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.     

Single screw extrusion of viscoplastic fluids subject to different slip coefficients at screw and barrel surfaces

Commonly encountered viscoplastic fluids including concentrated suspensions of polymeric and ceramic composites, foams, gels, concrete, food products, and energetic compounds exhibit wall slip during their flow and processing. For some viscoplastics fluids, especially highly filled suspensions, wall slip may dominate the flow and deformation and hence the processing behavior of the suspension. The wall slip velocity is generally a function of the wall shear stress and temperature. Various factors including the materials of construction i.e., chemical nature and the roughness of the wall surface affect the wall slip behavior of viscoplastic fluids. In this study an analytical model of the extrusion of viscoplastic fluids under isothermal and fully-developed conditions in shallow channels is developed. The model accommodates the use of different slip coefficients at barrel and screw surfaces. It thus permits the investigation of effects of introducing different materials of construction for the barrel and screw surfaces and development of design expressions.     

An analytical model for steady coextrusion of viscoplastic fluids in thin slit dies with wall slip

Coextrusion is widely used to fabricate multilayered products with each layer providing a separate functionality, including barrier resistance to gases, strength, and printability. Here an analytical model of the coextrusion die flow of two incompressible, viscoplastic fluids in a slit die, subject to nonlinear wall slip and under fully developed and isothermal conditions, is developed to allow the prediction of the steady‐state velocity and shear stress distributions and the flow rate versus pressure gradient relationship. The resulting model is applied to the coextrusion of two layers of viscoplastic fluids in a thin rectangular slit die (slit gap, h ? slit width, W). The analytical solution recognizes a number of distinct flow conditions (eleven cases) that need to be treated separately. The solutions for all eleven cases are provided along with an apriori identification methodology for the determination of the applicable case, given the shear viscosity and wall slip parameters of the two viscoplastic fluids, the slit geometry and the flow conditions. Simplifications of the model would provide the solutions for the fully developed and isothermal coextrusion flows of any combination of Hershel‐Bulkley, Bingham, power‐law and Newtonian fluids with or without wall slip at one or both walls of the slit die. POLYM. ENG. SCI., 2010. © 2009 Society of Plastics Engineers     

Rheological behavior of zirconia feedstock flowing through various channels considering wall-slip

The existence of wall slip for ZrO₂ feedstock flow in micro powder injection molding was investigated based on capillary rheometer experiments using dies of three dimensions. A power law function was derived by data fitting to determine the wall slip velocity based on which numerical simulation was carried out to explore the influence of wall slip on micro injection molding. Experimental results indicate that the feedstock is less sensitive to temperature fluctuation at higher shear rates. Power-law model can provide higher accuracy than the modified Cross model to depict the rheological behavior of the feedstock in capillary flows with different channels. Numerical simulation results show that in case of steady flow higher dynamic viscosity of the feedstock and higher pressure losses of the flow appeared when the wall slip boundary was included as compared to no-slip assumption in micro powder injection molding. This is because that when the wall slip boundary was included the shear rate distribution of the feedstock was lower than that of the feedstock assuming no-slip boundary.     

温度和固相粒径与浓度对水煤浆管内流动壁面滑移的影响

通过改变管径、温度、煤粉粒度和浓度,在中试规模的输送装置上研究水煤浆直管内的滑移流动规律,联合采用Mooney滑移修正方法和Tikhonov正则化方法确定浆体壁面滑移特性。结果表明,随温度和固相粒径的增大,临界剪切应力降低,壁面滑移速度显著增加;浓度越高,临界剪切应力及产生相同滑移速度所需的壁面剪切应力越大,温度升高对临界剪切应力和屈服应力的降低越显著;低壁面剪切应力下的滑移贡献率主要取决于临界剪切应力及屈服应力的相对大小,高壁面应力下主要取决于壁面滑移速度和浆体真实流变特性。     

The Rheological Behavior of Salt Tolerant Polyacrylamide Solutions

The rheological behavior of viscoelastic fluids was investigated with regard to the specialty of tertiary oil recovery. Aqueous polyacrylamide solutions at different concentrations were selected to simulate viscoelastic polymer systems, and the Haake RS 150 type rheometer was used to measure the rheological behavior. The experimental results showed that the viscoelasticity was positively influenced by polyacrylamide solution concentrations and negatively affected by solution temperatures. The coefficient of first normal stress deference decreased with increasing shear rate. In addition, the relationship between viscosity and the coefficient of first normal stress with shear rate obeyed a power law model. The viscosity decreased with increasing metal ion concentration and time.     

