RHEOLOGICAL PROPERTIES AND FLOW OF CONCENTRATED DISPERSE MEDIA. II - STEADY AND UNSTEADY FLOW ANALYSIS OF HEAVY CRUDE OIL EMULSIONS

Experimental study of steady flows of heavy crude oil emulsions in rectilinear ducts provides evidence of a non newtonian behaviour in good agreement with viscometric rheological data. Superimposing an unsteady flow on the mean one, the mean flow rate is shown to be strongly increased under conditions depending on the frequency and the values of the mean and oscillatory components of the pressure gradient. The mean features of such an enhancement are then interpreted in relation to the rheological behaviour of the fluid.     

RHEOLOGICAL PROPERTIES AND FLOW OF CONCENTRATED DISPERSE MEDIA. II - STEADY AND UNSTEADY FLOW ANALYSIS OF HEAVY CRUDE OIL EMULSIONS

Experimental study of steady flows of heavy crude oil emulsions in rectilinear ducts provides evidence of a non newtonian behaviour in good agreement with viscometric rheological data. Superimposing an unsteady flow on the mean one, the mean flow rate is shown to be strongly increased under conditions depending on the frequency and the values of the mean and oscillatory components of the pressure gradient. The mean features of such an enhancement are then interpreted in relation to the rheological behaviour of the fluid.     

EXTRUSION AND LUBRICATION FLOWS OF VISCOPLASTIC FLUIDS WITH WALL SLIP

The simplest model flow which approximates the extrusion (shallow screw channels) and lubrication flow is the steady, laminar flow occurring between two infinitely long parallel plates i.e., the generalized plane Couette flow. Here we develop an analytical model of the generalized plane Couette flow of viscoplastic fluids. The deformation and flow behavior of viscoplastic fluids can be realistically represented with the Herschel-Bulkley constitutive equation, which we have utilized as the basis for the development of our analytical model. Furthermore, as also demonstrated here, the deformation behavior of viscoplastic fluids is generally complicated by the presence of wall slip at solid walls, which occurs as a function of the wall shear stress. The wall slip versus the wall shear stress behavior of viscoplastic fluids can be experimentally characterized using viscomelric flows, including steady torsional and capillary flows. Thus determined Navier's wall slip coefficient can then be utilized in modeling of processing flows. In our analytical model of the generalized plane Couette flow of viscoplastic fluids the Navier's wall slip boundary condition was included. This model should be an important engineering tool, which provides design expressions for the extrusion and lubrication flows of viscoplastic fluids, with or without wall slip occurring at the walls. @KEYWORDS:Extrusion, lubrication, flow, viscoplastic, slip.     

Inertial Effects on Linear and Locally Linear Flows

The dynamics of a suspension of particles in a gas may be characterized by the coexistence of a nearly equilibrated incompressible component (the gas) with a highly compressible component, which is often very far from equilibrium (the particle phase). The governing equations for such a system are complicated due to the coupling between the two phases, and have been successfully solved in only a limited number of cases. In the first part of this paper the wide range of so-called “linear flows” (where the host gas velocity field varies linearly with position) for which the particle velocity field may be obtained analytically is introduced. Because the family of linear flows includes stagnation point flows, Couette flows, and solid body rotations, relatively wide conclusions may be reached on the particle behavior, with important implications for the aerodynamic separation of aerosols or heavy molecules. In particular, it is seen that sufficiently far downstream from particle injection points the particle velocity becomes independent of initial conditions and is a function of the local fluid properties only. This remarkable feature (“normal behavior”) always occurs for solid body rotations or parallel flows, but not for decelerated flows. For these, there is a critical value of the ratio between the particle relaxation time τ and the flow deceleration time to ω^?1, above which the “normal solutions” break down and the particle motion is influenced also by its past history rather than by local fluid properties only. In the second part, a phenomenological approach (constitutive law) is proposed for solving particulate problems. The particle velocity is given at every point as a function of the local host gas velocity and velocity gradient tensor, using the normal solutions obtained previously as if the flow were locally linear. The corresponding results are compared with numerical calculations (easily performed in the limit of small particle mass fraction) for two different nonlinear stagnation-type flows, and the agreement is quite good in both cases up to values of ωτ near critical. If more extensive testing of the proposed “locally linear flow approximation” proves successful, its use will simplify significantly the treatment of the flow of dusty gases.     

