EFFECT OF WALL SLIP ON SQUEEZE FLOW OF RIGID-PLASTIC MEDIA BETWEEN PARALLEL DISK

The squeeze flow of a rigid-plastic medium between parallel disks is considered for small gaps with partial wall slip. The stress distribution and the squeeze force between parallel disks of a rigid-plastic medium with the following four different slip boundary conditions are obtained. (1) The Coulombic friction condition is applied, and the stress distribution on the wall is derived, which is linear or exponential distribution in the no-slip area or slip area. (2) It is assumed that the slip velocity at the disks increases linearly with the radius up to the rim slip velocity, with the stress distribution and the squeeze force gained. (3) The assumption that the slip velocity at the disks is related to the shear stress component is used, with the stress distribution and the squeeze force obtained, which is equivalent to the result given in (2). (4) Rational velocity components are introduced, and the stress distribution is satisfied.     

Unsteady Flow Due to Concentric Rotation of Eccentric Rotating Disks

While two parallel disks are initially rotating with the same angular velocity about non-coincident axes, the axes are suddenly made coincident. The development of the flow is examined until the fluid rotates as a rigid body in the steady-state. The velocity field and the shear stress components on the disks are found exactly by a Fourier series solution. Furthermore, a series solution that converges rapidly at small times is obtained with the aid of the Laplace transform technique.     

MHD flow and heat transfer of micropolar fluid between two porous disks

A numerical study is carried out for the axisymmetric steady laminar incompressible flow of an electrically conducting micropolar fluid between two infinite parallel porous disks with the constant uniform injection through the surface of the disks. The fluid is subjected to an external transverse magnetic field. The governing nonlinear equations of motion are transformed into a dimensionless form through von Karman’s similarity transformation. An algorithm based on a finite difference scheme is used to solve the reduced coupled ordinary differential equations under associated boundary conditions. The effects of the Reynolds number, the magnetic parameter, the micropolar parameter, and the Prandtl number on the flow velocity and temperature distributions are discussed. The results agree well with those of the previously published work for special cases. The investigation predicts that the heat transfer rate at the surfaces of the disks increases with the increases in the Reynolds number, the magnetic parameter, and the Prandtl number. The shear stresses decrease with the increase in the injection while increase with the increase in the applied magnetic field. The shear stress factor is lower for micropolar fluids than for Newtonian fluids, which may be beneficial in the flow and thermal control in the polymeric processing.     

Acoustic filtration and sedimentation of soot particles

 Removal of soot particles from a static chamber by an intense acoustic field is investigated. Combustion of a solid fuel fills a rectangular chamber with small soot particles, which sediment very slowly. The chamber is then irradiated by an intense acoustic source to produce a three dimensional standing wave field in the chamber. The acoustic excitation causes the soot particles to agglomerate, forming larger particles which sediment faster from the system. The soot also forms 1–2 cm disks, with axes parallel to the axis of the acoustic source, which are levitated by the sound field at half-wavelength spacing within the chamber. Laser extinction measurements are made to determine soot volume fractions as a function of exposure time within the chamber. The volume fraction is reduced over time by sedimentation and by particle migration to the disks. The soot disks are considered to be a novel mechanism for particle removal from the air stream, and this mechanism has been dubbed acoustic filtration. An experimental method is developed for comparing the rate of soot removal by sedimentation alone with the rate of soot removal by sedimentation and acoustic filtration. Results show that acoustic filtration increases the rate of soot removal by a factor of two over acoustically-induced sedimentation alone. Received: 26 August 1996/Accepted: 31 March 1997     

Shear wave velocity in sand considering the effects of frequency based on particle contact theory

Since the shear waves involved in in-situ and laboratory measurement methods vary significantly in terms of the frequency range, it is necessary to consider the effects of frequency on the shear wave velocity. In this study, sand particles are assumed to be spherical solid particles with an equal radius and identical material properties, and sand skeletons are regarded as granular aggregations generated through the random packing of sand particles. It is also assumed that the sand particles only undergo elastic deformation during shear wave propagation. Based on a spherical particle model, a formula is obtained for calculating the shear wave velocity in sand, with the shear wave frequency as an extra influencing parameter. The quantitative calculations demonstrate that the shear wave velocity decreases with an increase of sand porosity, and accelerates with increases of vertical effective stress and elastic modulus of the sand particles. It is also indicated that both the particle density and Poisson’s ratio of the sand particles have negligible effects on the shear wave propagation. The frequency dispersion characteristics of shear wave propagating in sand are also discussed. Moreover, the critical frequency is defined and its analytical expression is derived. The calculation results obtained using the proposed equations agree well with the in-situ measurement results and bender element test data.     

