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.     

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.     

Investigations on the extrusion of rigid PVC on twin screw extruders

The processing of rigid-PVC is mainly performed on twin screw extruders. For a thermal sensitive material, such as rigid PVC, this implies certain advantages. They consist primarily in the fact that intermeshing counter-rotating twin screw extruders are axially closed pump systems, whereas single screw and co-rotating twin screw extruders represent axially open mixing systems, conveying by means of friction forces. This fundamental difference leads to totally different flow rate and shearing force distributions of the axial flow, which in turn affects the residence time distribution and the thermal dynamics of the process. Investigations have been carried out to determine the influence of screw speed, die resistances, barrel wall temperatures and different compounds on the melt temperature and its homogeneity. It could be shown that the melt temperature can be essentially influenced by heating the barrel wall and the screw. This even applies to the most diverging degrees of mechanical power consumption resulting from different compounds. The homogeneity of the melt temperature thus depends on the relationship between the barrel wall temperature and the melt temperature within the respective heating zone. The possibility is shown to establish a model theory based on energetic and rheological similarities, which can be employed in the construction of machines of different diameters. For this purpose the geometrical and operational data of an optimal operating machine serve as a basis.     

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 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.     

Effect of the surface roughness and construction material on wall slip in the flow of concentrated suspensions

Recent studies on polyethylene, elastomers, and thermoplastics have revealed that the construction material and surface roughness are two important factors affecting wall slip. In this study, to determine the true rheological behavior of model concentrated suspensions, a multiple‐gap separation method was used in a parallel disk rheometer. The model suspensions studied were poly (methyl methacrylate) particles with an average particle size of 121.2 μm in hydroxyl‐terminated polybutadiene. The aim of this study was to investigate the effect of disk R_a in the range of 0.49–1.51 μm and disk construction material on the wall slip and the true viscosity of the model concentrated suspensions. The wall slip velocity and the viscosity were found to be independent of R_a for particle size‐to‐disk R_a ratios of 80–247. Also, the true viscosity was found not to be affected by the rheometer surface construction material. Glass surfaces resulted in the highest slip velocity, whereas aluminum surfaces resulted in the lowest slip velocity. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 3341–3347, 2007     

Processing high oil content seeds in continuous screw presses

This paper covers a range of oilseeds from rapeseed to copra-including groundnuts, cocoa beans, and palmkernels—and gives a very brief definition of screw press operation and its terminology. Screw press operation and its essential similarity to that of the hydraulic stroking press are discussed, including an outline of the functions of the various worm assembly stages and how they are basically achieved and essential objectives which must be met as meal passes along the barrel. Also covered are radial and axial pressure gradients within the machine and their effect on processing of high oil content seeds; rates of pressure buildup within the press and their effect on various different high oil content seeds; and materials of construction. Finally, the effect of seed pre-treatment cooking and fines handling on the operation of a screw press on various seeds and essential differences between high pressure pressing and pre-pressing for solvent extraction are discussed.     

Temperature-induced pressure gradient in the clearance between screw flight and barrel of a single screw extruder

The effect of temperature-induced pressure gradients occurring in drag flow in a narrow gap between parallel walls, when a viscosity gradient in flow direction is present is described and analyzed. The effect dominates the technologically important clearance flow problem, where the viscosity gradient originates from temperature changes. The polymer layer in the clearance between screw flight and barrel of a single screw extruder supposedly has to separate the metallic surfaces from each other. In certain operating conditions this bearing function breaks down and dry friction between metallic surfaces occurs. This failure, which has not yet been explained, is reasoned to be caused by the temperature-induced pressure flow in the clearance.     

