Observations on sand jets in viscoplastic fluids

Sand jet in non-Newtonian viscoplastic fluid is associated with a number of industrial and engineering applications, including sand capping for the reclamation of oilsands tailings ponds and sediment deposition into soft mud. In this study, several experiments were carried out by depositing circular sand jets vertically into viscoplastic fluids, known as Laponite gel. The deformation regimes of sand jets in the gel were investigated. The yield-gravity parameter of the deformed sand drop in the gel was computed.     

Oscillating plate viscometer in the Hz to kHz range

A low and audio frequency viscometer with a frequency range 2 Hz to 1 kHz and possibly up to 10 kHz is described, which shears a liquid sample (shear volume < 0.3 ml) between an oscillating glass plate and the wall of a cuvette. Alternating velocity and force exerted on the oscillating plate are measured by a mechanical impedance head, designed for the frequency range 1 Hz to 10 kHz. This device permits the determination of frequency dependent viscous liquid properties. Real and imaginary part of the complex viscosity can be obtained from the complex mechanical impedance. Inertial forces from the oscillating plate are compensated in an adjustable electronic circuit.Significant shear parameters, as the frequency, the exciting wave form and the amplitude, can be set independently. In this way viscous spectral data and also nonlinear properties can be studied, e.g., in aqueous DNA solutions. In addition, processes with time constants >0.1 s in (relaxing) viscoelastic systems, which do not obey the Boltzmann superposition principle, can be monitored by means of the (nonlinear) modulation of an LF sampling signal. Some examples of measurements will be shown. Model calculations for water and for glycerol give typical values for the complex impedances to be obtained with this oscillatory rheometric device.     

Gas displacement of viscoplastic liquids in capillary tubes

The displacement of viscoplastic liquids in capillary tubes by gas injection is examined. The viscoplasticity alters the flow kinematics and changes dramatically the amount of mass left attached at the tube wall as compared to the Newtonian case, studied experimentally by G.I. Taylor in 1961 [G.I. Taylor, Deposition of a viscous fluid on the wall of a tube, J. Fluid Mech. 10 (1961) 161–165]. Experiments with Carbopol aqueous solutions were performed for different flow rates. A recently proposed viscosity function for viscoplastic liquids was fitted to the rheological data of the Carbopol solutions. A new dimensionless rheological property – the jump number – arises in the dimensionless version of this viscosity function. The results show the effect of the viscoplastic character of the liquid on the free surface shape and on the thickness of the film of liquid left attached to the wall. This thickness decreases with the jump number and increases with the flow rate. It is also observed that there is a critical dimensionless flow rate below which the displacement is apparently perfect, i.e. there is no observable liquid left attached to the wall. This behavior is shown to be directly related to the fully developed flow far ahead the air–liquid interface.     

Precise viscosity measurements of Newtonian liquids withv < 1 mm2/s for the selection of suitable standards

The application of long capillary Ubbelohde viscometers in the determination of low viscosities is described. Corrections and measurement uncertainties are discussed. Viscosity and density data are given for 18 Newtonian liquids of commercially available purity, with viscosities below about 1 mm²/s. For several liquids the commonly used purity specifications were found to be sufficient to qualify these liquids as viscosity standards, which can be used for viscometer calibration.     

粘塑性薄壁管中复合应力波的传播特性研究

以本构关系一般理论为基础,导出了计及材料功硬化效应和应变率硬化效应的粘塑性薄壁管的本构关系及管中复合应力波的控制方程,应用有限差分方法研究了在压扭复合冲击载荷作用下粘塑性薄壁管中复合应力波的传播特性与演化规律,分析了复合应力波的耦合效应以及薄壁管中粘塑性参数和功硬化效应对复合应力波传播与演化规律的影响,并对有关现象进行了分析和解释。     

粘塑性变截面杆中冲击波的演化

讨论了粘塑性变截面杆中的一维应力波传播规律。在粘塑性本构理论框架的基础上,利用特征关系和冲击波阵面上的突跃条件,得出了冲击波在传播过程中的演化规律,包括其微分方程和解析表达式,并对Bodner和Johnson-Cook材料和不同收缩形式的杆中冲击波的演化规律进行了讨论,同时计算和讨论了杆中冲击波后方应力波传播规律的特点。     