An interactive micro-void shear localization mechanism in high strength steels

Ductility of high strength steels is often restricted by the onset of a void-sheet mechanism in which failure occurs by a micro-void shear localization process. For the first time, the micro-void shear instability mechanism is identified here by examining the interactions occurring within a system of multiple embedded secondary particles (carbides ∼10-100 nm), through a finite element based computational cell modeling technique (in two and three dimensions). Shear deformation leads to the nucleation of micro-voids as the secondary particles debond from the surrounding alloy matrix. The nucleated micro-voids grow into elongated void tails along the principal shear plane and coalesce with the micro-voids nucleated at neighboring particles. At higher strains, the neighboring particles are driven towards each other, further escalating the severity of the shear coalescence effect. This shear driven nucleation, growth and coalescence mechanism leads to a decrease in the load-bearing surface in the shear plane and a terminal shear instability occurs. The mechanism is incorporated mathematically into a hierarchical steel model. The simulated response corresponds to experimentally observed behavior only when the micro-void shear localization mechanism is considered.     

A New Shear-Compression Test for Determining the Pressure Influence on the Shear Response of Elastomers

A new shear-compression experiment for investigating the influence of hydrostatic pressure (mean stress) on the large deformation shear response of elastomers is presented. In this new design, a nearly uniform torsional shear strain is superposed on a uniform volumetric compression strain generated by axially deforming specimens confined by a stack of thin steel disks. The new design is effective in applying uniform shear and multiaxial compressive stress on specimens while preventing buckling and barreling during large deformation under high loads. By controlling the applied pressure and shear strain independently of each other, the proposed setup allows for measuring the shear and bulk response of elastomers at arbitrary states within the shear-pressure stress space. Thorough evaluation of the new design is conducted via laboratory measurements and finite element simulations. Practical issues and the need for care in specimen preparation and data reduction are explained and discussed. The main motivation behind developing this setup is to aid in characterizing the influence of pressure or negative dilatation on the constitutive shear response of elastomeric coating materials in general and polyurea in particular. Experimental results obtained with the new design illustrate the significant increase in the shear stiffness of polyurea under moderate to high hydrostatic pressures.     

Numerical investigations of asymmetric flow of a micropolar fluid between two porous disks

Numerical solution is presented for the two- dimensional flow of a micropolar fluid between two porous coaxial disks of different permeability for a range of Reynolds number Re （-300≤ Re 〈 0） and permeability parameter A （1.0≤A ≤2.0）. The main flow is superimposed by the injection at the surfaces of the two disks. Von Karman＇s similarity transformations are used to reduce the governing equations of motion to a set of non-linear coupled ordinary differential equations （ODEs） in dimensionless form. An algorithm based on the finite difference method is employed to solve these ODEs and Richardson＇s extrapolation is used to obtain higher order accuracy. The results indicate that the parameters Re and A have a strong influence on the velocity and microrotation profiles, shear stresses at the disks and the position of the viscous/shear layer. The micropolar material constants cl, c2, c3 have profound effect on microrotation as compared to their effect on streamwise and axial velocity profiles. The results of micropolar fluids are compared with the results for Newtonian fluids.     

Effect of an unsteady swirled turbulent flow on the motion of a single solid particle

An unsteady swirled turbulent flow between two rotating flat disks is modeled. The flow is directed along the radius toward the rotation axis. A quasi-steady character of the turbulent flow, caused by oscillations of the radial velocity at the entrance to the gap between the disks with a period close to the time of dynamic relaxation of the particle, is studied with the use of the known two-equation Wilcox’s k-ω model of turbulence. The influence of the Stokes number and the frequency and amplitude of oscillations of the carrier medium on the motion of single particles in the field of centrifugal and aerodynamic forces is considered.     

Wall material and roughness effects on transmittable shear stresses of magnetorheological fluids in plate–plate magnetorheometry

A direct comparison of plate–plate magnetorheometry results for nonmagnetic (titanium/brass) and ferromagnetic plates is presented, using a modified Anton Paar magnetocell MRD180/1T. Necessary corrections to derive the true flux density in the magnetorheological fluid (MRF) from the online Hall probe reading and to account for the gap opening effect caused by normal forces on shear stress and flux density are addressed. The measured shear stress versus magnetic flux density characteristics agree in the low flux density regime <0.1 T but yield distinctly higher transmittable shear stresses for ferromagnetic plates at elevated flux densities (49% increase at 1 T for 90% by weight carbonyl iron powder (CIP) and 84% for 85% by weight CIP). Remarkably, the normal force, if corrected for its magnetostatic part, remains independent of the type of plates up to about 0.6 T. We address the role of normal forces, of magnetic interactions between CIP and wall, as well as the role of wall roughness in a solid body friction model. A systematic variation of wall properties and materials was achieved by introducing both a modular rotor and stator, which ease the variation of the walls in contact to the MRF. The transmittable shear stress of nonmagnetic plates (e.g., brass) may be increased up to the level of ferromagnetic disks by a higher wall roughness or by grooves. No shear stress increase is obtained for grooves in ferromagnetic plates, which is explained by the different local flux density modulation at the grooves for ferromagnetic compared to nonmagnetic plates. Finally, we address the effect of ferromagnetic and nonmagnetic coatings on brass and steel disks, and show that, e.g., a layer of CIP on brass efficiently increases the transmittable shear stress.     

