Flow behavior of polypropylenes with different molecular structures in a coat‐hanger die

An experimental investigation of the flow behavior of three polypropylene melts with different molecular structures during extrusion through a coat‐hanger die is presented. Two linear and one long‐chain branched material, rheologically characterized in shear and elongation, were investigated. Using laser–Doppler velocimeter measurements of the velocity profiles across the gap height were performed at five various locations along the die. The uniformity of the velocity distribution along the die has been assessed using the maximum velocities v₀ of the corresponding velocity profiles across the gap. The velocity distribution along the die changes with throughput and temperature. Regarding the rheological properties, it was found that the power‐law index of the viscosity as a function of shear rate has a decisive influence on the uniformity of flow but that the pronounced strain hardening in elongation typical of the long‐chain branched polypropylene is not reflected by the velocity distribution along the die. POLYM. ENG. SCI., 2012. © 2012 Society of Plastics Engineers     

Kinematics of the stick-slip capillary flow of high-density polyethylene

A study of the kinematics of the stick-slip capillary flow of high-density polyethylene has been carried out in this work by using particle image velocimetry (PIV). The experiments covered a wide range of shear rates and the velocity maps and profiles across the die were obtained for the different regimes of the discontinuous flow curve. In the low shear rate region, the melt exhibited shear thinning without slip. In the unstable stick-slip regime, an alternating behavior between full adhesion and slip was observed, whereas both, the maximum velocity and the slip velocity of the melt, changed continuously during pressure oscillations. In addition, non-homogenous slip, characterized by regions with and without slip at the die wall, was occasionally observed during the oscillations. In contrast to the general assumption, the flow in the high shear rate region was found to be unstable, and characterized by high frequency pressure oscillations. A steep rise of the slip velocity took place from the onset of the stick-slip regime and reached values higher than 70% of the maximum velocity for the profiles in the high shear rate branch. However, a true plug flow was never observed due to shear thinning of the melt. Finally, a direct proof of the Mooney hypothesis to account for slip in polymer melts is given on the basis of the comparison of velocity profiles measured in the low and high shear branch.     

Influence of slip on the flow of a yield stress fluid around a flat plate

This experimental study deals with the influence of slip on the non‐inertial flow of a viscoplastic fluid around a flat plate moving at a constant velocity. The bulk and interfacial properties of the fluid have been finely characterized. The drag force has been analyzed with regards to the flow velocity and for two tribological conditions: adherence and slip. This force decreases with the velocity and is reduced in the presence of slip. Kinematic fields have also been measured by Particle Image Velocimetry (PIV), to determine the influence of both the velocity and the tribological conditions on the liquid and solid regions of the flow. The results highlight no significant influence of the flow velocity on the thickness of the boundary layer and rigid zones. The wall shear stresses along the plate obtained from force measurements and slip velocities are then compared to rheometrical measurements. © 2015 American Institute of Chemical Engineers AIChE J, 62: 1356–1363, 2016     

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.     

Measurements of slip velocity and frictional heating in the capillary extrusion of linear‐low‐density polyethylene with a fluoropolymer processing aid

The slip velocity and frictional or slip heating of linear‐low density polyethylene with a fluoropolymer processing aid in capillary flow were measured by rheo‐particle image velocimetry and thermal imaging. The pure polymer did not show slip before the stick‐slip regime but exhibited strong slip when blended with the processing additive. However, for shear stresses beyond the stick‐slip regime, the pure polymer and the blend exhibited the same flow behavior with slip. The slip velocity increased with the shear stress at two different rates before and after the stick‐slip and the contribution of slip to the total flow rate exhibited a minimum. Significant rises in temperature were measured under slip and no slip conditions, being these much higher than the values predicted by the adiabatic flow assumption. Clear difference was made between viscous and frictional heating before the stick‐slip regime, even though they could not be distinguished from one another at higher stresses. Overall, in the presence of slip, frictional and viscous heating act synergistically producing higher temperature rises in the melt. Finally, in contrast to predictions by numerical simulations of viscous heating, measured velocity profiles did not evidence the heating effects in the shear stress range analyzed in this work. POLYM. ENG. SCI., 56:837–845, 2016. © 2016 Society of Plastics Engineers     

Effects of wall slip on the rheological measurement and extrusion die design of a filled rubber compound

We investigate the rheological properties of a filler-reinforced rubber compound using a rotorless shear rheometer specially designed for rubber and a rotational rheometer with parallel-plate geometry. Our aim is to evaluate the effects of wall slip on both the oscillatory and steady shear modes of the rotational rheometer. The rheological measurements show that the slip generally does not affect the oscillatory shear but does exist in the steady shear flow and tends to make the measured shear viscosity lower than the true value. Besides, we extend the investigation into engineering applications. The extrusion die for a given extrudate profile is obtained using a finite-element model in which the wall slip is considered as a boundary condition. To validate the die design, an extrusion experiment is carried out and the results confirm that, for filled elastomers, it is necessary to consider the effect of wall slip in the extrusion die design.     

