一种测试剪切黏度与拉伸黏度的方法

基于一种新型黏度模型,并通过实验证明了该黏度模型的可行性。采用截面渐变收缩的拉伸流动实验,从实验和数值计算两方面分别研究了牛顿流体和非牛顿流体的剪切黏度和拉伸黏度。同时,从实际加工生产的角度出发,强调了聚合物实际加工过程中真实黏度的重要性,并提出黏度具有唯一性的原理。采用几种常见的商业流变仪,测试了相同材料的剪切黏度与拉伸黏度,通过比较发现,新的黏度测试方法具有一定的合理性,为开发大应变速率范围的、复合流动的流变仪研究提供了理论依据。     

Extensional deformation of non-Newtonian liquid bridges

A numerical method for simulating the extensional dynamics of elongating filaments of non-Newtonian fluids in a filament stretching rheometer is presented. The boundary element method, in conjunction with either the Oldroyd-B or the generalized multimode Upper-Convected Maxwell constitutive model, is used to calculate the transient evolution of the liquid interface, the applied force on the stationary end plate and the polymeric stresses. The numerical results are compared to experimental results and are in excellent agreement at low Hencky strains (Newtonian response) but provide less accurate modeling of the stress growth observed in experiments at higher strains. A comparison of different methods for measuring the apparent extensional viscosity from global measurements of the net force and the mid-point radius of the filament is presented. At large strains calculations show that the fluid motion in these devices closely approximates ideal uniaxial elongation.     

Shear-thinning and constant viscosity predictions for rotating sphere flows

The steady motion of a rotating sphere is analysed through two contrasting viscoelastic models, a constant viscosity (FENE-CR) model and a shear-thinning (LPTT) model. Giesekus (Rheol. Acta 9:30–38, 1970) presented an intriguing rotating viscoelastic flow, which to date has not been completely explained. In order to investigate this flow, sets of parameters have been explored to analyse the significant differences introduced with the proposed models, while the momentum-continuity-stress equations are solved through a hybrid finite-element/finite volume numerical scheme. Solutions are discussed for first, sphere angular velocity increase (\(\varOmega\)), and second, through material velocity-scale increase (\(\alpha\)). Numerical predictions for different solvent-ratios (\(\beta\)) show significant differences as the sphere angular velocity increases. It is demonstrated that an emerging equatorial anticlockwise vortex emerges in a specific range of \(\varOmega\). As such, this solution matches closely with the Giesekus experimental findings. Additionally, inside the emerging inertial vortex, a contrasting positive second normal stress-difference (\(N_{2} ( \dot{\gamma} ) = \tau_{rr} - \tau_{\theta\theta}\)) region is found compared against the negative \(N_{2}\)-enveloping layer.     

Mathematical modeling of heat and mass transfer effects on MHD peristaltic propulsion of two-phase flow through a Darcy-Brinkman-Forchheimer porous medium

This article deals with the combined effects of heat and mass transfer on the peristaltic propulsion of two-phase fluid flow through a Darcy-Brinkman-Forchheimer porous medium with compliant walls. The Sisko fluid model together with small particles is considered in the presence of extrinsic magnetic field and chemical reaction. It is well-known that different biological fluids behave like a Newtonian or non-Newtonian fluid depending upon the shear rates. The non-Newtonian fluid models are more complicated than Newtonian fluid and difficult to express using the single constitutive relationship between stress and strain rate. These constitutive equations provide a complex mathematical formulation and become numerous challenges to find numerical and analytical solutions. Small magnetic particles are helpful to manipulate and control the two-phase flow by magnetic force. Moreover, it is also beneficial in drug targeting for the treatment of different diseases. Further, two-phase flow plays an important role to examine the muscular expansion and contraction during the propagation of various biological fluids. An appropriate approximation is considered such as long wavelength and creeping flow regime to model the governing equations. Analytical solutions are obtained using the perturbation method. Moreover, numerical computations are performed to determine the features of peristaltic pumping. The results of different rheological properties for particle and fluid phase are discussed mathematically as well as graphically for different sundry parameters. The current analysis has an extensive amount of applications in medical engineering and also significant importance of smart fluid pumping systems in various engineering processes.     

Die entry flow of reinforced polymers

The model describes the contributions of extensional and shear flow to the pressure drop at convergences, such as die entries, nozzles and mould gates for reinforced melts under injection moulding conditions. Fibre and molecular orientation lead to high extensional viscosities and hence large pressure losses with reinforced polymers. The model treats the flowing melt as an anisotropic fluid with extensional and shear flow governed by independent power law relations. Use of the model with real systems is described and power law constants are given for some commercial reinforced polymers.     