Effect of process variables on melt temperature profiles in extrusion process using single screw plastics extruder

Abstract

Melt temperature is an important parameter in the melt processing of polymers. However, it is not possible to control melt temperature directly, only to influence it using processing parameters such as processing temperature settings. It is therefore important to know the influence of controllable process parameters on melt temperature. In this work, the relationships between controllable process parameters and melt temperature have been investigated for a 50 mm S + B single screw extruder. The extruder was equipped with a thermocouple mesh at the die inlet to determine melt temperature. It was found that melt pressure, die size, feed section barrel temperature, and compression section barrel temperature had a negligible effect on the melt temperature profiles generated, while increasing the screw speed resulted in higher melt temperatures. The metering section barrel temperature had a significant effect on melt temperature, thermal conduction effects being more important than shear heating effects. Equipment wall temperatures, downstream of the screw, produced changes in the melt temperature in the melt located within 7 mm of the wall. It was found that melt temperatures can be significantly different from those set on the equipment.     

Experimental analysis of the influence of pellet shape on single screw extrusion

Extrusion technology is one of the most prominent methods for processing polymers. The shape of polymer pellets plays an important role in conveying solid material through the extruder and thus directly influences the mass flow rate. In the course of this article, the influence of the pellet shape of a polypropylene homopolymer on the processing conditions using a smooth barrel single‐screw extruder is evaluated. Especially the mass flow rate, the melt temperature, and the pressure build up in the barrel are investigated. It can be shown that processing long cylindrical pellets leads to a higher mass flow rate than comparable experiments with virgin pellets or short cylinders. Additionally, screw cool and pull‐out tests, measurements of the external coefficient of friction as well as the bulk density of the different pellet geometries are performed. The interaction of the screw geometry and the pellet shape is found to have the biggest influence. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 41716.     

Effect of volume fraction and particle size on wall slip in flow of polymeric suspensions

For especially highly concentrated suspensions, slip at the wall is the controlling phenomenon of their rheological behavior. Upon correction for slip at the wall, concentrated suspensions were observed to have non‐Newtonian behavior. In this study, to determine the true rheological behavior of model concentrated suspensions, “multiple gap separation method” was applied using a parallel‐disk rheometer. The model suspensions studied were polymethyl methacrylate particles having average particle sizes, in the range of 37–231 μm, in hydroxyl terminated polybutadiene. The effects of particle size and solid particle volume fraction on the wall slip and the true viscosity of model concentrated suspensions were investigated. It is observed that, as the volume fraction of particles increased, the wall slip velocity and the viscosity corrected for slip effects also increased. In addition, for model suspensions in which the solid volume fraction was ≥81% of the maximum packing fraction, non‐Newtonian behavior was observed upon wall slip correction. On the other hand, as the particle size increased, the wall slip velocity was observed to increase and the true viscosity was observed to decrease. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 98: 439–448, 2005     

Dynamic behavior of a single screw plasticating extruder part I: Experimental study

The dynamic responses of a 2–1/2 inch single screw plasticating extruder and extrusion line were investigated. Step changes in screw speed, take-up speed, back pressure, and processing materials were used to determine the transient responses of barrel pressures, die pressure, melt temperature, and extrudate thickness. Dynamic responses of the entire extrusion line can be explained by the flow mechanism of the extruder and the logical properties of the polymer used. A capillary rheometer was also used to determine if it could simulate pressure responses in the extruder for screw speed changes. Results showed that capillary rheometer was helpful in estimating the short term pressure responses in the die.     

Steady and transient flow of a non‐Newtonian chemically reactive fluid in a twin‐screw extruder

The flow of chemically reactive non‐Newtonian materials, such as bio‐polymers and acrylates, in a fully intermeshing, co‐rotating twin‐screw extruder is numerically investigated. A detailed study of the system transient behavior is carried out. The main transient aspects, including response time, variation of system variables, and instability of operation, are studied for both single‐ and twin‐screw extruders, since single‐screw extruder modeling closely approximates the region away from the intermeshing zone in a twin‐screw extruder. The effect of a time‐dependent variation in the boundary conditions is studied. The coupling due to conduction heat transfer in the screw barrel is found to be very important and is taken into account for single‐screw extruders. In the absence of this conjugate coupling, the response time is much shorter. Several other interesting trends are obtained with respect to the dependence of the transient response on the materials and operating conditions. Steady state results are obtained at large time. The calculated velocity distributions in the screw channel are compared with experimental results in the literature for steady state flow and good agreement has been obtained. The calculated results for transient transport agree with the few experimental observations available on this system. Chemical reaction, leading to chemical conversion of the material, is also considered and the resulting effects on the flow and transport determined. These results will be useful in the design, control and optimization of polymer extrusion processes.     