Thickness uniformity of HDPE blown film: Relation to rheological properties and density

Previous work has elucidated that the wall slip velocity and viscosity of polymer melts influence the thickness uniformity of blown film. The present study investigates the effects of the stress dependence of wall slip, the shear thinning and the density on the uniformity. We have prepared high‐density polyethylenes with a variety of molecular weight distributions, which have different rheological properties. Examination of the thickness uniformity of their blown film has shown that the uniformity is correlated with wall slip velocity, the stress dependence of the velocity, melt viscosity, shear thinning and density; the coefficient of the correlation is determined to be 0.990. The reason why the stress dependence of wall slip and the shear thinning affect the uniformity is explained in terms of polymer melt flow behavior in a die, while the effect of density is interpreted considering bubble fluctuation in the blow‐up process. Polym. Eng. Sci. 44:965–972, 2004. © 2004 Society of Plastics Engineers.     

FLOW OF VISCOPLASTIC FLUIDS ON AN INCLINED PLANE: EVALUATION OF YIELD STRESS

Within the general category of so called generalized Newtonian fluids, there exists a class of materials which do not deform until the applied shear stress exceeds a critical value called yield stress. Conversely, such a material behaves like a solid as long as the shear stress is less than the yield stress. This class of materials is called viscoplastic fluids. The question whether the true yield stress exists or not is indeed far from settled (1), but the notion of a yield stress has proved to be quite useful in practice in describing the steady shear rheological behaviour of a range of materials especially of particulate suspensions. Consequently, yield stress appears as a parameter in all constitutive relations (which purport to describe the steady shear behaviour of viscoplastic materials), and its evaluation is important before an engineering flow problem can be solved. Conversely, there are some simple hydrodynamic situations which allow the value of the yield stress to be extracted from macroscopic quantities such as flow rate-pressure drop data. In this paper, we examine this possibility using gravity driven flow of a viscoplastic material on an inclined plane.     

Wall Slip of Linear Polymer Melts During Ultrasonic‐assisted Micro‐injection Molding

The wall slip of linear polymer melts under ultrasonic vibration is investigated by correcting the slip mechanism, and melt flow behaviors in ultrasonic‐assisted micro‐injection molding (UμIM) method are discussed. Based on the effect mechanism of ultrasonic vibration on the melt, theoretical models of the critical shear stresses for the onset of weak and strong wall slip during UμIM are established, and the change in rheological properties due to the onset of wall slip under ultrasonic vibration is experimental investigated by a built measurement system. The results show that the onset of weak and strong wall slip of the melt in micro cavity are promoted by ultrasonic vibration, which agree with the built theoretical models, and the melt filling capability in micro cavity is enhanced by reducing apparent viscosity and releasing shear stress of the polymer melt, which improves the molding quality of micro polymer parts via UμIM method. POLYM. ENG. SCI., 59:E7–E13, 2019. © 2018 Society of Plastics Engineers     

Dilatancy of concentrated suspensions with Newtonian matrices

Suspensions filled close to their maximum packing fraction present special challenges in their processing and in their rheological characterization. In this report, the literature in the area of dilatancy of concentrated suspensions is reviewed. Furthermore, the shear viscosity of a Newtonian polymeric liquid filled with 60 vol. percent of ammonium sulfate has been investigated. Both capillary and parallel disk torsional flows, were employed, spanning three decades in shear stress. Upon correction for slip, the suspension exhibited shear thinning at low shear stresses and shear thickening at higher shear stresses. Above a critical wall shear stress, the shear viscosity of the suspension increased unboundedly and the flow became pluglike with apparent slip at the wall. These findings have important ramifications in the processing of composites from such concentrated suspensions.     

Slip flow of coal water slurries in pipelines

Experiments were carried out on a pilot scale slurry transport apparatus to investigate slip flow behavior of coal water slurries (CWSs) in pipes with various diameters (25, 32, 40 and 50 mm). The effects of volume concentration, particle size and slurry temperature on wall slip behavior (wall slip velocity, critical wall shear stress and slippage contribution) were investigated. A numerical technique based on Tikhonov regularization was applied to determine the wall slip behavior. As the slurry temperature or the particle size increased, the critical wall shear stress was observed to decrease and the wall slip velocity was observed to increase significantly, while when the solid concentration was very close to the maximum packing fraction, a slight increase in volume concentration would lead to a rapid decrease in wall slip velocity and a sharp increase in critical wall shear stress. The temperature influence on critical wall shear stress and yield stress increased as volume concentration increased. At low wall shear stress, the slippage contribution was mainly dependent on the difference between yield stress and critical shear stress. While at high wall shear stress, it was dependent on both of the shear viscosity of the bulk slurries and the wall slip velocity.     

