Wall slip and its implications in the design of single screw melt-fed extruders

The phenomenon of wall slip during the capillary flow of polymer melt is investigated for low and high density polyethylene. It is found that wall slip occurs in both cases, and that the effect is related to melt fracture. In addition, it is shown that a silicone fluid exhibits wall slip. The performance of the metering zone of a 38 mm diameter single-screw extruder is discussed in relation to wall slip. It is suggested that the power consumption of the extruder is reduced as a result of slip at the polymer/metal interface. Results based on experiments with the silicone fluid tend to support this hypothesis. A theoretical analysis of the effects of wall slip upon throughput rate and power consumption for a one-dimensional isothermal Newtonian case is included.     

Flow instability in polymer solutions and melts

The existing experimental data concerning the problem of flow instability in polymer solutions and melts is considered and critically discussed. The instability is understood as both regular distortions of the jet surface shape and turbulence of the flow as such. The visual manifestations and physical mechanisms determining the development of flow instability are analyzed and classified. The following principal forms of instability are distinguished: small-scale regular surface defects, periodic oscillations with the scale of the jet diameter, the slip—stick periodic transition phenomenon, self-oscillations of the stream, jet spurt, and large-scale distortions passing into stream discontinuities. In all cases, the instability of the jet is due to rubber elasticity of polymer fluids, a property which causes storage of elastic energy during deformation with its subsequent release in the form of stream distortions. Therefore, the general criterion for the onset of instability is a certain critical value of the Weissenberg number. The key factors determining the loss of the flow stability are concentration of stresses at the channel outlet, transition from laminar flow to slip along a solid wall (adhesive ruptures) under certain critical conditions, and mechanical fracture (cohesive ruptures) of a material. In the appearance of hysteresis oscillations, bulk elasticity and compressibility of the melt also play a certain role. Alternative mechanisms proposed in the literature are also discussed. Examples illustrating the possibility of suppressing jet distortions are given; this suppression is important for many industrial applications in polymer processing.     

Gas‐Solid Drag Coefficient for Ordered Arrays of Monodisperse Microspheres in Slip Flow Regime

Numerous analytical and numerical correlations for the drag force of particles in packed arrays are not applicable to microspheres because of the invalidity of the no‐slip assumption at a solid wall. The slip flow through assemblages of spheres is investigated by the lattice Boltzmann method (LBM). Three periodic arrays of static and monodisperse particles, i.e., a simple cubic, a body‐centered cubic, and a face‐centered cubic array, each with a relatively wide range of solid volume fraction, are considered. The LBM is validated for the slip flow over a single unbounded sphere and the continuum flow through spheres in a simple cubic array. The LBM results agree well with the experimental and numerical data in the literature. Simulations of slip flow through the three ordered arrays of spheres are performed. The effects of solid volume fraction and slip are both quantified within the developed drag laws.     

气体在任意截面形状微尺度槽道中的滑移流动

利用正交函数法对气体在具有任意截面形状的微尺度槽道内的充分发展层流滑移流动特性进行了理论分析,获得了任意截面形状微槽道内的速度分布和流动阻力特性的分析解,并以矩形微槽为例分析了微槽截面上的速度分布和阻力特性.结果表明：随Kn数的增加,由于壁面处滑移流动的影响,气体流经微槽的流动阻力常数小于大尺度理论预测值;理论分析解的结果与实验结果吻合较好,表明在一定的Kn数范围内Navier-Stokes方程在考虑了速度滑移后可以描述微通道内的气体流动过程;正交函数法在微槽内滑移流动的分析中是可行的.     

