Magnetorheology in an aging, yield stress matrix fluid

Field-induced static and dynamic yield stresses are explored for magnetorheological (MR) suspensions in an aging, yield stress matrix fluid composed of an aqueous dispersion of Laponite? clay. Using a custom-built magnetorheometry fixture, the MR response is studied for magnetic field strengths up to 1?T and magnetic particle concentrations up to 30?v%. The yield stress of the matrix fluid, which serves to inhibit sedimentation of dispersed carbonyl iron magnetic microparticles, is found to have a negligible effect on the field-induced static yield stress for sufficient applied fields, and good agreement is observed between field-induced static and dynamic yield stresses for all but the lowest field strengths and particle concentrations. These results, which generally imply a dominance of inter-particle dipolar interactions over the matrix fluid yield stress, are analyzed by considering a dimensionless magnetic yield parameter that quantifies the balance of stresses on particles. By characterizing the applied magnetic field in terms of the average particle magnetization, a rheological master curve is generated for the field-induced static yield stress that indicates a concentration–magnetization superposition. The results presented herein will provide guidance to formulators of MR fluids and designers of MR devices who require a field-induced static yield stress and a dispersion that is essentially indefinitely stable to sedimentation.     

Rheology of shear thickening suspensions and the effects of wall slip in torsional flow

The rheological characterisation of concentrated shear thickening materials suspensions is challenging, as complicated and occasionally discontinuous rheograms are produced. Wall slip is often apparent and when combined with a shear thickening fluid the usual means of calculating rim shear stress in torsional flow is inaccurate due to a more complex flow field. As the flow is no longer “controlled”, a rheological model must be assumed and the wall boundary conditions are redefined to allow for slip. A technique is described where, by examining the angular velocity response in very low torque experiments, it is possible to indirectly measure the wall slip velocity. The suspension is then tested at higher applied torques and different rheometer gaps. The results are integrated numerically to produce shear stress and shear rate values. This enables the measurement of true suspension bulk flow properties and wall slip velocity, with simple rheological models describing the observed complex rheograms.     

A Two-Layer Mathematical Model of Blood Flow in Porous Constricted Blood Vessels

In this paper, we discussed a mathematical model for two-layered non-Newtonian blood flow through porous constricted blood vessels. The core region of blood flow contains the suspension of erythrocytes as non-Newtonian Casson fluid and the peripheral region contains the plasma flow as Newtonian fluid. The wall of porous constricted blood vessel configured as thin transition Brinkman layer over layered by Darcy region. The boundary of fluid layer is defined as stress jump condition of Ocha-Tapiya and Beavers–Joseph. In this paper, we obtained an analytic expression for velocity, flow rate, wall shear stress. The effect of permeability, plasma layer thickness, yield stress and shape of the constriction on velocity in core & peripheral region, wall shear stress and flow rate is discussed graphically. This is found throughout the discussion that permeability and plasma layer thickness have accountable effect on various flow parameters which gives an important observation for diseased blood vessels.     

Hydromagnetic flow through uniform channel bounded by porous media

The combined effects of the magnetic field, permeable walls, Darcy velocity, and slip parameter on the steady flow of a fluid in a channel of uniform width are studied. The fluid flowing in the channel is assumed to be homogeneous, incompressible,and Newtonian. Analytical solutions are constructed for the governing equations using Beavers-Joseph slip boundary conditions. Effects of the magnetic field, permeability,Darcy velocity, and slip parameter on the axial velocity, slip velocity, and shear stress are discussed in detail. It is shown that the Hartmann number, Darcy velocity, porous parameter, and slip parameter play a vital role in altering the flow and in turn the shear stress.     

Two-fluid non-linear model for flow in catheterized blood vessels

Blood flow through a catheterized artery is analyzed, assuming the flow is steady and blood is treated as a two-fluid model with the suspension of all the erythrocytes in the core region as a Casson fluid and the plasma in the peripheral region as a Newtonian fluid. The expressions for velocity, flow rate, wall shear stress and frictional resistance are obtained. The variations of these flow quantities with yield stress, catheter radius ratio and peripheral layer thickness are discussed. It is noticed that the velocity and flow rate decrease while the wall shear stress and resistance to flow increase when the yield stress or the catheter radius ratio increases while all the other parameters were held fixed. It is found that the velocity and flow rate increase while the wall shear stress and frictional resistance decrease with the increase of the peripheral layer thickness. The estimates of the increase in the frictional resistance are significantly very small for the present two-fluid model than those of the single-fluid Casson model.     

