetic field. For illustration, the equations are applied, in the case of an incompressible fluid, to the solution of some basic problems. We consider unidirectional flow in a region confined by two infinite parallel plates with a magnetic field applied perpendicular to the plates. Next, we examine two problems involving a circular cylindrical geometry with the fluid occupying the region between two concentric cylinders: axial flow subjected to an axial magnetic field and circumferential flow with a circumferential field. After making some simplifying assumptions on the constitutive law and choosing material parameters, numerical solutions for the velocity profiles are illustrated.     

Steady mixed convection stagnation-point flow of upper convected Maxwell fluids with magnetic field

The steady MHD mixed convection flow of a viscoelastic fluid in the vicinity of two-dimensional stagnation point with magnetic field has been investigated under the assumption that the fluid obeys the upper-convected Maxwell (UCM) model. Boundary layer theory is used to simplify the equations of motion, induced magnetic field and energy which results in three coupled non-linear ordinary differential equations which are well-posed. These equations have been solved by using finite difference method. The results indicate the reduction in the surface velocity gradient, surface heat transfer and displacement thickness with the increase in the elasticity number. These trends are opposite to those reported in the literature for a second-grade fluid. The surface velocity gradient and heat transfer are enhanced by the magnetic and buoyancy parameters. The surface heat transfer increases with the Prandtl number, but the surface velocity gradient decreases.     

Nonisothermal two‐ and three‐dimensional flow simulations of inelastic and viscoelastic fluids by a finite‐volume method

This paper applies the finite‐volume method to computations of steady flows of viscous and viscoelastic incompressible fluids in complex two and three‐dimensional geometries. The materials adopted in the study obey different constitutive laws: Newtonian, purely viscous Carreau–Yasuda as also Upper‐Convected Maxwell and Phan‐Thien/Tanner differential models, with a Williams–Landel–Ferry (WLF) equation for temperature dependence. Specific analyses are made depending on the rheological model. A staggered grid is used for discretizing the equations and unknowns. Stockage possibilities allow us to solve problems involving a great number of degrees of freedom, up to 1 500 000 unknowns with a desk computer. In relation to the fluid properties, our numerical simulations provide flow characteristics for various 2D and 3D configurations and demonstrate the possibilities of the code to solve problems involving complex nonlinear constitutive equations with thermal effects. Copyright © 2009 John Wiley & Sons, Ltd.     

Preparation and characterization of carbonyl iron/strontium hexaferrite magnetorheological fluids

The heat transfer oil-based magnetorheological fluid (MRF) was prepared using oleic acid-modified micron carbonyl iron powder as a magnetic dispersed phase and strontium hexaferrite (SrFe₁₂O₁₉) nanoparticles as an additive. The sedimentation stability of MRFs was studied. The results indicated that the stability of MRFs was improved remarkably by adding SrFe₁₂O₁₉ nanoparticles and the sedimentation ratio was only 0.88 in 20 days when the content of nanoparticles reached 10 wt%. The rheological properties were characterized by a HAAKE rheometer without a magnetic field and a capillary rheometer with and without a magnetic field. The effects of SrFe₁₂O₁₉ nanoparticles, the temperature, and magnetic field strength were investigated. In addition, the rheological properties could be predicted well using the improved Herschel–Bulkley model, even under a magnetic field. A theoretical model was also proposed to predict the yield stress based on the microstructure of the MRF under an applied magnetic field.     

Viscoelastic properties of magnetorheological fluids

We have studied the rheological properties of some magnetorheological fluids (MRF). MRF are known to exhibit original rheological properties when an external magnetic field is applied, useful in many applications such as clutches, damping devices, pumps, antiseismic protections, etc. While exploiting parameters such as magnetic field intensity, particle concentration and the viscosity of the suspending fluid, we highlighted the importance of each one of these parameters on rheology in the presence of a magnetic field. We made this study by conducting rheological experiments in dynamic mode at very low strain which facilitates the comprehension of the influence of the structure on MRF rheology. Our results confirmed the link between the magnetic forces which ensure the cohesion of the particles in aggregates, and the elastic modulus. Moreover, we found that the loss modulus varies with the frequency in a similar manner than the elastic modulus. The system, even with the smallest deformations, was thus not purely elastic but dissipates also much energy. Moreover, we demonstrated that this dissipation of energy was not due to the matrix viscosity. Actually, we attributed viscous losses to particle movements within aggregates.     