On the spin coating of viscoplastic fluids

The spin coating of a viscoplastic material is studied using a continuous viscosity function. Thus, the transient model requires the calculation of only velocity, pressure and the moving-free surface of the liquid film, but not the calculation of the yield surface within the liquid. A Finite Element/Newton-Raphson method is presented for solving this moving boundary problem after mapping the deforming domain onto a fixed one. Assuming axial symmetry, the effect of the Bingham, Reynolds, Capillary and gravitational Bond numbers is examined. The magnitude of the first two parameters affects significantly the flow field and the shape of the film as well as the required spinning time in order to produce a film of uniform thickness. Depending on their values, large departures from the corresponding Newtonian solution may be obtained. In these cases the film does not thin out uniformly, but a maximum in its profile is created at the center of the disk. Then, the magnitude of the Capillary number also affects the size of this maximum. The gravitational Bond number affects the film thickness and its profile to a lesser extent.Dedicated to the memory of Professor Tasos C. Papanastasiou     

Discernment of non-Newtonian behavior in liquids by acoustic means

An experiment was conducted with the use of a „sonic viscometer” to demonstrate that a change in the constitutive nature of a fluid will alter the overtones that occur from the nonlinearity of the propagation of a sine wave through the fluid. Pure sine waves ranging octave-wise from 500 to 8000Hz were introduced into distilled water, and FFT analyses of the signals received were compared with those resulting from transmission of the same set of sine waves through a 1% solution of polyethylene oxide in distilled water. Differences in the FFT spectra which occur as the result of introducing the polymeric solute indicate that the device could prove viable in indicating small changes in viscous properties. Received: 10 February 1998 Accepted: 1 June 1998     

黏塑性本构计算的稳定性分析

提出本构方程计算方法的稳定性问题,针对黏塑性本构计算的显式精确算法的稳定性进行分析,发现该算法并非无条件稳定,使用小扰动方法给出了其计算稳定的必要条件,稳定性条件对数值计算中的时间步长提出限制要求。通过有限元算例验证了分析的正确性,计算结果也表明理论推导得到的稳定性公式能够准确预测满足计算稳定性条件要求的最大时间步长与各参数之间关系。     

Theory of oscillatory experiments with a coaxial cylinder viscometer

Equations are derived for the coaxial cylinder system in the combined oscillatory and steady-state shear mode. The limitations of the use of the various equations are presented. If the usual linear equations are used, the main limitation, in the case of oscillatory shear only, is that the frequency of measurement should be below 0.016 | ^*|/(r ₂ –r ₁ )². Here | ^*| is the modulus of the complex viscosity, is the density of the liquid andr ₁ andr ₂ are the radii of the cylinders. Furthermore it is shown that there is a small error in the numerical factor of the usually applied equations. The calculations are set up in such a way that extension to higher harmonics follows in a natural way. An experimental example illustrates the use of the derived equations.     

Determining the shear modulus of water in experiments with a floating disk

The problem of decaying rotation of a disk floating on the surface of a viscoelastic fluid in a cylindrical container is solved by numerical methods. The motion is found to have the form of decaying oscillations observed previously for water. In addition to the viscosity coefficient, the constructed mathematical model of the viscoelastic fluid has two more independent parameters: shear modulus and time of relaxation of elastic stresses. Elastic parameters of water are determined through comparisons with experimental data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 100–103, January–February, 2008.     

Free circular viscoplastic fluid flow with a hydrolubricant layer in the gap between coaxial cylinders

Free circular viscoplastic fluid flow in the gap between coaxial cylinders with a hydrolubricant layer on the inner cylinder is investigated theoretically. Mathematical models of the velocities and shear stresses for the transported and lubricating fluids in the laminar flow regime are proposed.     

Bammann-Chiesa-Johnson粘塑性本构模型材料参数的一种识别方法

粘塑性本构模型能否成功模拟金属高应变率大应变变形过程依赖于材料参数识别结果的好坏。由于BCJ模型考虑了应变率、温度与材料硬化之间的耦合效应以及应变率、温度历史效应,同时模型中包含了多个材料参数,因此很难通过试验直接识别模型的材料参数。本文针对BCJ模型中的耦合效应和历史效应,基于对模型中材料参数物理涵义的界定,给出了一种对材料参数解耦、分离并进行估计的方法,获得了模型材料参数估计公式,估计了材料参数的取值范围。在此基础上,编制了BCJ模型应力积分径向返回算法和粒子群优化算法的计算程序,应用重新设计了BCJ模型耦合效应和历史效应的反分析方法,在参数取值范围内对材料参数进行了优化识别。以OFHC Cu为例,应用提出的识别方法对BCJ模型的材料参数进行了识别,计算结果和试验结果符合较好。     