Flow modelling of quasi-Newtonian fluids in two-scale fibrous fabrics

Permeability is the fundamental macroscopic material property needed to quantify the flow in a fibrous medium viewed as a porous medium. Composite processing models require the permeability as input data to predict flow patterns and pressure fields. In a previous work, the expressions of macroscopic permeability were derived in a double-scale porosity medium for both Newtonian and generalized Newtonian (shear-thinning) resins. In the linear case, only a microscopic calculation on a representative volume is required, implying as many microscopic calculations as there are representative microscopic volumes in the whole fibrous structure. In the non-linear case, and even when the porous microstructure can be described by a unique representative volume, a large number of microscopic calculations must be carried out as the microscale resin viscosity depends on the macroscopic velocity, which in turn depends on the permeability that results from a microscopic calculation. An original and efficient offline-online procedure was proposed for the solution of non-linear flow problems related to generalized Newtonian fluids in porous media. In this paper, this procedure is generalized to quasi-Newtonian fluids in order to evaluate the effect of extensional viscosity on the resulting upscaled permeability. This work constitutes a natural step forward in the definition of equivalent saturated permeabilities for linear and non-linear fluids.     

Finite element approximations for quasi-Newtonian flows employing a multi-field GLS method

This article concerns stabilized finite element approximations for flow-type sensitive fluid flows. A quasi-Newtonian model, based on a kinematic parameter of flow classification and shear and extensional viscosities, is used to represent the fluid behavior from pure shear up to pure extension. The flow governing equations are approximated by a multi-field Galerkin least-squares (GLS) method, in terms of strain rate, pressure and velocity (D-p-u). This method, which may be viewed as an extension of the formulation for constant viscosity fluids introduced by Behr et al. (Comput Methods Appl Mech 104:31–48, 1993), allows the use of combinations of simple Lagrangian finite element interpolations. Mild Weissenberg flows of quasi-Newtonian fluids—using Carreau viscosities with power-law indexes varying from 0.2 to 2.5—are carried out through a four-to-one planar contraction. The performed physical analysis reveals that the GLS method provides a suitable approximation for the problem and the results are in accordance with the related literature.     

A numerical case study of a non-Newtonian flow problem

This paper addresses some of the theoretical aspects involved in the numerical study of non-Newtonian flow problems. We consider the second-order Rivlin–Erickson constitutive model due to the simple differential form that emerges for the system of equations that govern the flow when expressed in stream function–vorticity variables. This model describes slightly elastic fluids that exhibit a constant viscosity behaviour. A steady two-dimensional flow is studied through a planar contraction geometry. An auxiliary variable is introduced into the problem formulation producing a non-linear system of differential equations comprising two elliptic equations and one hyperbolic equation. This system is discretized by finite difference methods and the resulting system of non-linear algebraic equations is solved iteratively by successive substitutions. The simple structure of this iteration permits a convergence analysis which is presented in Section 2. This analysis is performed prior to the spatial discretization and establishes the dependence of the iteration upon the material parameters. At the discrete linearized equation level a combination of inner iterations for elliptic equations and direct marching for the hyperbolic equation is used. The stability of the marching scheme is considered in Section 4.3 and a discussion on the results is given in Section 5.     

注射成型中聚合物熔体应力分布的研究

对聚苯乙烯在注射成型过程中全展区的熔体进行了应力分布的研究计算结果与理论预测和实验值具有较好的一致性。     

Recent advances in the continuum mechanics of viscoelastic liquids

The kinematics of viscoelastic fluid flows, the development of constitutive relations and their use in viscometric and nonviscometric flows is given. Experimental data in viscometric flows, extensional flows and the eccentric rotating disk motion along with oscillatory shear flows are presented and compared with theoretical predictions. The flow classification scheme for the selection of the appropriate constitutive equation, the perturbation schemes applicable to fixed and variable domains are described. These are applied to review the literature on particle motions, lubrication problems and rotating flows. Stability of the flows is discussed along with some recent work on existence, uniqueness and the use of dynamical system and hyperbolic theory in connection with propagating singular surfaces.     

Simulating sedimentation of liquid drops

This work was carried out to investigate the effect of fluid properties on the flow pattern and on the sedimentation velocity of an axisymmetric steady flow of a Newtonian fluid past a liquid drop in an unbounded region. The governing equations of motion were solved by the finite element method. The results show that the flow pattern of a liquid drop depends strongly both on the Reynolds number and on the ratio of the viscosity between the drop and the surrounding flowing fluids. The viscosity ratio in the range 0.02<μ^*<50 has appreciable effect on the drag coefficient. Finally, a correlation for the sedimentation velocity is presented. Copyright © 2004 John Wiley & Sons, Ltd.     