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.     

Modeling heat transfer in screw extrusion with special application to modular self‐wiping co‐rotating twin‐screw extrusion

This paper proposes two important models useful for describing heat transfer and temperature profiles in single and modular self‐wiping co‐rotating twin‐screw extruders. One model predicts heat transfer coefficients. Calculations of the barrel and screw heat transfer coefficients are made for various modules in different diameter extruders. We compare the values of the heat transfer coefficients from the model with those from literature. The second model predicts the axial screw temperature profile when the barrel, but not the screw, is heated, Example calculations of the cup mixing and screw temperature profiles are also made for different diameter extruders.     

Research on the micro-extrusion characteristic of mini-screw in the screw extruding spray head

Extrusion production capacity is a chief factor of measuring how good the extruding spray head of Fused Deposition Modeling (FDM) is. The main geometrical parameters of screw and barrel (the active length of screw, the diameter of screw, the helix angle, the width of screw arris, the depth of screw channel, the clearance between screw, and barrel, etc.,) and the processing parameters such as screw speed, the pressure of nozzle are closely related to extrusion production capacity. In this article, the spray head is designed to be a special mini-screw extruding spray head and the mini-screw is different from common screw. The characteristics of the mini-screw in the research are that it is small in size, with narrow screw channel and wide screw arris structurally. Based on hydrodynamics and melt conveying theory, the micro-extrusion characteristics of mini-screw used in the screw extruding spray head of FDM were discussed in detail in this article. The relationship between extrusion production capacity and the main geometrical parameters of screw and barrel and the processing parameters is researched. Theoretical analysis was performed to find out the quantitative relationships between production capacity of extrusion and main parameters (the screw speed, main geometrical size of screw, the clearance between screw and barrel, and the pressure of nozzle, etc.,) so that the theoretical guidance on the design of spray head with mini-screw could be provided. The characteristic curves of mini-screw and nozzle are analyzed to find out the jointed work point of spray head. The main factors influencing extrusion capacity of nozzle are discussed in this article. Furthermore, the development of FDM will be promoted and the micro-extrusion theory would be more perfect by the research.     

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.     

Theoretical model for intermeshing twin screw extruders: Axial velocity profile for shallow channels

Positive displacement intermeshing twin screw extruders have been analyzed by a simple model for flow in the channel formed by the screw root and screw flights. The model considers the down channel flow to be a combination of drage flow resulting from the relative motion of the barrel and screw and pressure flow resulting from the positive displacement action of the device. The pressure flow in this situation is distinguished from pressure flow in a single screw extruder in that the pressure forces induce flow toward the die for the twin screw model rather than away from the die as in a single screw extruder. Comparison of the down channel shear rate profile of apositive displacement twin screw extruder with that of a single screw extruder with no net flow reveals that they are identical but inverted with respect to channel depth. The model presented does not consider leakage between the twin screws or the rotational motion of the second screw.     

橡胶在销钉机筒挤出机中的流动分析

建立了销钉机筒挤出机的非牛顿流体流动模型,并计算出压力场、流动场和螺杆的特性曲线,结果表明,随着流体非牛顿特性的增强,螺杆的生产能力降低;随着螺杆螺槽上切口的增多,逆流增多,挤出产量降低,机筒上的销钉对挤出特性影响很小,销钉式挤出机的挤出特性与螺杆上有切口的挤出机的挤出特性相似。