Physical and transport properties governing bubble column operations

In this work, physical and transport properties governing fluid dynamics in bubble columns were studied in the heterogeneous liquid circulation regime of operation based on several published experimental data. It was confirmed that the axial dispersion phenomenon of the liquid phase could be defined by the constant Peclet number predicated on the two-phase slip velocity, which comprised the time-averaged bubbly flow velocity superimposed by the velocity of large bubbles rising in the fluid. In addition, the slip velocity of mean bubbles in the bubbly flow not only indicated a constant rising velocity of a particular liquid but also apparently reduced to that for the Higbie model with respect to the bubble diameter and its terminal rising velocity, when applied to Akita and Yoshida's dimensionless correlation for mass transfer operation (Akita and Yoshida, 1974). In the course of demonstration, it was confirmed that a semi-theoretical correlation for the gas holdup proposed by Mersmann (1978) is similar to the empirical correlation proposed by Akita and Yoshida (1973) with respect to the expression and the physical perspective.     

A two-fluid model for pulsatile flow in catheterized blood vessels

The pulsatile flow of blood through a catheterized artery is analyzed, assuming the blood as a two-fluid model with the suspension of all the erythrocytes in the core region as a Casson fluid and the peripheral region of plasma as a Newtonian fluid. The resulting non-linear implicit system of partial differential equations is solved using perturbation method. The expressions for shear stress, velocity, flow rate, wall shear stress and longitudinal impedance are obtained. The variations of these flow quantities with yield stress, catheter radius ratio, amplitude, pulsatile Reynolds number ratio and peripheral layer thickness are discussed. It is observed that the velocity distribution and flow rate decrease, while, the wall shear, width of the plug flow region and longitudinal impedance increase when the yield stress increases. It is also found that the velocity increases, but, the longitudinal impedance decreases when the thickness of the peripheral layer increases. The wall shear stress decreases non-linearly, while, the longitudinal impedance increases non-linearly when the catheter radius ratio increases. The estimates of the increase in the longitudinal impedance are considerably lower for the present two-fluid model than those of the single-fluid model.     

Influence of yield stress on the fluid droplet impact control

The impact and the spreading of a drop of the yield stress fluid on a solid surface have been experimentally investigated. A yield stress fluid chosen as a model fluid can shed some light on the manner in which it is possible to control the impacted drop's profile. Several gels based on polymer concentration were prepared to obtain different levels of yield stress. Their shear rheological behaviours were characterized and their flow behaviours were modeled using Herschell–Bulkley equation. Droplets were impacted in a wide range of velocities upon a dry and smooth polymethylmetacrylate substrate. Their dynamics on the impacted surface were captured using a high-speed camera. The spreading and recoil of drops are studied and their behaviour was compared to that of a Newtonian fluid at each impact velocity.Influence of the yield stress level and intensity of inertia on the transient and final stages of drops impact were studied. It was shown how the increasing yield stress dictates the drop formation and also led to an emphasis of the inhibition of spreading and the weakening of retraction in the case of high inertial impacts. It was also noticed that the magnitude of the gravitational subsidence observed for the low impact velocities, is governed by the initial non-spherical shape of droplets. Dimensionless numbers were defined in the case of yield stress fluids, allowing us to compare the effects of forces present in the process and better understand the phenomena observed. Wall slip of gels on the PMMA substrate was characterized. Its influence on the drop spreading has been discussed.     

Transient squeeze flow of viscoplastic materials

The transient, axisymmetric squeezing of viscoplastic materials under creeping flow conditions is examined. The flow of the material even outside the disks is followed. Both cases of the disks moving with constant velocity or under constant force are studied. This time-dependent simulation of squeeze flow is performed for such materials in order to determine very accurately the evolution of the force or the velocity, respectively, and the distinct differences between these two experiments, the highly deforming shape and position of all the interfaces, the effect of possible slip on the disk surface, especially when the slip coefficient is not constant, and the effect of gravity. All these are impossible under the quasi-steady state condition used up to now. The exponential constitutive model, suggested by Papanastasiou, is employed. The governing equations are solved numerically by coupling the mixed finite element method with a quasi-elliptic mesh generation scheme in order to follow the large deformations of the free surface of the fluid. As the Bingham number increases, large departures from the corresponding Newtonian solution are found. When the disks are moving with constant velocity, unyielded material arises only around the two centers of the disks verifying previous works in which quasi-steady state conditions were assumed. The size of the unyielded region increases with the Bingham number, but decreases as time passes and the two disks approach each other. Their size also decreases as the slip velocity or the slip length along the disk wall increase. The force that must be applied on the disks in order to maintain their constant velocity increases significantly with the Bingham number and time and provides a first method to calculate the yield stress. On the other hand, when a constant force is applied on the disks, they slow down until they finally stop, because all the material between them becomes unyielded. The final location of the disk and the time when it stops provide another, probably easier, method to deduce the yield stress of the fluid.     