Flow behavior of polyacrylamide solution. III. Mathematical treatment

The flow behavior of polyacrylamide solutions was systematically determined over a wide range of temperatures (20–50°C) and concentrations (20–50 ppm) by using a coaxial cylinder viscometer. The results indicated that the rheological behavior of low-concentration polyacrylamide solution behaves similar to non-Newtonian fluids at all these concentrations. The effect of temperature on the consistency coefficient and flow behavior index of polyacrylamide solution of the different concentrations followed an Arrhenius-type relationship. Moreover, the effect of concentration on consistency coefficient and flow behavior index followed an exponential-law relationship at the temperatures used. The rheological constants for the Arrhenius and exponential-law models were determined. The combined effect of temperature and concentration on the coefficient of dynamic shear stress can be represented by a single equation: shear stress = 2.446 × 10⁻⁷exp(0.0639C + 3613/RT)(shear rate)^{2.337 exp(−0.00707C−245/RT)}. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 82: 2784–2789, 2001     

Experimental study and modeling of wall slip of polymethylmethacrylate considering different die surfaces

Wall slip of polymethylmethacrylate (PMMA) was studied on different flow channel surfaces using a rheological slit die and a high pressure capillary rheometer. As die surfaces polished steel, ground steel, and Si doped Diamond like carbon (DLC) were used. A new wall slip model is presented in this paper which assumes a lubricating film between the polymer melt and the die surface. The slip velocity has a power law dependency on wall shear stress. In the double logarithmic plot the wall slip curves are linear and can be parallel shifted to higher values with increasing temperature. The predicted dependencies of the wall slip velocity could be confirmed with experiments conducted with PMMA on polished steel. Furthermore, the die surface influences the flow behavior of PMMA. No wall slip was found on ground steel and on DLC. No complete film could be established by the lubricant on the ground steel die wall. The DLC‐coating exhibits a similar surface roughness and surface energy to polished steel, but the chemical composition is different. It is a metastable form of amorphous carbon containing sp² and sp³ bonds. As a consequence slip additives have a low ability to bond to this material. POLYM. ENG. SCI., 58:1391–1398, 2018. © 2017 Society of Plastics Engineers     

水焦浆的流变特性与壁面滑移效应

在浆体流动试验系统上采用不同管径的直管考察了水焦浆的流变特性以及壁面滑移效应对水焦浆流动特性的影响。采用Tikhonov 正则化方法确定了水焦浆的真实流变特性和壁面滑移特性。结果表明：浓度为59.8%的水焦浆随剪切速率增大呈现由伪塑性流体到胀塑性流体的转变,浓度增加,水焦浆变为单一的胀塑性流体,当浓度达到63.4%时,水焦浆表现为由胀塑性流体到伪塑性流体的转变;水焦浆的流变特性对滑移速度的变化趋势具有较大影响,滑移速度在水焦浆为胀塑性流体时随剪切应力增加呈加速增加,水焦浆为伪塑性流体时滑移速度随剪切应力的增长速率变化不明显;滑移贡献率的变化趋势迟滞于流变特性曲线。     

Tribological Design by Molecular Dynamics Simulation: Influence of the Molecular Structure on Wall Slip and Bulk Shear

The tribological properties of a complex branched-hydrocarbon oil under shear in a gap between smooth iron atom surfaces were studied by large-scale molecular dynamics (MD) simulation. The liquid was a nonpolar lubricant, i.e. a polyalphaolefin (PAO) oil mixture of 1-decane dimer, trimer, and tetramer molecules. The rheological characteristics of the lubricant, including the shear stress and viscosity as well as the relaxation time of the liquid molecule, were calculated. The results show that, as the number of branches of the liquid molecule increases, the shear stresses and the wall slip increase. However, for a mixture fluid containing three different branched molecules, the wall slip decreases in comparison to a liquid consisting of only one kind of branched molecule.     

Scherfließen und Wandgleiten von Massen für den Pulverspritzguss

This contribution presents coupling of laws for shear flow and wall slipping by the shear stress at the slipping interface. It includes the special case of Coulombian friction postulated by Uhland as well as the assumption of a constant sliding velocity along the flow channel according to Mooney. As an example, Ostwald and de Waele's law of shear thinning flow is combined with a shear stress of sliding depending on internal pressure by a power law. Examined feedstocks for metal injection molding showed a rheological behavior according to the model presented.     