Squeezing flow of viscoplastic fluids subject to wall slip

Polymer processing operations such as compression molding, sheet forming and injection molding can be modeled by squeezing flows between two approaching parallel surfaces in relative motion. Squeezing flows also find applications in the modeling of lubrication systems, and in the determination of rheological properties. Here, analytical solutions are developed for the constant-speed squeezing flow of viscoplastic fluids. It is assumed that the fluid is purely viscous, and hence viscoelastic effects unimportant. The rheological behavior of the viscoplastic fluids is represented by the Herschel-Bulkley viscosity function. The deformation behavior of commonly encountered viscoplastic fluids is generally complicated by the presence of wall slip at solid walls, which is a function of the wall shear stress. The slip coefficient that relates the slip velocity to the shear stress is affected by the material of construction and also the roughness of the solid surfaces, leading to the possibility of different slip coefficients at various solid surfaces. The model developed in this study accommodates the use of different slip coefficients at different solid surfaces. The accuracy of the solutions is established, and the effects of various parameters such as slip coefficient and apparent yield stress are examined. The solutions provide useful design expressions that can be utilized for squeezing flows of viscoplastic fluids, with or without wall slip at the solid boundaries.     

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     

Effects of wall-heating on the linear instability characteristics of pressure-driven two-layer channel flow

The linear stability analysis of a pressure-driven two-layer channel flow of two immiscible, Newtonian and incompressible fluids is considered. The walls of the channel are maintained at different constant temperatures and Nahme's law is applied to model the temperature dependence of the fluid viscosity. A modified Orr–Sommerfeld equation for the disturbance streamfunction coupled to a linearized energy equation is derived and solved using a spectral collocation method. Our results indicate that increasing the dimensionless top wall temperature has a non-monotonic effect on the linear stability characteristics. We also found that increasing the thermal conductivity and density ratios stabilise the flow for the set of parameter values considered; the viscosity ratio has a non-monotonic effect on the maximal growth rate. An energy ‘budget’ analysis shows that the most dangerous mode is of ‘interfacial’ type.     

EVALUATION OF POLYMER ADSORPTION-GEL FORMATION AND SLIP IN POLYMER SOLUTION FLOWS

A superposition model for evaluation of the effects of polymer adsorption-gel formation and slip of polymer solutions exhibiting both phenomena has been applied to the capillary flow of aqueous solutions of two molecular weight grades of hydroxyethyl cellulose (Natrosol 250, types G and HR, supplied by Hercules Powder Company). The flow behaviour of the solutions investigated was non-Newtonian. Evaluations are presented of the effective thicknesses of polymer adsorption-gel formation and pure solvent layers, as a function of the wall shear stress, tube radius and polymer concentration, corresponding to the determinations of the effective velocity at the wall.

The results of the analysis indicate the surface characteristics undergo a dramatic change from polymer adsorption-gel formation at the tube surface to the phenomenon characterized by slip in a narrow tube radius interval which has important implications in enhanced oil recovery by polymer solution floods. It also provides an explanation for the contrasting behaviours observed in the flow of aqueous Natrosol solutions through packed beds (Sadowski, 1963) and filter cakes (Kozicki et al., 1972).     

Surface phenomena in capillary flow of polymer solutions

Evaluations of apparent slip and polymer adsorption are reported for laminar capillary flow of dilute aqueous solutions of the three homologues WSR 301, Coagulant and FRA of Polyox. Measurements were carried out using glass tubes coated with a silane compound (dimethyldiethoxysilane) as well as for the untreated glass tubes. The results indicate that flow enhancement is dominant at the very low polymer concentrations and flow retardation is dominant at the higher concentrations comprising the polymer concentration range investigated. A transition from a positive to a negative effective velocity at the wall was observed with increasing polymer concentration. A new analysis was applied to separate the contributions of polymer adsorption and slip in the evaluation of the effective velocity at the wall. Effective hydrodynamic thicknesses of the adsorbed polymer layers are presented as a function of the polymer molar mass and concentration and the wall shear stress. The thickness of the adsorbed layer at zero shear was also evaluated from the capillary flow data.     

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.     

Effect of wall slip on the uniformity of flow from sheeting extrusion dies

A theoretical study for analyzing the uniformity of flow from sheeting extrusion dies is presented. In this study it is assume that a slip condition exists at the wall of the die, the magnitude of slip velocity is proportional to the shear stress at the wall, the flow is isothermal and steady state, and a power law model is valid for viscosity. Two extrusion dies, T-dies and coat-hanger dies, are examined. The flow uniformity at the exit of the die is calculated and compared with that for a nonslip analysis. The discrepancies between the slip and nonslip models imply that the wall slip condition induces a significant nonuniform flow distribution. Traditional design criticism based on the nonslip model are invalid for flow with the wall slip condition, and it is necessary to increase the length of the die land to even the flow distribution at the exit of the die.     