On the mechanisms for drag reduction: A viscoelastic evaluation based on a bead-spring model

Two possible drag reduction mechanisms were examined by studying the viscoelastic effects of polymer solutions for the separate cases of oscillatory shear flow and elongational flow. The constitutive equation used was based on a modified dumbbell molecular model which predicts non-Newtonian viscosity and both the primary and the secondary normal stress differences. It can be shown that when this constitutive equation is arranged in the form of the Oldroyd model, the latter becomes a special case of this more general equation. The present results show that viscoelastic effects on the mean local rate of energy dissipation of a fluid element in an oscillatory motion are negligibly small. However, such effects introduce very large increases in the elongational viscosity as the stretching rate exceeds a certain limiting value and the flow time exceeds the terminal relaxation time of the fluid. The relative merits of these findings as possible explanations of turbulent drag reduction are briefly discussed.     

A continuum constitutive model for cohesionless granular flows

A constitutive model is developed to represent shear granular flows of cohesionless solids. The model is based on the postulate that the friction coefficient and the solids fraction in a moving granular material are exclusive functions of the inertial number, which represents the ratio of inertial to normal stress forces. The constitutive equation obtained has the same form as a multidimensional Bingham fluid model, albeit with apparent viscosity and yield stress that depend on the vertical normal stress. The model is applied to previously published experimental results dealing with shear flows of granular beds made up of cohesionless spherical particles. The first case analyzed corresponds to a granular bed moving on top of a rotating disk. The model captures the main trends of the velocity profiles with a single adjustable parameter. The second case is a conventional Couette flow, for which the model is capable of representing the velocity and solids fraction profiles measured experimentally.     

MATHEMATICAL MODELING OF OSCILLATORY MHD COUETTE FLOW IN A ROTATING HIGHLY PERMEABLE MEDIUM PERMEATED BY AN OBLIQUE MAGNETIC FIELD

We study theoretically the incompressible, viscous, oscillatory hydromagnetic Couette flow in a horizontal fluid-saturated highly permeable porous medium parallel-plate channel rotating about an axis perpendicular to the plane of the plates under the action of a uniform magnetic field, B₀, inclined at an angle θ to the axis of rotation. The flow is generated by the non-torsional oscillation of the lower plate of the channel. The reduced unsteady momentum equations are nondimensionalized with appropriate variables. Exact solutions under specified boundary conditions are obtained using the Laplace transform method (LTM). The flow regime is found to be controlled by a rotational parameter (K²), which is the reciprocal of the Ekman number (Ek), the square of the Hartmann magnetohydrodynamic number (M²), a porous medium permeability parameter (K_p), which is the inverse of the Darcy number (Da), oscillation frequency (ω), dimensionless time (T), and magnetic field inclination (θ). The influence of these parameters on the primary (u₁) and secondary (v₁) velocity field is presented graphically and studied in detail. Asymptotic behavior of the solutions is also examined for several cases of the square of the Hartmann number, rotation parameter, and oscillation angular frequency. The existence of modified Hartmann boundary layers is also identified. The present study has important applications in MHD (magnetohydrodynamic) energy generator flows, chemical engineering magnetic materials processing, conducting blood flows, and process fluid dynamics.     