Rheological characterization of tomato concentrates and the effect on uniformity of processing

Rheological characterization of tomato concentrates was performed using MR flow imaging with a 0.6T 1H spectrometer. The experimental design included four concentrations (6,9,12, and 16 degress Brix) and four temperatures (20, 50, 90, and 110 degrees C). The flow profiles were best characterized by a Herschel-Bulkley expression. Apparent viscosity showed Arrhenius-type behavior with temperature. Yield stress values were determined directly from the plug region of the flow profiles and independent pressure drop measurements. Yield stresses ranged from 1.3 to 51 Pa and were a function of both temperature and concentration. In addition, slip velocities, which ranged from 2.3 to 7.8 cm/s, were obtained directly from velocity profiles. The slip velocities were analyzed by ANOVA; the mean values were significantly different with respect to both temperature and concentration. Based on this study, the RTD of tomato concentrates is narrower with increasing temperature and concentration during thermal processing due to the slip velocity and yield stress behavior.     

Melt fracture of two broad molecular weight distribution high‐density polyethylenes

The melt fracture instabilities of two broad molecular weight distribution (MWD) high‐density polyethylenes (one Ziegler–Natta and one metallocene HDPEs) are studied as functions of the temperature and geometrical details and type of die (cylindrical, slit, and annular). It is found that sharkskin and other melt fracture phenomena are distinctly different for these resins, despite their almost identical rheology. It is also found that the critical conditions for the onset of various melt fracture phenomena depend significantly on the type of die used for their study. For example, sharkskin melt fracture in slit and capillary extrusion was obtained at much small critical shear stress values compared with those found in annular extrusion. Moreover, the metallocene HDPE shows significant slip at the die wall in the sharkskin flow regime. On the other hand, the Ziegler–Natta HDPE has shown no sign of slip. These differences are discussed on the basis of differences in their MWDs that influence their melt elasticity. POLYM. ENG. SCI., 2011. © 2011 Society of Plastics Engineers     

RHEOLOGICAL CHARACTERIZATION OF TOMATO CONCENTRATES AND THE EFFECT ON UNIFORMITY OF PROCESSING

Rheological characterization of tomato concentrates was performed using MR flow imaging with a 0.6T 1H spectrometer. The experimental design included four concentrations (6,9,12, and 16 degress Brix) and four temperatures (20, 50, 90, and 110 degrees C). The flow profiles were best characterized by a Herschel-Bulkley expression. Apparent viscosity showed Arrhenius-type behavior with temperature. Yield stress values were determined directly from the plug region of the flow profiles and independent pressure drop measurements. Yield stresses ranged from 1.3 to 51 Pa and were a function of both temperature and concentration. In addition, slip velocities, which ranged from 2.3 to 7.8 cm/s, were obtained directly from velocity profiles. The slip velocities were analyzed by ANOVA; the mean values were significantly different with respect to both temperature and concentration. Based on this study, the RTD of tomato concentrates is narrower with increasing temperature and concentration during thermal processing due to the slip velocity and yield stress behavior.     

A dual slit in‐line die for measuring the flow properties of S‐PVC formulations

We have developed an instrumented dual slit die mounted on a twin‐screw extruder. This device allows us to distinguish the predominant flow pattern and calculate the shear viscosity, Cogswell elongational viscosity, and a Mooney wall‐slip velocity. The melt‐down process is also monitored by measuring the screw torque together with temperatures and pressures along the screw barrel. So far, we have seen that many pipe and profile formulations have a predominant plug or slip‐dominated flow behavior in the die, while others can be more sticky. Generally, the sticky highly viscous formulations will be more affected by shear heating effects when exposed to high rates during processing. We also give a detailed discussion, with examples, of how data from the device are to be analyzed and how the correct flow boundary condition is to be identified.     

Sharkskin and oscillating melt fracture: Why in slit and capillary dies and not in annular dies?