Effect of local thermal non-equilibrium on unsteady heat transfer by natural convection of a nanofluid over a vertical wavy surface

This paper uses thermal non-equilibrium model to study transient heat transfer by natural convection of a nanofluid over a vertical wavy surface. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. Three-temperature model is applied to represent the local thermal non-equilibrium among the particle, fluid, and solid-matrix phases. Finite difference method is used to solve the dimensionless governing equations of the problem. The obtained results are displayed in 2D graphs to illustrate the influences of the different physical parameters on local skin-friction coefficient, local Nusselt numbers for fluid, particle and solid phases and local Sherwood number. The results for velocity component, nanoparticle volume fraction, fluid temperature, particle temperature and solid-matrix temperature are presented in 3D graphs as a function of the axial and transverse coordinates. All the obtained results are discussed.     

Active and passive controls of nanoparticles in Maxwell stagnation point flow over a slipped stretched surface

A steady stagnation-point flow of an incompressible Maxwell fluid towards a linearly stretching sheet with active and passive controls of nanoparticles is studied numerically. The momentum equation of the Maxwell nanofluid is inserted with an external velocity term as a result of the flow approaches the stagnation point. Conventional energy equation is modified by incorporation of nanofluid Brownian and thermophoresis effects. The condition of zero normal flux of nanoparticles at the stretching surface is defined to impulse the particles away from the surface in combination with nonzero normal flux condition. A hydrodynamic slip velocity is also added to the initial condition as a component of the entrenched stretching velocity. The governing partial differential equations are then reduced into a system of ordinary differential equations by using similarity transformation. A classical shooting method is applied to solve the nonlinear coupled differential equations. The velocity, temperature and nanoparticle volume fraction profiles together with the reduced skin friction coefficient, Nusselt number and Sherwood number are graphically presented to visualize the effects of particular parameters. Temperature distributions in passive control model are consistently lower than in the active control model. The magnitude of the reduced skin friction coefficient, Nusselt number and Sherwood number decrease as the hydrodynamic slip parameter increases while the Brownian parameter has negligible effect on the reduced heat transfer rate when nanoparticles are passively controlled at the surface. It is also found that the stagnation parameter contributes better heat transfer performance of the nanofluid under both active and passive controls of normal mass flux.     

Newtonian flow in a triangular duct with slip at the wall

We consider the Newtonian Poiseuille flow in a tube whose cross-section is an equilateral triangle. It is assumed that boundary slip occurs only above a critical value of the wall shear stress, namely the slip yield stress. It turns out that there are three flow regimes defined by two critical values of the pressure gradient. Below the first critical value, the fluid sticks everywhere and the classical no-slip solution is recovered. In an intermediate regime the fluid slips only around the middle of each boundary side and the flow problem is not amenable to analytical solution. Above the second critical pressure gradient non-uniform slip occurs everywhere at the wall. An analytical solution is derived for this case and the results are discussed.     

Wall slippage with siloxane gum and silicon rubbers

A slip analysis has been developed to calculate the slip velocities from the capillary rheometry data for a polydimethylsiloxane (PDMS) gum, and two silicon rubber compounds. The analysis generalises the classical Mooney method [J. Rheol. 2 (1931) 210–222] to incorporate the influence of die geometry on the slip behaviour. For the PDMS gum, no slippage was observed below a stress level of about 60 kPa, and there was a jump in the slip velocity at a stress level of about 80 kPa. The complex rheological behaviour of the rubbers meant that the analysis was only applicable at higher stress levels. For each material, a reasonable fit to the slip velocity was obtained using a generalised Navier slip law, which can easily be implemented into computational fluid dynamic simulations. Ultimately, a more realistic slip law is required to model the observed flow behaviour correctly.     