Linear gravity waves on Maxwell fluids of finite depth

Linear surface gravity waves on Maxwell viscoelastic fluids with finite depth are studied in this paper. A dispersion equation describing the spatial decay of the gravity wave in finite depth is derived. A dimensionless memory (time) number 0 is introduced. The dispersion equation for the pure viscous fluid will be a specific case of the dispersion equation for the viscoelastic fluid as θ=0. The complex dispersion equation is numerically solved to investigate the dispersion relation. The influences of θ and water depth on the dispersion characteristics and wave decay are discussed. It is found that the role of elasticity for the Maxwell fluid is to make the surface gravity wave on the Maxwell fluid behave more like the surface gravity wave on the inviscid fluid.     

UNIFIED COMPUTATION OF FLOW WITH COMPRESSIBLE AND INCOMPRESSIBLE FLUID BASED ON ROE＇S SCHEME

A unified numerical scheme for the solutions of the compressible and incompressible Navier-Stokes equations is investigated based on a time-derivative preconditioning algorithm. The primitive variables are pressure, velocities and temperature. The time integration scheme is used in conjunction with a finite volume discretization. The preconditioning is coupled with a high order implicit upwind scheme based on the definition of a Roe＇s type matrix. Computational capabilities are demonstrated through computations of high Mach number, middle Mach number, very low Mach number, and incompressible flow. It has also been demonstrated that the discontinuous surface in flow field can be captured for the implementation Roe＇s scheme.     

UNIFIED COMPUTATION OF FLOW WITH COMPRESSIBLE AND INCOMPRESSIBLE FLUID BASED ON ROE''''S SCHEME

A unified numerical scheme for the solutions of the compressible and incompressible Navier-Stokes equations is investigated based on a time-derivative preconditioning algorithm. The primitive variables are pressure, velocities and temperature. The time integration scheme is used in conjunction with a finite volume discretization. The preconditioning is coupled with a high order implicit upwind scheme based on the definition of a Roe's type matrix. Computational capabilities are demonstrated through computations of high Mach number, middle Mach number, very low Mach number, and incompressible flow. It has also been demonstrated that the discontinuous surface in flow field can be captured for the implementation Roe's scheme.     

Conservation laws and constitutive relations for density-gradient-dependent viscous fluids

Conservation laws and constitutive relations for a density-gradient-dependent viscous fluid as a multipolar continuum obeying an entropy inequality with generalized entropy flux and supply density are considered in this paper. A decomposition of the rate of work of dipolar stress, which reveals the contribution of various parts of this stress to the energy equation, is used to discuss the inconsistencies between the results obtained here and those obtained by Bluestein and Green [1] on the basis of the pioneering work of Green and Rivlin [8]. Furthermore, we discuss the connection between the model presented here and the materials of Korteweg type considered by Dunn and Serrin [6]. In particular, we relate the rate of work of dipolar stress and the interstitial working introduced by Dunn and Serrin [6].Received: 3 April 2004, Accepted: 6 December 2004, Published online: 4 March 2005 Correspondence to: M.M. Mehrabadi     

Boundary layer flow of Maxwell fluid due to torsional motion of cylinder: modeling and simulation

This paper investigates the boundary layer flow of the Maxwell fluid around a stretchable horizontal rotating cylinder under the influence of a transverse magnetic field. The constitutive flow equations for the current physical problem are modeled and analyzed for the first time in the literature. The torsional motion of the cylinder is considered with the constant azimuthal velocity E. The partial differential equations (PDEs) governing the torsional motion of the Maxwell fluid together with energy transport are simplified with the boundary layer concept. The current analysis is valid only for a certain range of the positive Reynolds numbers. However, for very large Reynolds numbers, the flow becomes turbulent. Thus, the governing similarity equations are simplified through suitable transformations for the analysis of the large Reynolds numbers. The numerical simulations for the flow, heat, and mass transport phenomena are carried out in view of the bvp4c scheme in MATLAB. The outcomes reveal that the velocity decays exponentially faster and reduces for higher values of the Reynolds numbers and the flow penetrates shallower into the free stream fluid. It is also noted that the phenomenon of stress relaxation, described by the Deborah number, causes to decline the flow fields and enhance the thermal and solutal energy transport during the fluid motion. The penetration depth decreases for the transport of heat and mass in the fluid with the higher Reynolds numbers. An excellent validation of the numerical results is assured through tabular data with the existing literature.     