Dynamics and rheology of a dilute suspension of dipolar nonspherical particles in an external field: Part 1. Steady shear flows

Suspensions of small nonspherical particles having dipolar moments exhibit non-Newtonian behavior under the influence of shear and external fields. Numerical methods are presented for calculating the rheological and rheo-optical properties of dilute suspensions of Brownian particles having permanent dipoles subject to time-dependent shear and external fields. The numerical methods employ the Galerkin method of weighted residuals to solve the differential equation for the particle orientation distribution function. The steady-state shear flow intrinsic viscosity of suspensions of particles with sufficiently extreme aspect ratio is predicted to exhibit a maximum value attained for intermediate shear rates at selected field orientations. These numerical results provide valuable insight into the coupling which occurs between the effects of rotary Brownian motion, the hydrodynamic resistance of nonspherical particles, and the external torque exerted on dipolar particles. The results are applicable to both suspensions of magnetic particles and electrically dipolar particles.     

A numerical analysis of the shear behavior of granular soil with fines

Shear behavior of granular soil with fines is investigated using the discrete element method(DEM) and particle arrangements and inter-particle contacts during shear are examined.The DEM simulation reveals that fine particles play a vital role in the overall response of granular soil to shearing.The occurrence of liquefaction and temporary reduction of strength is ascribed mainly to the loss of support from the fine particle contacts(S-S) and fine particle-to-large particle contacts(S-L) as a consequence of the removal of fine particles from the load-carrying skeleton.The dilative strain-hardening response following the strain-softening response is associated with the migration of fine particles back into the load-carrying skeleton,which is thought to enhance the stiffness of the soil skeleton.During shear,the unit normal vector of the large particle-to-large particle(L-L) contact has the strongest fabric anisotropy,and the S-S contact unit normal vector possesses the weakest anisotropy,suggesting that the large particles play a dominant role in carrying the shear load.It is also found that,during shear,fine particles are prone to rolling at contacts while the large particles are prone to sliding,mainly at the S-L and L-L contacts.     

Rheological properties of suspensions of TiO2 particles in polymer solutions. 1. Shear viscosity

This paper presents results on the rheological behaviour of suspensions of two kinds of TiO₂ particles in two different polymer solutions. The particles differ in their hydrophilic or hydrophobic properties. The dispersing media are a solution of high molecular weight polyisobutylene in decalin and a solution of a low molecular weight polybutene in decalin. The concentrations of polymer are adjusted in order to get the same zero shear viscosity. The shear viscosity measurements display an apparent yield stress in some cases. The existence and the values of the yield stress depend on the volume fraction of solid particles and on the type of particles. The evolution of the intrinsic viscosity and of the maximum packing fraction vs the shear rate is interpreted in terms of evolution of the size and of the shape of aggregates of particles under shear. The effect of temperature on the development of the yield stress is also discussed. The results are completed by microscopic observations.     

Theoretical and experimental investigation of the flow of a viscoelastic fluid in the gap between two rotating disks

A theory of the nonlinear viscoelastic behavior of polymer fluids has been constructed in [1]. The theory was used in [2] to investigate the motion of a nonlinear viscoelastic medium under steady and unsteady deformation rates in simple shear flow, and a comparison was made with experiment. The experiments in [2], which were performed on a cone-plate Weissenberg rheogoniometer, indicate that this arrangement is unsuitable for measurements of normal stresses under unsteady conditions in fluids with a fairly high viscosity. Below, we will show the suitability of using a disk-disk Weissenberg rheogoniometer to measure normal stresses in this case for unsteady conditions (transition to steady flow and stress relaxation). In this regard, a theoretical study of the flow of a viscoelastic fluid in the gap between rotating disks is needed. Note that in this case new information will be obtained from a comparison with simple uniform shear flow, since in the flow of a polymer between two disks all three normal stress components contribute to the axial force, while in the gap between a cone and a plate only the first normal stress difference contributes to the normal force.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 25–30, March–April, 1976.     

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.      