Flow of Particulate-Fluid Suspension in a Channel with Porous Walls

The problem of the dispersed particulate-fluid two-phase flow in a channel with permeable walls under the effect of the Beavers and Joseph slip boundary condition is concerned in this paper. The analytical solution has been derived for the longitude pressure difference, stream functions, and the velocity distribution with the perturbation method based on a small width to length ratio of the channel. The graphical results for pressure, velocity, and stream function are presented and the effects of geometrical coefficients, the slip parameter and the volume fraction density on the pressure variation, the streamline structure and the velocity distribution are evaluated numerically and discussed. It is shown that the sinusoidal channel, accompanied by a higher friction factor, has higher pressure drop than that of the parallel-plate channel under fully developed flow conditions due to the wall-induced curvature effect. The increment of the channel’s width to the length ratio will remarkably increase the flow rate because of the enlargement of the flow area in the channel. At low Reynolds number ranging from 0 to 65, the fluids move forward smoothly following the shape of the channel. Moreover, the slip boundary condition will notably increase the fluid velocity and the decrease of the slip parameter leads to the increment of the velocity magnitude across the channel. The fluid-phase axial velocity decreases with the increment of the volume fraction density.     

Rheo-PIV analysis of the slip flow of a metallocene linear low-density polyethylene melt

The continuous extrusion of a metallocene linear low-density polyethylene through a transparent capillary die with and without slip was analyzed in this work by rheometrical measurements and particle image velocimetry (PIV). For this reason, a comparison was made between the rheological behaviors of the pure polymer and blended with a small amount of fluoropolymer polymer processing additive. Very good agreement was found between rheometrical and PIV measurements. The pure polymer exhibited stick-slip instabilities with nonhomogeneous slip at the die wall, whereas the blend showed stable flow. The slip velocity was measured directly from the velocity profiles and was negligible for the pure polymer before the stick-slip but increased monotonously as a function of the shear stress for the blend. The flow curves and the slip velocity as a function of the shear stress deviated from a power law and were well fitted by continuous “kink” functions. Comparison of PIV data with rheometrical ones permitted a direct proof of the basic assumption of the Mooney theory. Finally, the analysis of the velocity profiles showed that there is a maximum in the contribution of slip to the average fluid velocity, which is interpreted as the impossibility for the velocity profile to become plug like in the presence of shear thinning.     

Simulation of particles released near the wall in a turbulent boundary layer

A direct numerical simulation was used along with a Lagrangian particle tracking technique to study particle motion in a horizontal, spatially developing turbulent boundary layer along an upper-wall (with terminal velocity directed away from the wall). The objective of the research was to study particle diffusion, dispersion, reflection, and mean velocity in the context of two parametric studies: one investigated the effect of the drift parameter (the ratio of particle terminal velocity to fluid friction velocity) for a fixed and finite particle inertia, and the second varied the drift parameter and particle inertia by the same amount (i.e. for a constant Froude number). A range of drift parameters from 10⁻⁴ to 10⁰ were considered for both cases. The particles were injected into the simulation at a height of four wall units for several evenly distributed points across the span and a perfectly elastic wall collision was specified at one wall unit.Statistics collected along the particle trajectories demonstrated a transition in particle movement from one that is dominated by diffusion to one that is dominated by gravity. For small and intermediate sized particles (i.e. ones with outer Stokes numbers and drift parameters much less than unity) transverse diffusion away from the wall dominated particle motion. However, preferential concentration is seen near the wall for intermediate-sized particles due to inhomogeneous turbulence effects (turbophoresis), consistent with previous channel flow studies. Particle–wall collision statistics indicated that impact velocities tended to increase with increasing terminal velocity for small and moderate inertias, after which initial conditions become important. Finally, high relative velocity fluctuations (compared to terminal velocity) were found as particle inertia increased, and were well described with a quasi-one-dimensional fluctuation model.     