Wall slip heating

When molten plastic is extruded, the upper limiting throughput is often dictated by fine irregular distortions of the extrudate surface. Called sharkskin melt fracture, plastics engineers spike plastics formulations with processing aids to suppress these distortions. Sharkskin melt fracture is not to be confused with gross melt fracture, a larger scale distortion arising at throughputs higher than the critical throughput for sharkskin melt fracture. Sharkskin melt fracture has been attributed to a breakdown of the no slip boundary condition in the extrusion die, that is, adhesive failure at the die walls, where the fluid moves with respect to the wall. In this article, we account for the frictional heating at the wall, which we call slip heating. We focus on slit flow, which is used in film casting, sheet extrusion, curtain coating, and when curvature can be neglected, slit flow is easily extended to pipe extrusion and film blowing. In slit flow, the magnitude of the heat flux from the slipping interface is the product of the shear stress and the slip speed. We present the solutions for the temperature rise in pressure‐driven slit flow and simple shearing flow, each subject to constant heat generation at the adhesive slip interface, with and without viscous dissipation in the bulk fluid. We solve the energy equation in Cartesian coordinates for the temperature rise, for steady temperature profiles. For this simplest relevant nonisothermal model, we neglect convective heat transfer in the melt and use a constant viscosity. We arrive at a necessary dimensionless condition for the accurate use of our results: Pé?1. We find that slip heating can raise the melt temperature significantly, as can viscous dissipation in the bulk. We conclude with two worked examples showing the relevance of slip heating in determining wall temperature rise, and we show how to correct wall slip data for this temperature rise. POLYM. ENG. SCI., 55:2042–2049, 2015. © 2014 Society of Plastics Engineers     

Wall slip of concentrated suspension melts in capillary flows

The effects of wall slip of concentrated suspension melts in capillary flows were investigated at elevated temperature. The modeled material is a mixture of polymer EVA (Ethylene Vinyl Acetate) and non-colloidal spherical powder (glass microspheres) with mean particle size within 53∼63 μm. The effect of particle concentration on wall slip was studied experimentally in a capillary rheometer. For suspensions with different particle loadings (35%, 40%, and 45% by volume), the slip velocity V_s increased with an increase of particle concentration at the same testing temperature. A master slip curve can be obtained by plotting slip velocity versus the product of wall shear stress and square root of particle concentration. As such, a new particle concentration-dependent slip model is proposed. A theoretical approach coupled with the new slip model and flow equation is employed to characterize the flow behavior of concentrated suspension in a capillary rheometer, with reasonable agreement obtained with experimental observations.     

Flow of wet powder in a conical centrifugal filter—an analytical model

A one-dimensional analytical model is developed for the steady state, axisymmetric, slender flow of saturated powder in a rotating perforated cone. Both the powder and the fluid spin with the cone with negligible slip in the hoop direction. They migrate up the wall of the cone along a generator under centrifugal force, which also forces the fluid out of the cone through the powder layer and the porous wall. The flow thus evolves from an over-saturated paste at inlet into a nearly dry powder at outlet. The powder is treated as a Mohr–Coulomb granular solid of constant void fraction and permeability. The shear traction at the wall is assumed to be velocity and pressure dependent. The fluid is treated as Newtonian viscous. The model provides the position of the colour line (the transition from over- to under-saturation) and the flow velocity and thickness profiles over the cone. Surface tension effects are assumed negligible compared to the centrifugal acceleration. Two alternative conditions are considered for the flow structure at inlet: fully settled powder at inlet, and progressive settling of an initially homogeneous slurry. The position of the colour line is found to be similar for these two cases over a wide range of operating conditions. Dominant dimensionless groups are identified which control the position of the colour line in a continuous conical centrifuge. Experimental observations of centrifuges used in the sugar industry provide preliminary validation of the model.     