Numerical modeling of nonisothermal polymer crystallization kinetics: Flow and thermal effects

A numerical model able to simulate polymer crystallization under nonisothermal flows is developed. It is based on the assumption that the trace of the extra‐stress tensor, calculated according to a viscoelastic multimode Upper Convected Maxwell (UCM) model, is the driving force of the flow‐induced extra nucleation. Two distinct sets of Schneider equations are used to describe the growth of thermally and flow induced nuclei. The model is then coupled with the momentum equations and the energy equation. As an application, a shear flow configuration between two plates (Couette flow) is simulated. The relative influence of the mechanical and thermal phenomena on the crystallization development as well as the final morphology distribution is then analyzed as a function of the shearing intensity and the cooling kinetics, in terms of nucleation density and crystallite mean sizes. POLYM. ENG. SCI., 50:2044–2059, 2010. © 2010 Society of Plastics Engineers     

同轴圆筒流变仪初始瞬态黏度的解析与数值研究

同轴圆筒流变仪在恒剪速或恒应力测试初始过程中测试黏度远高于真实值的现象与流场非稳态作用等因素有关。测量间隙内的Couette流动研究主要集中在边界条件为恒值或某一具体时间函数下的理论推导,而测量间隙的边界条件实际为某一动边界。假设动边界为任意f(t),将同轴圆筒间Newtonian流体初始流变测试过程简化为无限大平板间Couette流动,采用特征函数法和Laplace变换推导应力和剪速边界下流场及表观黏度精确解,同时依据不同间隙尺寸和运动黏度对6种边界条件下的瞬态表观黏度进行数值计算。结果表明:当u <20 mm²·s^-1时,控制剪速边界下流场及表观黏度平衡时间更短;当20 mm²·s^-12·s^-1时,控制应力边界下流场及表观黏度平衡时间更短;当u >20000 mm²·s^-1时,两类边界条件下的平衡时间相近。     

Viscoelastic properties of fly ash‐filled natural rubber compounds: Effect of fly ash loading

Fly ash (FA) as a by‐product of power station plants is known to consist of silicon dioxide similar to precipitated silica. The use of FA as filler in natural rubber (NR) was of interest to reinforce and/or reduce product cost. In this article, viscoelastic properties of FA‐filled NR composites with various FA loadings were investigated with the utilization of two different modes of shear flow, namely, oscillatory and steady shear flow. It is found that the addition of FA to NR increases storage modulus (G′) and shear viscosity under both oscillatory and steady shear flow. Moreover, the oscillatory test results exhibit the unexpected increase in magnitude of viscous response with increasing FA loading in FA‐filled NR compounds. The explanation is proposed in terms of the ball‐bearing effect of FA with spherical shape associated with the occurrence of molecular degradation induced by inorganic constituents particularly manganese, iron, and copper in nonrubber component of NR as well as the small amount of heavy metals including iron, copper in FA. An isoprene rubber (IR) containing no nonrubber component was used to validate the proposed explanation. In addition, with the use of Cox‐Merz concept, the results of both complex viscosity under oscillatory shear flow and apparent shear viscosity under steady shear flow can effectively be superimposed in the case of FA‐filled compounds, supporting the promotion of viscous response by FA. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

A fully coupled quadrature-based moment method for dilute to moderately dilute fluid–particle flows

A third-order quadrature-based moment method for simulating dilute and moderately dilute fluid–particle flows has been implemented with full coupling in a computational fluid dynamics code. The solution algorithm for the particle phase uses a kinetic-based finite-volume technique to solve the velocity moment equations derived from kinetic theory. The procedure to couple the particle-phase volume-fraction and momentum equations with the Eulerian solver for the fluid phase is explained in detail. As an example application, simulations of a particle-laden vertical channel flow at fluid-phase Reynolds number 1379 and particle Stokes numbers 0.061 and 0.61 were carried out. The fluid and particle velocities, particle-phase volume fraction and granular temperature were observed to reach a steady state in the case of Stokes number 0.061, while instabilities that led to the formation of structures and initiated the particle segregation process were observed in the case with the higher Stokes number. These results are validated against results from a classical two-fluid model derived from the kinetic theory of granular flows in the small Knudsen number limit, and Euler–Lagrange simulations of the same flow.     