Rheological properties and dispersion stability of magnetorheological (MR) suspensions

In the present article, the rheological responses and dispersion stability of magnetorheological (MR) fluids were investigated experimentally. Suspensions of magnetite and carbonyl iron particles were prepared as model MR fluids. Under an external magnetic field (H ₀) and a steady shear flow, the yield stress depends upon H ₀ ^3/2. The Yield stress depended on the volume fraction of the particle (φ) linearly only at low concentration and increased faster at high fraction. Rheological behavior of MR fluids subjected to a small-strain oscillatory shear flow was investigated as a function of the strain amplitude, frequency, and the external magnetic field. In order to improve the stability of MR fluid, ferromagnetic Co-γ-Fe₂O₃ and CrO₂ particles were added as the stabilizing and thickening agent in the carbonyl iron suspension. Such needle-like particles seem to play a role in the steric repulsion between the relatively large carbonyl iron particles, resulting in improved stability against rapid sedimentation of dense iron particles. Furthermore, the additive-containing MR suspensions exhibited larger yield stress, especially at higher magnetic field strength. Received: 4 April 2000 Accepted: 6 November 2000     

Rheo-PIV of a yield-stress fluid in a capillary with slip at the wall

An analysis of the yielding and flow behavior of a model yield-stress fluid, 0.2 wt% Carbopol gel, in a capillary with slip at the wall has been carried out in the present work. For this, a study of the flow kinematics in a capillary rheometer was performed with a two-dimensional particle image velocimetry (PIV) system. Besides, a stress-controlled rotational rheometer with a vane rotor was used as an independent way to measure the yield stress. The results in this work show that in the limit of resolution of the PIV technique, the flow behavior agrees with the existence of a yield stress, but there is a smooth solid?Cliquid transition in the capillary flow curve, which complicates the determination of the yield stress from rheometrical data. This complication, however, is overcome by using the solely velocity profiles and the measured wall shear stresses, from which the yield-stress value is reliably determined. The main details of the kinematics in the presence of slip were all captured during the experiments, namely, a purely plug flow before yielding, the solid?Cliquid transition, as well as the behavior under flow, respectively. Finally, it was found that the slip velocity increases in a power-law way with the shear stress.     

Electro-magneto-hydrodynamic flow of couple stress nanofluids in micro-peristaltic channel with slip and convective conditions

This study explores the effects of electro-magneto-hydrodynamics,Hall currents,and convective and slip boundary conditions on the peristaltic propulsion of nanofluids(considered as couple stress nanofluids)through porous symmetric microchannels.The phenomena of energy and mass transfer are considered under thermal radiation and heat source/sink.The governing equations are modeled and non-dimensionalized under appropriate dimensionless quantities.The resulting system is solved numerically with MATHEMATICA(with an in-built function,namely the Runge-Kutta scheme).Graphical results are presented for various fluid flow quantities,such as the velocity,the nanoparticle temperature,the nanoparticle concentration,the skin friction,the nanoparticle heat transfer coefficient,the nanoparticle concentration coefficient,and the trapping phenomena.The results indicate that the nanoparticle heat transfer coefficient is enhanced for the larger values of thermophoresis parameters.Furthermore,an intriguing phenomenon is observed in trapping:the trapped bolus is expanded with an increase in the Hartmann number.However,the bolus size decreases with the increasing values of both the Darcy number and the electroosmotic parameter.     

活性流体流变行为的布朗动力学模拟研究

活性流体在用于开发新材料方面具有巨大潜力, 满足这一需求就要定量掌握活性流体所表现的特殊力学行为, 特别是流变行为. 扩展布朗运动方程, 建立自驱动活性粒子的运动模型, 基于反向非平衡法确定活性流体的黏度, 考察活性粒子体积分数、直行速度和转向扩散系数对活性流体流变行为的影响规律, 确定活性流体特殊流变行为的形成机理. 结果表明, 活性流体的流变曲线可被划分为黏度下降区、过渡区和牛顿区; 活性粒子体积分数越高, 活性流体的非牛顿特性越显著, 活性粒子的直行运动引起活性流体在低剪切速率区域黏度下降, 直行运动和转向运动的耦合作用导致中剪切速率区域流变曲线非单调变化, 活性粒子频繁发生转向运动会导致活性流体非牛顿特性受到抑制; 活性流体的宏观流变学特性和粒子的涨落直接相关, 活性粒子体积分数越高、直行速度越快和转向扩散系数越小, 活性流体中活性粒子越容易产生显著的涨落; 低剪切速率区域内活性粒子涨落明显, 随着剪切速率增大, 活性粒子的涨落逐渐被削弱, 粒子的聚集结构不断被破坏, 最终体系的流变行为类似一般被动流体.