Numerical 2D models of consolidation of dense flocculated suspensions

A mathematical 2D model for a consolidation process of a highly concentrated, flocculated suspension is developed. The suspension is treated as a mixture of a fluid and solid particles by an Eulerian two-phase fluid model. The suspension is characterized by constitutive relations correlating the stresses, interaction forces, and inter-particle forces to concentration and velocity gradients. This results in three empirical material functions: a permeability, a non-Newtonian viscosity and a non-reversible particle interaction pressure. Parameters in the models are fitted to experimental data. A simulation program using finite difference methods both in time and space is applied to one and two dimensional test cases. The effect of different viscosity models as well as the effect of shear on consolidation rate is studied. The results show that a shear thinning viscosity model yields a higher consolidation rate compared to a model that only depends on the volume fraction. It is also concluded that the size of the viscosity influences the time scale of the process and that the expected effect of shear on the process is not weil reproduced with any of the models.     

Properties of an elementary class of fluids with nondissipative viscous stresses

A class of fluids with both dissipative and nondissipative viscous stresses is analyzed. The class is delineated by the three assumptions, (1) the stress is isotropic, (2) the fluid admits no natural time scale, (3) the Stoke's assumption, tr(t) = − 3p, is satisfied. The constitutive relations are shown to be uniquely determined in terms of the linear bulk viscosity and the linear shear viscosity. The characteristic features of such fluids are obtained and experimental distinguishability between these fluids and the classic Navier-Stokes fluid is examined in detail. In general, it is surprisingly difficult to distinguish between the fluids considered here and the classic Navier-Stokes fluids, even though there are characteristic anomalies associated with the nondissipative stresses.     

Steady viscous flow in constricted elastic tubes subjected to a uniform external pressure

Cardiovascular illness is most commonly caused by a constriction, called a stenosis. A non-linear mathematical model with a free moving boundary was introduced to study viscous flow in tapered elastic tubes with axisymmetric constrictions subject to a prescribed pressure drop and a uniform external pressure. An iterative numerical scheme using a boundary iteration method was developed to solve the model. Effects of stenosis severity and stiffness, pressure drop, external pressure and stiffness of the vessel wall on the flow and wall motion were evaluated. It was found that stenosis severity, pressure drop and external pressure played more dominant roles than tube wall stiffness and stenosis stiffness perturbation. Tubes with 71 and 78 per cent stenoses showed two areas of negative transmural pressure and complex contraction–expansion–contraction wall motion patterns. Two types of tube diameter contraction and negative transmural pressure were observed, one was just distal to the stenosis and the other was near the outlet of the tube. Experiments using stenotic silicone tubes were conducted to quantify the tube law and verify the predicted pressure–flow relationship. The agreement between the numerical results and experimental measurements is better than that from a previous model which assumed periodicity of the tube and imposed different pressure conditions. © 1998 John Wiley & Sons, Ltd.     

Thermo-hydraulic behavior of ice slurry in an offset strip-fin plate heat exchanger

Ice slurry is a promising alternative to conventional single-phase coolants in indirect refrigeration systems. In this paper, an experimental analysis of an offset strip-fin heat exchanger operating with ice slurry as working fluid is presented. The pressure drop and thermal performance have been determined. In order to obtain the partial thermal resistance in the ice slurry side an empirical correlation for the secondary fluid side was determined by applying the Wilson plot method in a set of tests performed previously. An empirical correlation in terms of the Colburn j-factor to describe the thermal behavior of the heat exchanger with ice slurry was obtained. On the other hand, the direct pressure drop measurements operating with different flow rates and ice fractions are shown and compared with values obtained with single-phase fluids. Pressure drop instabilities have been observed for flow rates lower than the nominal value provided by the manufacturer.     

The rheological modelling of carbon nanotube (CNT) suspensions in steady shear flows

This paper is concerned with the rheological modelling of both chemically treated and untreated carbon nanotube (CNT) suspended in a Newtonian epoxy resin. CNT suspensions generally exhibited shear-thinning characteristic—the apparent viscosity decreases as shear rate increases—when subject to steady shear flows. Chemically treated CNT suspensions with little optical microstructure were found to exhibit a less significant shear-thinning effect compared with untreated CNT suspensions where clear optical aggregates were observed. In the case of treated CNT suspensions, the shear-thinning characteristic could be described using a Fokker–Planck based orientation model. The model assumed that the treated CNTs behaved as high aspect ratio rods and that shear flow was able to align the CNTs in the flow direction, thereby resulting in a decrease in the shear viscosity. Despite the success in describing the rheological response of treated CNT in steady shear flows, the orientation model failed to explain the more pronounced shear-thinning effect observed in untreated CNT suspensions having a hierarchy of aggregate structures. A new model called the aggregation/orientation (AO) model was formulated by modifying the Fokker–Planck equation. The AO model considered elements of aggregation as well as CNT orientation and it was capable of capturing the steady shear response of untreated CNT suspensions.     