Experimental and numerical investigation on mixing and axial dispersion in Taylor–Couette flow patterns

Taylor–Couette flows between two concentric cylinders have great potential applications in chemical engineering. They are particularly convenient for two-phase small scale devices enabling solvent extraction operations. An experimental device was designed with this idea in mind. It consists of two concentric cylinders with the inner one rotating and the outer one fixed. Moreover, a pressure driven axial flow can be superimposed. Taylor–Couette flow is known to evolve towards turbulence through a sequence of successive hydrodynamic instabilities. Mixing characterized by an axial dispersion coefficient is extremely sensitive to these flow bifurcations, which may lead to flawed modelling of the coupling between flow and mass transfer. This particular point has been studied using experimental and numerical approaches. Direct numerical simulations (DNS) of the flow have been carried out. The effective diffusion coefficient was estimated using particles tracking in the different Taylor–Couette regimes. Simulation results have been compared with literature data and also with our own experimental results. The experimental study first consists in visualizing the vortices with a small amount of particles (Kalliroscope) added to the fluid. Tracer residence time distribution (RTD) is used to determine dispersion coefficients. Both numerical and experimental results show a significant effect of the flow structure on the axial dispersion.     

不同代数端羟基超支化聚酯及其二元共混物的流变行为

系统研究了消除热历史后的G1~G5端羟基超支化聚酯熔体及组分质量比为1∶1的二元共混物的流变行为。结果表明,无论是稳态剪切测试还是振荡测试,消除热历史后的G2~G5端羟基超支化聚酯熔体均表现为牛顿流体的流变行为。G3~G5端羟基超支化聚酯的流变行为均遵循Cox-Merz方程。G2端羟基超支化聚酯在振荡测试的高频区出现了剪切增稠现象。对于组分质量比为1∶1的低代/高代端羟基超支化聚酯二元共混物,无论是稳态剪切还是振荡剪切,只要一种组分是牛顿流体,那么二元共混体系也是牛顿流体。高代数组分决定了二元共混物的流变特性,而低代数组分主要影响二元共混物的黏度。     

Prediction of lower/upper limiting viscosities

An analysis based on steady uniform laminar flow of a non-Newtonian fluid in a tube is presented which predicts Newtonian flow behaviour in the limits of zero and infinite shear, respectively. It is shown that an upper limiting viscosity occurs in the limit of infinite shear for a fluid with or without a yield stress, whereas a lower limiting viscosity is obtained for a fluid without a yield stress in the limit of zero shear. For a fluid with a yield stress, an infinite viscosity is found in the limit as the shear stress approaches the yield stress.     

Viscoelastic properties of polystyrene–poly(vinyl methyl ether) blends in oscillatory and steady shear flows near the phase separation temperature

Viscoelastic properties of a polystyrene-poly(vinyl methyl ether) blend were measured in oscillatory and steady shear flows near the phase separation temperature. In the one-phase region, the viscoelastic properties are independent of the type of flow and flow geometry, and their shear and frequency dependences are the same as those of homopolymers. When phase separation occurred, a change in viscoelastic properties was observed in all types of flow and flow geometries, and they are different in the different types of flow and/or different flow geometries in the two-phase region. In the shear rate dependence of viscosity of the polymer blend in the two-phase region at quiescence, a plateau region was observed, in which the shear viscosity can be regarded as the zero shear viscosity of the homogenized polymer blend at that temperature.     

Fully developed multilayer polymer flows in slits and annuli

A numerical method has been developed for simulating fully developed multilayer shear flows of non-Newtonian fluids with arbitrary viscosity functions. Poiseuille and combined Poiseuille/Couette flows in both slits arid annuli may be modeled. The method employs a finite difference system where grid points lie on streamlines and move to their correct positions as the solution procedure converges. Interfaces are easily handled as particular stream lines with the equation of motion replaced by a boundary condition. The method is stable for high interface viscosity ratios and readily handles a large number of layers. Many authors have employed power law models to model multi-layer non-Newtonian flows. We find that the power law is sufficient to predict pressure gradients and interface positions in most cases, but gives unrealistically flat velocity profiles, even when truncated at finite viscosity. Results are presented for the Carreau fluid and for the rubber-like liquid with shear thinning via Wagner's strain functional.     