Flow of a shear-thinning liquid in a cylindrical container with a rotating end wall

The flow patterns produced by rotating one end wall of a circular cylinder completely filled with a strongly shear-thinning viscoelastic liquid have been investigated using the laser-induced fluorescence flow visualization technique. An intense toroidal vortex is produced in the vicinity of the rotating end wall with outward spiraling flow over the end wall itself. This vortex drives a second countercirculating vortex of low intensity in the region of the stationary end wall. Under some circumstances an axial jet of fluid is observed moving away from the rotating end wall. This jet showed evidence of instability, whereas all flows were otherwise completely steady. The double-vortex structure is different from those recently observed in either a Newtonian or slightly shear-thinning liquid or in the low Reynolds number flow of an elastic liquid. There are, however, similarities with older work for a viscoelastic liquid at relatively high Reynolds numbers. The observations highlight the suitability of the cylinder/rotating end wall configuration as a sensitive test case for computational work.     

Motion of an inclusion in uniformly and nonuniformly vibrating liquids

An approach to constructing the quantitative nonuniformity characteristics of liquid vibrations is proposed. A new problem of the motion of an inclusion in a vibrating liquid is considered. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 1, pp. 79–85, January–February, 2007.     

Film flow of pseudoplastic liquids along an oscillating wall

The film thickness of pseudoplastic liquids flowing down a vertical wall can be decreased by the longitudinal oscillations of the wall. This phenomenon is treated in the term of the flow enhancement which is common in the flows in oscillating tube. The theoretical predictions of the flow rate enhancement are reviewed for the boundary layer and creeping flow regimes. The experiments were done in the transient regime between these two asymptotic regimes. As high as five-fold decrease of the film thickness, which corresponds to the flow rate enhancements 10⁵, was measured with concentrated kaolin suspensions with the flow index 0.15. Empirical correlations which describe the flow rate enhancement and the film thickness of the liquids with the power law viscosity function in the transient regime were found.     

On the determination of material parameters for internal variable thermoelastic–viscoplastic constitutive models

The work presented in this paper deals with the determination of material parameters used in internal variable constitutive models. In order to determine the best suited material parameter set, in the less computationally expensive way, two optimization approaches are used: (i) a gradient-based method and (ii) a continuous evolutionary algorithm (EA) method. The first approach uses a combination of the steepest descent gradient and the Levenberg–Marquardt techniques. The performance of this method is known to be highly dependent on the starting set of parameters and its results are often inconsistent. The EA-based technique provides a better way to determine an optimized set of parameters (the overall minimum). Thus, the difficulty of choosing a starting set of parameters for this process is minor. The main application in this work is a 16 parameter thermoelastic–viscoplastic constitutive model. Experimental data was obtained from tensile and shear tests at different temperatures and used to compare with numerical results and to determine the correct set of material parameters. Numerical constraints were introduced to enforce physical requirements on the material parameters. Both methods are used to determine the 12 material parameters needed for an AA1050-O aluminium alloy. Although the EA-based method achieved a slightly better result, it proved to be computationally more expensive than the gradient-based method.     

考虑微观结构特征长度演化的内变量黏塑性本构模型

在金属晶体材料高应变率大应变变形过程中,存在强烈的位错胞尺寸等微观结构特征长度细化现象,势必对材料加工硬化、宏观塑性流动应力产生重要影响。基于宏观塑性流动应力与位错胞尺寸成反比关系,提出了一种新型的BCJ本构模型。利用位错胞尺寸参数,修正了BCJ模型的流动法则、内变量演化方程,引入了考虑应变率和温度相关性的位错胞尺寸演化方程,建立了综合考虑微观结构特征长度演化、位错累积与湮灭的内变量黏塑性本构模型。应用本文模型,对OFHC铜应变率在10-4~103 s-1、温度在298~542 K、应变在0~1的实验应力-应变数据进行了预测。结果表明:在较宽应变率、温度和应变范围内,本文模型的预测数据与实验吻合很好;与BCJ模型相比,对不同加载条件下实验数据的预测精度均有较大程度的提高,最大平均相对误差从9.939%减小为5.525%。