Modelling laminar pulsed flow in rectangular microchannels

Fully developed laminar pulsed flow of an incompressible Newtonian fluid through rectangular ducts has been modelled and analyzed using Green functions. Based on the solutions for the velocity profile presented previously [Fan, C., Chao, B.-T., 1965. Unsteady, laminar, incompressible flow through rectangular ducts. Zeitschrift für Angewandte Mathematik und Physik 16, 351-369], exact analytical solutions in series form for wall shear stress and volumetric flow rate have been obtained. Various flow effects in periodic pulsed flow through rectangular microchannels, including flow reversal, phase shift and wall shear stress enhancement were calculated indicating that a substantial increase in local wall shear stress can be achieved with a modest increase of average flow rate over a cycle. The analytical solutions and the calculated results will help optimize parameters in cleaning of microfluidic devices by pulsed flow.     

Tube flow of a particulate-filled thermosetting polymer

The conservation equations of momentum, energy, and mass are numerically solved for the flow of filled thermosets reacting In a tube. The flow is assumed to be laminar and adiabatic with a constant volumetric flow rate. The critical radii are parameters that define the processability limits. The lower one is the value of the radius where an undesirable advance in the reaction extent takes place at the wall or where viscous heating leads to degradation. The upper critical radius is the radius where wall velocity is low and gelation takes place. The effects of filler volumetric fraction, wall slip velocity, and different inlet conditions are taken into account. Increasing wall slip velocity or filler fraction and decreasing inlet temperature or tube length amplify the processability zone.     

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.     

Analysis on the apparent slip and depleted layer of polymer flow in narrow-bore capillaries

Polymer solutions flowing through small-diameter capillaries of which length scale is much larger than that of polymers were experimentally demonstrated to have the enhanced flow rate as compared to in bulk flow. Thisapparent slip phenomenon was analyzed by obtaining theslip velocity and concentrationdepleted layer thickness. Hydrolyzed polyacrylamide (HPAM) of highly flexible polymer and Xanthan of rigid rodlike polymer were made to flow through stainless steel capillaries having the diameter range of about 100 to 250 μm. The results showed that both slip velocity and depleted layer thickness decreased markedly with increasing polymer concentration. This behavior can be interpreted as being due to the reduction of diffusion coefficient and flexibility of polymer chains as the concentration is increased. The depleted layer thickness of HPAM was much larger than the polymeric length scale and was shown to increase with increasing wall shear stress. This is considered as an evidence of thestress-induced diffusion of polymer chains being a dominant factor for the apparent slip of flexible polymer solution. On the other hand, the depleted layer thickness of Xanthan solution was almost constant with the wall shear stress, which can not be explained by the stress-induced diffusion mechanism alone.     

Effect of wall slip on blown film thickness distribution

One of the most important materials for blown film is high‐density polyethylene (HDPE) with wide molecular weight distribution. First, we computed a wall stress at the entrance of a spiral groove in a particular die during blown film processing on a particular condition, to which a similar condition is widely utilized in a film works. The computed value is about 170 kPa, while the HDPE melt slips at die wall at stresses above approximately 50 kPa. The stress of 170 kPa is sufficiently large for the slip occurrence of the melt. Then, we investigated the effects of wall slip and melt visosity on film thickness distribution in the circumferential direction; the distribution tends to decrease with decreasing wall slip and melt viscosity. This tendency is explained by considering flow distribution in a spiral mandrel die and polymer melt flow characteristics.     

Vérification expérimentale de l'épaisseur du film pour des liquides non-newtoniens s'écoulant par gravité sur un plan incliné

The film thickness of twelve different polymeric solutions in a stable, laminar flow on a plane of known inclination has been measured as a function of the volumetric flow rates of the fluid. The theoretical value of the film thickness has been calculated using the Ostwald-de Waele model, neglecting any apparent slip at the wall. The results obtained from over 250 experimental determinations show that the film thickness can be predicted within 4% by using the Ostwald-de Waele model. However evaluation of the film thickness based on a Newtonian behavior with viscosity determined at the wall clearly indicates that the thickness is not much influenced by any variation of viscosity across the film. Hence the gravity flow along inclined plane surfaces is not a severe test of a rheological equation.