近壁泊肃叶流中活性粒子迁移规律研究

研究活性粒子在剪切流中的迁移规律对实现颗粒分离和过程强化均具有重要意义.基于耗散粒子动力学理论,建立了描述微通道内近壁泊肃叶流中活性粒子迁移运动的数学模型,考察了活性粒子圆周运动角速度、手性诱导角速度、直行运动速度和转向扩散系数对大肠杆菌和常规活性粒子横向迁移速度和受迫转向频率的影响规律,并确定近壁剪切流中活性粒子横向迁移的形成机制.结果表明,近壁剪切流场中大肠杆菌的横向迁移速度随剪切速率增大先快速增加继而趋于稳定;大肠杆菌横向迁移速度随圆周运动角速度增大而减小,随手性诱导角速度、直行运动速度和转向扩散系数的增大而增大;大肠杆菌的受迫转向频率受圆周运动角速度、直行运动速度和转向扩散系数的影响小,而随手性诱导角速度的增大而加快;相比大肠杆菌,常规活性粒子横向迁移速度显著减小、受迫转向频率明显变慢,二者受直行运动速度和转向扩散系数的影响规律与大肠杆菌类似.直行运动是活性粒子形成横向迁移运动的前提,其他运动参数和结构参数均可一定程度促进或抑制活性粒子在近壁剪切流场中的横向迁移.     

Brownian dynamics simulation of multiphase suspension of disc-like particles and polymers

A computational model is proposed for simulating the flow of polymer nanocomposites. This model is based on a multiphase suspension of disc-like particles and polymers. The particles are represented by oblate spheroid particles that interact with each other via the Gay-Berne (GB) potential, and the polymers are modeled by finitely extensible nonlinear elastic (FENE) chains that interact with each other via the repulsive Lennard-Jones potential. The interaction between an oblate spheroid particle and a FENE chain is also considered using a modified GB potential. A Brownian dynamics simulation of the shear flows of this system was conducted to investigate the orientation behavior of disc-like particles and the rheological properties of this system. The orientation of disc-like particles was affected by polymers, and the particles in a suspension were well aligned in flows because of the flow orientation property of polymers. The predicted shear viscosity exhibited shear thinning, and the normal stress differences agree qualitatively with experimental measurements of polymer/clay nanocomposites. The simulation results suggest that the present model has the potential to be used as a computational model for polymer nanocomposites.     

Shear and squeeze rheometry of suspensions of magnetic polymerized chains

We present the first experimental results on the magnetorheology of suspensions of non-Brownian magnetic ellipsoidal particles. These particles are made of spherical iron particles linked by polymers and are called polymerized chains. Steady shear, oscillatory shear, and oscillatory squeeze rheological tests have been performed. The rheological properties of the suspension of polymerized chains have been compared with those of the suspension of spherical iron particles. In shear flow, both suspensions develop nearly the same yield stress, while in squeeze flow, the yield stress is several times higher for the suspension of polymerized chains. We show that the squeezing force of a suspension of spherical particles is an increasing function of the magnetic field intensity at low magnetic fields but decreases dramatically at higher fields. Surprisingly, this phenomenon, attributed to cavitation or air entrainment, does not occur in the suspension of polymerized chains.     

Formation of adiabatic shear band in metal matrix composites

A modified single-pulse loading split Hopkinson torsion bar (SSHTB) is introduced to investigate adiabatic shear banding behavior in SiCp particle reinforced 2024 Al composites in this work. The experimental results showed that formation of adiabatic shear band in the composite with smaller particles is more readily observed than that in the composite with larger particles. To characterize this size-dependent deformation localization behavior of particle reinforced metal matrix composites (MMCp), a strain gradient dependent shear instability analysis was performed. The result demonstrated that high strain gradient provides a deriving force for the formation of adiabatic shear banding in MMCp.     

Überlegungen zur Scherviskosität von Suspensionen aufgrund einer Dimensionsanalyse

Dimensional analysis of the motion of solid particles suspended in a fluid phase shows that the macroscopic relative shear viscosity of suspensions generally depends not only on the volume concentration and particle shape but also on two Reynolds numbers and a dimensionless sedimentation number. These dimensionless numbers are formed using parameters characterizing the structure and motion of the suspension at the microscopic level. The analysis was based on the assumptions that the dispersed particles are rigid and sufficiently large that Brownian motion may be neglected, that the continuous fluid phase is Newtonian and that the interactions between particles and between particles and fluid phase are only hydrodynamic. The Reynolds numbers describe the influence of the inertial forces at the microscopic level, and the sedimentation number the influence of gravity. The dimensionless numbers can be neglected if their values are much smaller than one. For each of the dimensionless numbers both the shear rate and the particle size influence the shear viscosity. Thus sedimentation number is large for low shear rates, whereas the Reynolds numbers are large for high shear rates. The viscosity function for one suspension can be transformed into the viscosity function for another suspension with geometrically similar particles but of a different size. The scale-up rules are derived from the requirement that the relevant dimensionless numbers must be constant. The influence of non-hydrodynamic effects at the microscopic level on the shear viscosity can be detected by deviations from the derived scale-up rules.