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.     

A new fluid model for particles settling in a viscoplastic fluid

The study of the settling behaviour of particles in viscoplastic fluids is closely related to the study of rheology. In this paper, a thorough examination of the flow behaviour of viscoplastic fluids, in the form of aqueous polyacrylamide solutions, has been presented. The results of this study suggest that the experimental fluids exhibit time-dependent flow characteristics, where the apparent viscosity of the solutions depends highly on their shear history. This time dependency has been attributed towards the processes of destruction and rejuvenation in the ‘structural network’ of the fluids (due to the presence of hydrogen bonding between polyacrylamide and water molecules), as they are subjected to changing rates of shear. A new fluid model was thus developed to capture this flow behaviour. This model, termed as ‘semi-viscoplastic’, features temporary yield stress characteristics that tend to dissipate once the structural network of the fluid is destroyed due to the application of shear. The time dependency of the fluid viscous parameters becomes apparent in the settling sphere experiment, where it has been demonstrated that a sphere that is following the flow path of another sphere tends to attain a fall velocity that is significantly higher than the preceding sphere. Based on this finding, a new generalised correlation has been developed, through which predictions of the fall velocity of spherical particles settling through viscoplastic fluids, of various shear history, can be made.     

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.     

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.     

Prediction of lower/upper limiting viscosities

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

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 PROPERTIES AND FLOW OF CONCENTRATED DISPERSE MEDIA I - MODELLING OF STEADY AND UNSTEADY BEHAVIOR

A steady viscosity model, including both volume fraction and shear rate variables, is shown to be applicable to a large class of complex liquids which can be considered as highly concentrated disperse media. The effect of yield stress is taken into account. For unsteady measurements, this model, which includes thixotropy, can be simply extended to viscoelastic behaviour. Some examples of application will be given, specially to heavy crude oil emulsions.     

RHEOLOGICAL PROPERTIES AND FLOW OF CONCENTRATED DISPERSE MEDIA I - MODELLING OF STEADY AND UNSTEADY BEHAVIOR

Abstract

A steady viscosity model, including both volume fraction and shear rate variables, is shown to be applicable to a large class of complex liquids which can be considered as highly concentrated disperse media. The effect of yield stress is taken into account. For unsteady measurements, this model, which includes thixotropy, can be simply extended to viscoelastic behaviour. Some examples of application will be given, specially to heavy crude oil emulsions.     

Rheological behavior of cement pastes from MRI velocimetry

From MRI measurements, it is shown that in a flowing cement paste the thixotropic effects dominate over short time scales, while aging effects become significant over larger timescales. The steady state behavior, defined as flow properties in the intermediate period, exhibits a yielding behavior which differs from the prediction of usual yield stress models. The transition from the “solid” to the “liquid” regime is abrupt: the shear rate changes suddenly from zero to a finite value (critical shear rate) when the shear stress overcomes a critical value. These critical shear rates and shear stresses are independent of the flow conditions so that they may be considered as intrinsic material parameters. It was also shown that these results are consistent with usual macroscopic observations from conventional rheometry.     

AXIAL FLOW OF GENERALIZED VISCOPLASTIC FLUIDS IN NON-CIRCULAR DUCTS

Viscoplastic fluids are well known in industry. There is a huge literature on plastic flow of the Bingham type, but comparatively little has been published on the flow of generalized viscoplastic fluids in non-circular ducts. The present study analyzes the duct flow of generalized viscoplastic fluids using a finite-element method. The problem of tracking the yield surface is solved by the regularization technique whose existence theorem has been established through the theory of variational inequalities. Flows in eccentric annuli and a square duct are investigated. Mobile plug zones exist in the duct center. Stagnant plugs exist at the narrow side in eccentric annuli at large eccentricity or large Bingham number, and near the apex of corners in a square duct. It is shown that the sizes and the contours of the plug zones are mainly determined by the force balance between transverse shearing and yield stress. In addition these zones are almost identical for various plastic models considered here despite their different shear-thinning behaviors.     

Morphology and rheology of composites based on anisotropic polymer matrix and different clays

Structure and rheological properties of hybrids with polymer matrix and layered silicates as filler were studied. Solution containing 60% wt of hydroxypropylcellulose (HPC) in oligomeric polyethyleneglycol (PEG) was used as a matrix. The peculiarity of this study is that the matrix depending on temperature can form different phase states including liquid‐crystalline (LC). So, a possibility of coexistence and superposition of different ordered structures can be realized at different temperatures. Three different fillers were used: natural Na‐montmorillonite (MMT) and organoclays obtained by treating MMT with surfactants varying in polarity of their molecules. Depending on the type of clay, materials with different morphology can be obtained. X‐ray data showed that PEG intercalates all types of clay used whereas penetration of HPC macromolecules into clay galleries during mixing does not occur. Clay modified with more polar surfactant should be treated as the most convenient material to be intercalated by PEG. Rheological studies (included steady‐state and dynamic shear properties in a wide temperature range) demonstrate that composites are viscoplastic materials and the yield stress is observed already at 5% fillers loading. The level of the yield stress depends on the phase state of the matrix being induced by the superposition of structures formed by clay particles as well as by the LC phase (if it exists). The same conclusion can be made on the base of linear oscillatory measurements because the existence of the LC phase and/or the presence of filler lead to a pseudo solid‐like behavior of a system as whole. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Flow simulation of herschel-bulkley fluids through extrusion dies

The flow of viscoplastic materials through extrusion dies has been studied numerically using the finite element method. Rheological data for viscoplastic doughs have been fitted by the Herschel-Bulkley model, which incorporates a yield stress into the power-law model. Non-isothermal simulations show the extent and shape of yielded/unyielded regions and the development of temperature field assuming different modes of heat transfer at the boundaries. The results reveal that viscous dissipation causes appreciable temperature rises in the extrudate in agreement with measured values at the extruded material surface. The extrudate swell results show a maximum for a certain range of apparent shear rates also observed experimentally. However, the inelastic simulations based on the Herschel-Bulkley model always under-predict the experimental swelling values. A heuristic approach is also used to determine the level of elasticity required to produce the experimental values.     