Couette grain flow experiments: The effects of the coefficient of restitution, global solid fraction, and materials

Granular flows are complex flows of solid granular material which are being studied in several industries. However, it has been a challenge to understand them because of their non-linear and multiphase behavior. The present experimental work investigates granular flows undergoing shear, by specifically studying the interaction between rough surfaces and granular flows when the global solid fraction and the material comprising the rough shearing surface are varied. A two-dimensional annular shear cell, with a stationary outer ring and inner driving wheel, and digital particle tracking velocimetry (DPTV) technique were used to obtain local granular flow properties such as velocity, local solid fraction, granular temperature, and slip. A customized particle drop test apparatus was built to experimentally determine the coefficient of restitution (COR) between the granular and surface materials using high-speed photography. Results showed that wheel surface materials that produce higher COR values exhibit higher velocity and granular temperature values near the wheel, and lower slip velocities. The local solid fraction appears inversely related to the COR values. The global solid fraction seemed to correspond with velocity and granular temperature, while displaying an inverse relationship to slip. Results also showed an initial decrease in the kinetic energy of the flow as the global solid fraction increased, due to the formation of a distinct contact region. This was followed by a rise in kinetic energy as the global solid fraction continued to increase, based on the increase of particles present in the kinetic region of the flow.     

A mechanism for extrusion instabilities in polymer melts

A mechanism for explaining some of the instabilities observed during the extrusion of polymer melts is further explored. This is based on the combination of non-monotonic slip and elasticity, which permits the existence of periodic solutions in viscometric flows. The time-dependent, incompressible, one-dimensional plane Poiseuille flow of an Oldroyd-B fluid with slip along the wall is studied using a non-monotonic slip equation relating the shear stress to the velocity at the wall. The stability of the steady-state solutions to one-dimensional perturbations at fixed volumetric flow rateis analyzed by means of a linear stability analysis and finite element calculations. Self-sustained periodic oscillations of the pressure gradient are obtained when an unstable steady-state is perturbed, in direct analogy with experimental observations.     

Compression molding of glass reinforced thermoplastics: Modeling and experiments

The shearing and extensional behavior of glass mat‐thermoplastic (GMT) material under compression molding was investigated with a special model being developed for the case of non‐lubricated mold‐plate surfaces. Mathematical expressions for the radial and through‐thickness flow velocities were derived that enabled the derivation of extensional and shear strain rates. The GMT non‐lubricated (no‐slip wall conditions) compression molding was modeled as a combination of extensional and shearing flow and the two extensional and shear viscosities were determined. Scott's approach was used in this work to determine the radial velocit in the r‐direction, which depends on the shear power‐law expression. The velocity component in the z‐direction was then calculated using the continuity equation. The velocity profiles were used to calculate the shear and extensional strain rates. Scott's shear viscosity did not satisfy the constitutive equation for the extensional part, but a power‐law expression with new parameters depending on the deformation tensors was successfully used to calculate an independent extensional viscosity using the same non‐lubricated squeezing experiment. Lubricated squeezing flow was carried out for the same material to achieve a pure extensional flow, and the extensional viscosity calculated using this approach agreed with the extensional viscosity determined using the non‐lubricated experiment. GMT material used in this study is confirmed to have two layers of continuous long fibers orientated randomly inplane, separated by short chopped fibers in the middle, which suggests that the material can be treated as an isotropic material, and the fiber‐matrix separation is seen to be high at the extremities of the flow.     

Das Beschichten von Oberflächen

The coating of different substrates is an important part of many industrial manufacturing processes. The fluids used in these processes have very different rheological properties. They are coated to solid surfaces with high substrate velocities by dipping, spraying, casting or by the use of knives, blades and rollers. The field of flow between two rotating rollers is influenced by the free surface of the fluid and the contact point between the three phases, solid roller, coating fluid, and the surrounding gas. Viscous, inertial, gravitational and capillary forces control the velocity field between the rollers. Stable fluid coatings that satisfy the increasingly stringent demands on the quality of their surface structure have to be created within certain limits of the forces occurring. In order to predict these limits, the flow fields have to be completely calculated. Therefore all three conservation equations and an additional equation for the position of the free surfaces are solved with consideration of the constitutive equations and possible wall slip effects of the coating fluids.