A model viscoelastic fluid

Shear stress and first normal stress difference data are presented for materials which exhibit a constant viscosity and yet at the same time exhibit elasticity levels of the same order as polymer melts. Flow pattern observations in circular die entry flows in conjunction with independent shear and normal stress measurement strongly suggest that these fluids would make excellent model fluids for melt studies. Studies in which the influence of elasticity in the absence of shear thinning and fluid inertia can easily be made. Furthermore it is clearly shown that a realistic solution to the die entry flow problem is not obtained using second order flow theory. In the second order region the secondary cell is observed to be almost identical in size to the cell observed for an inelastic Newtonian fluid in creeping flow. Marked growth in the secondary cell as a function of elasticity is not observed until the shear rates exceed the region of second order behavior. This growth in cell size as a result of elasticity is followed at higher shear rates by a spiraling flow instability like that observed for some polymer melts.     

Steady-shear rheological behavior of the suspension of spherical particles in a second-order fluid

In this paper we study the rheological behavior of a dilute suspension of rigid spherical particles in a second-order fluid. We extend the results of viscous fluids to discuss the expression for the bulk stress tensor of a second-order fluid and also obtain an approximate solution to the shear flow problem of this fluid. By combing these results, we write an approximate constitutive equation for the bulk stress tensor for such a suspension and study it in a shear flow. It is found that the new equation predicts no variation in the shear viscosity, but predicts enhancement of the pre-existing non-Newtonian nature of the suspending fluid with regard to the normal stress functions.     

KINETIC THEORY OF FLOW IN STRONGLY INHOMOGENEOUS FLUIDS

Enskog's kinetic theory of dense hard sphere fluids, modified to allow long-ranged attractive interactions in a mean field sense, is solved for the case of slow flow in strongly inhomogeneous fluids, such as fluids near solid surfaces or liquid-vapor interfaces. In the equilibrium limit the theory yields the exact Yvon-Born-Green equation for the density distribution. In the slow flow limit the viscosity is a tensorial functional of the density distribution. Expressions for the velocity profile are derived for plane laminar and Couette flows. The density dependence of the transport coefficients is smoothed once through the angle averaging of the binary collisions of the Enskog theory. In the planar flows the velocity profile obeys a second order differential equation with variable coefficients and so the density dependence is further muted by two successive spatial integrations. The result leads one to expect the velocity profile to depend relatively weakly on density variations. This conclusion is in agreement with recently available computer simulations of flow in micropores. Another conclusion of the work is that one cannot introduce a flow or pore size independent effective viscosity to describe flow in micropores.     

On helical flows of polymer fluids

Isothermal and non‐isothermal steady helical flows are theoretically investigated under the assumption that the flow is fully developed in both the thermal and hydrodynamic senses. It is well known that the basic gross characteristics of steady isothermal helical flows of non‐Newtonian liquids can be found relatively easily if the flow curve (or non‐Newtonian viscosity) in simple shearing is known. Nevertheless, evaluation of more detailed viscoelastic properties in this type of flow is also sometimes desirable. These properties are shown to be exactly determined in both the isothermal and non‐isothermal cases as soon as a nonlinear viscoelatic constitutive equation is specified. Shear thinning due to fluid rotation and strong temperature dependence of Newtonian viscosity highly increase dissipative heat. This can produce significant non‐isothermal effects in intense helical flows, even when the wall temperature is kept uniform and constant. It is shown that the energy consumption in isothermal and non‐isothermal helical flows is always higher than in respective annular flows with the same flow rate. Comparisons between our calculations and available experimental data are also discussed.