基于Maxwell-Rivlin-Ericksen理论的MRM本构关系的算法探究

从Maxwell电磁场理论出发,得到磁流变材料的电磁学本构方程,基于Rivlin-Ericksen理论,结合质量守恒定律及动量守恒定理,提出了普适的磁流变材料Cauchy应力σ的一种本构关系.与牛顿粘性流体及热力学第二定律相结合确定了算法中磁流变材料本构关系的基本参数.以平行板间磁流变材料运动为算例,计算结果验证了本模型切实有效.最后与美国Lord公司配置的典型磁流变材料MRM-132LD结果进行比较,结论吻合良好,希望该工作能有力推动磁流变材料的迅猛发展.     

Constitutive Equations in Continuum Mechanics

One of the main research areas in continuum mechanics is constitutive equations. There is no generally accepted viewpoint on or method for this research. Several concepts have appeared, but further studies are still necessary. The paper elucidates some problems and viewpoints of such research     

Flow on oscillating rectangular duct for Maxwell fluid

This paper presents an analysis for the unsteady flow of an incompressible Maxwell fluid in an oscillating rectangular cross section.By using the Fourier and Laplace transforms as mathematical tools,the solutions are presented as a sum of the steady-state and transient solutions.For large time,when the transients disappear,the solution is represented by the steady-state solution.The solutions for the Newtonian fluids appear as limiting cases of the solutions obtained here.In the absence of the frequency of oscillations,we obtain the problem for the flow of the Maxwell fluid in a duct of a rectangular cross-section moving parallel to its length.Finally,the required time to reach the steady-state for sine oscillations of the rectangular duct is obtained by graphical illustrations for different parameters.Moreover,the graphs are sketched for the velocity.     

Preparation of well-dispersed magnetorheological fluids and effect of dispersion on their magnetorheological properties

In this work, we describe methods for the preparation of suspensions of micron-sized iron particles grafted with different surfactants. The aim is to obtain well-dispersed magnetorheological (MR) fluids. The effectiveness of the surfactants as dispersants was analyzed quantitatively by means of rheological measurements. With this objective, the viscosity of the suspensions was measured, and the results were compared with the prediction of the Batchelor’s formula (Batchelor, J Fluid Mech 83:97–117, 1977). The effect of dispersion on the MR properties of the suspensions was also studied. It was found that the quality of the dispersion of a suspension does not have an important effect on the magnitude of the field-induced yield stress but does on the change of viscosity induced by the field. It was also found that the transition from the solid-like state to the liquid-like one happens very smoothly for well-dispersed suspensions, contrarily to the abrupt transition for poorly dispersed suspensions.     

Three-dimensional motion of a viscous incompressible fluid in a narrow tube

An approximate solution of the problem of unsteady motion of a viscous incompressible fluid in a long narrow deformable tube at low Reynolds numbers is obtained. Pressure oscillations and tube deformation are shown to be related by an integrodifferential equation. The solution obtained extends the Poiseuille solution in elliptic tubes to the case of comparatively arbitrary small deformations in terms of the tube length and angle. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 28–32, July–August, 2009.     

Some Considerations on Modeling Heat and Mass Transfer in Porous Media

In this paper some considerations are presented about the equations needed to set up a model of the process of heat and mass transfer in porous media. A clear classification is made of the various types of equations used and of their physical meaning. Special attention is paid to the thermodynamic equilibrium equations and to their derivation since they are too often taken for granted. The importance of the various transport mechanisms (of mass and energy) is analyzed and the consequences that can arise when some term is neglected are indicated.