Numerical study of flow and heat-transfer characteristics of cryogenic slush fluid in a horizontal circular pipe (SLUSH-3D)

Cryogenic slush fluids, such as slush hydrogen and slush nitrogen, are two-phase, single-component fluids containing solid particles in a liquid. Since their density and refrigerant capacity are greater than those of liquid-state fluids alone, there are high expectations for use of slush fluids as functionally thermal fluids in various applications, such as fuels for spacecraft engines, clean energy fuels to improve the efficiency of transportation and storage, and as refrigerants for high-temperature superconducting equipment. In this research, a three-dimensional numerical simulation code (SLUSH-3D), including the gravity effect based on the thermal non-equilibrium, two-fluid model, was constructed to clarify the flow and heat-transfer characteristics of cryogenic slush fluids in a horizontal circular pipe. The calculated results of slush nitrogen flow performed using the numerical code were compared with the authors’ experimental results obtained using the PIV method. As a result of these comparisons, the numerical code was verified, making it possible to analyze the flow and heat-transfer characteristics of slush nitrogen with sufficient accuracy. The numerical results obtained for the flow and heat-transfer characteristics of slush nitrogen and slush hydrogen clarified the effects of the pipe inlet velocity, solid fraction, solid particle size, and heat flux on the flow pattern, solid-fraction distribution, turbulence energy, pressure drop, and heat-transfer coefficient. Furthermore, it became clear that the difference of the flow and heat-transfer characteristics between slush nitrogen and slush hydrogen were caused to a large extent by their thermo-physical properties, such as the solid–liquid density ratio, liquid viscosity, and latent heat of fusion.     

A simultaneous solution procedure for strong interactions of generalized Newtonian fluids and viscoelastic solids at large strains

The paper presents a methodology for numerical analyses of coupled systems exhibiting strong interactions of viscoelastic solids and generalized Newtonian fluids. In the monolithic approach, velocity variables are used for both solid and fluid, and the entire set of model equations is discretized with stabilized space–time finite elements. A viscoelastic material model for finite deformations, which is based on the concept of internal variables, describes the stress‐deformation behaviour of the solid. In the generalized Newtonian approach for the fluid, the viscosity depends on the shear strain rate, leading to common non‐Newtonian fluid models like the power‐law. The consideration of non‐linear constitutive equations for solid and fluid documents the capability of the monolithic space–time finite element formulation to deal with complex material models. The methodology is applied to fluid‐conveying cantilevered pipes in order to determine the influence of material non‐linearities on stability characteristics of coupled systems. Copyright © 2005 John Wiley & Sons, Ltd.     

Numerical simulation of the motion and deformation of a non-Newtonian shear-thinning drop suspended in a Newtonian circular Couette flow using DR-BEM

The motion and deformation of a non-Newtonian shear-thinning drop suspended in a Newtonian circular Couette flow is studied using a boundary element numerical simulation. Non-linear effects from the dependency of the viscosity on the velocity field are treated in an implicit manner and the resultant domain integral is transformed into an equivalent series of boundary integrals using the Dual Reciprocity Method. The non-homogeneous (non-linear) system of algebraic equations resulting from the discretization of the boundary element formulation is solved using a modified Newton–Raphson method for drops with values of the power law index of $n=0.8$ and $0.6$ and compared to the corresponding Newtonian cases ($n=1$). The viscosity of the fluid inside the drop follows the truncated power law model. By using this model, the shear-thinning behaviour of the viscosity is correctly represented while avoiding the shear thickening which can be observed using the standard power law in small gradient flows. The simulations showed that the non-Newtonian drops had larger deformations than the corresponding Newtonian drops due to a general decrease in the viscosity. The value of the local viscosities was found to be dependant not only on the velocity field created by the motion of the internal cylinder, but strongly dependant on the surface tension forces. The rate of deformation of the drops was greater in the beginning of the simulation and decreased toward the end showing the drops found a more or less stable shape.     

Time-dependent Poiseuille flows of visco-elasto-plastic fluids

Summary A general constitutive equation of the stress tensor for non-Newtonian fluids is presented, which contains many well-known constitutive models, e.g., Oldroyd-B, Maxwell-A, Maxwell-B, Johnson-Segalman and Bingham models. We examine this constitutive equation with reference to a simple plane fluctuating flow of an incompressible fluid through a horizontal channel bounded by two infinite parallel plates under the exertion of a periodic longitudinal pressure gradient. Numerical solutions are obtained and discussed, especially in connection with viscous, elastic and plastic behaviors of such non-Newtonian fluids.