The sharkskin and stick‐slip polymer extrusion instabilities are studied primarily as functions of the type of die geometry. Experimental observations concerning the flow curves, the critical wall shear stress for the onset of the instabilities, the pressure and flow rate oscillations, and the effects of geometry and operating conditions are presented for linear low‐density polyethylenes. It is found that sharkskin and stick‐slip instabilities are present in the capillary and slit extrusion. However, annular extrusion stick‐slip and sharkskin are absent at high ratios of the inside‐to‐outside diameter of the annular die. This observation also explains the absence of these phenomena in other polymer processing operations such as film blowing. These phenomena are explained in terms of the surface‐to‐volume ratio of the extrudates, that is, if this ratio is high, sharkskin and stick‐slip are absent. POLYM. ENG. SCI., 2008. © 2007 Society of Plastics Engineers     

Velocity profiling inside a ram extruder using magnetic resonance (MR) techniques

The extrusion of soft-solid materials is an important industrial process. Magnetic resonance imaging (MRI) has been used to acquire in situ velocity profiles during the ram extrusion of two opaque materials representative of those often extruded in industry; a mixture of 5 cSt poly-dimethylsiloxane (PDMS) added to a commercial soap (Dove^TM) (a soft solid), and a stiff biscuit dough (a paste). Radial velocity profiles have been acquired in both the axial and radial directions at different positions within the barrel (25 mm diameter) and die land, during extrusion through two 8 mm diameter cylindrical dies (length 8 and 16 mm), and through a multi-holed die. At a height of 24 mm above the die entrance, both materials exhibit plug flow with pure slip at the barrel wall. Nearer to the die, the flow has converged towards the centre of the barrel and static zones are observed at the barrel walls. The shape of the velocity profiles was found to be independent of ram speed (0.6-1.2 mm/s), and die length. The shape of the velocity profiles is material dependent, with greater shear effects evident in the biscuit dough and compression effects evident in the soap material.     

Using Rheology to Achieve Co-Extrusion of Cement-Based Materials with Graded Cellular Structures

Co-extrusion involves simultaneous extrusion of multiple layers and can be used to produce functionally graded materials whose layers have different properties. Rheological control is vital for successful co-extrusion. During extrusion, flow in the barrel and die land in a ram extruder should be plug-like, while the paste should be sheared and uniformly elongated in the die entry region. In the barrel of the extruder, the paste flow velocity field was inferred by direct observation of the paste left in the barrel, and evidence for plug flow in the barrel was seen only at low-extrudate velocities. In the die land, the Benbow nonlinear model was employed to assess the paste flow behavior, and plug flow was achieved only when the shear stress applied to the paste by the die land wall was smaller than its yield stress. For co-extrusion, a simple method using thin-walled tubes was found to be effective to prepare layered feedrods. Functionally graded cellular structures of cement-based materials were successfully co-extruded by using a low-extrudate velocity when the paste had decreasing shear viscosity from inner to outer layers.     

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     

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     

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.     

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.     

Rheological behavior of uncured styrene‐butadiene rubber at low temperatures,pure and filled with carbon black

The flow behavior of an uncured styrene‐butadiene rubber (SBR) has been studied by using a specific preshearing capillary rheometer in the range of temperatures encountered in extrusion, i.e. between 40°C and 90°C. A pure SBR and various SBR compounds filled with different amounts of carbon black (from 17 to 33 wt%) have been characterized. It was observed, for all tested materials, that the flow curve could be divided in different parts: at low shear rate, the material exhibits a classical behavior, where stress increases regularly with the shear rate. Above a certain critical stress, flow features changed, characterized by the simultaneous onset of wall slip and upstream instabilities. This critical stress is independent of temperature but increases linearly with carbon black amount. Flow curves at different filler contents were superimposed, using a shift factor that varies with filler content. Two theories for time/filler content superposition were proposed. Finally, a general viscosity law for uncured SBR compounds was introduced. This law is based on a Carreau‐Yasuda equation, where zero‐shear viscosity and characteristic time depend on both temperature and filler content, through Arrhenius and Krieger‐Dougherty expressions, respectively. POLYM. ENG. SCI., 55:2156–2162, 2015. © 2015 Society of Plastics Engineers     

Hydrodynamics and flow regimes in turbulent bed contactor with non‐Newtonian liquids

The flow regimes normally encountered in a turbulent bed contactor (TBC) are static, partially fluidised, completely fluidised and flooding regimes. Experiments were conducted in a TBC operating in Type I mode to identify the flow regimes with non‐Newtonian liquid. Flow regime transition velocities were obtained from the pressure drop and bed expansion measurements at various operating and geometric variables. The variables include apparent viscosity of the liquid, gas and liquid velocities, size and density of the particles, and static bed height. The effect of the above variables on delineation of flow regime transition was studied. Based on the experimental data, correlations were proposed for predicting the transition velocity from one regime to the other. The influence of the variables on regime transition velocities is more or less similar to that observed for Newtonian liquids. © 2011 Canadian Society for Chemical Engineering