ON NONISOTHERMAL FLOWS OF BINGHAM PLASTICS

A numerical scheme based on the Galerkin's finite element method is used to analyze nonisothermal flows of Bingham plastics. These fluids exhibit yield stresses, below which the material does not flow. This condition is enforced by introducing the bi-viscosity model in which the plug behaviour is approximated by a highly viscous fluid. The bi-viscosity model approaches the ideal Bingham plastic model if the pre-yield viscosity becomes large. This numerical method is applied to solve three problems namely the Graetz-Nusselt, recirculating flow, and sinusoidal channel flow problems for various values of the yield stress. The size of the plug as well as the velocity and temperature fields correspond closely with values available in literature.     

Use of artificial neural networks for modelling rate dependent behaviour of adhesive materials

This research work highlights the use of artificial neural networks (ANN) for modelling the rate-dependent response of adhesive materials with the purpose of expanding the established method for modelling the response of adhesively bonded structures, and in particular single lap joints. The motivation for this work comes after a viscoplastic model developed in a previous research work failed to predict the response of single lap joints bonded with a rate dependent adhesive material. The viscoplastic model, however, was successful in replicating both bulk and shear properties of the used adhesive system. Predictions made using the rate-dependent von Mises material model proved to be successful in predicting the behaviour of single lap joints, but it could not model the shear data using the tensile data due to hydrostatic stress sensitivity in the adhesive itself. Accurate predictions of the rate-dependent behaviour using artificial neural networks are possible with the availability of stress and strain data sets from experiments. This is where the neural network constitutive model directly acquires the information on the material behaviour from experimental data sets. Material data defining both the tensile and shear response of the adhesive system was extracted from previous research work. An artificial neural network constitutive model was developed and then used to replicate experimental data and also to generate further data at other strain rates. The available model could be slightly modified and then used to investigate various geometrical parameters, such as overlap length, plate thickness and adhesive thickness on joint strength.     

Computational rheology of carbonaceous mesophases

Mesophase pitches are multicomponent discotic nematic liquid crystals (DNLCs), whose characteristic molecular weight is intermediate between low molar mass and polymeric nematic liquid crystals. Flow modelling of these fluids is performed using a previously formulated mesoscopic viscoelastic rheological theory [J. Non-Newtonian Fluid Mech. 94 (2000) 87] that takes into account flow-induced texture transformations. A complete extra stress tensor equation is developed from first principles for liquid crystal materials under non-homogeneous arbitrary flow. This mesoscopic viscoelastic model has been adapted to describe the rheology of flow-aligning thermotropic DNLCs as models of mesophase pitches. We develop a fundamental understanding of the relations between rheology and flow of carbonaceous mesophases using theory and simulation by characterizing the steady and transient shear rheological material functions of flow-aligning DNLCs. Predictions for simple shear flow (under non-homogeneous conditions) for the apparent shear viscosity and first normal stress differences are presented. The predicted relations among rheological properties, shear-induced microstructure, processing conditions and material parameters of discotic mesophases are characterized and discussed.     

VISCOMETRIC MEASUREMENT OF CHROMIUM(III)-POLYACRYLAMIDE GELS†

Gelled polymers are being used increasingly to modify the movement of injected fluids in secondary and enhaced oil recovery processes. A common gelation process involves the reduction of Cr(VI) to Cr(III) in the presence of polyacrylamide. The Cr(III) reacts or interacts with the polymer to form a gel network. Although correlations of gelation time with principal process variables have been obtained, viscometric data have not been reported during or after gelation. These data are needed for fluid flow calculations in surface equipment and estimation of flow behaviour in reservoir rocks.

A Weissenberg Rheogoniometer, with cone and plate geometry, was used to obtain viscometric data for the gelation of polyacrylamide and chromium (III). Solutions consisting of polyacrylamide polymer, sodium dichromate-dihydrate and sodium bisulfite were gelled under a steady shear field at constant temperature. The shear stress versus time profile for the galation process was interpreted to define a gelation time and to determine the apparent viscosity of the gelled fluid. The gelation time decreased as the applied shear rate increased up to about 14.25 sec^-1 and was affected by shear rate history. Viscometric properties of the gelled solutions were determined. Apparent viscosity of the gelled solutions decreased as the shear rate under which they were formed increased.

Post gelation studies indicated that gels exhibited a residual stress at zero shear rate and behaved as Bingham plastics under steady shear. Gels formed at low shear rates were more viscous than gels formed at high shear rates. However, the structure of these gels was susceptible to shear degradation.     

On the interpretation of orifice extrusion data for viscoplastic materials

An analytical model of orifice extrusion has been developed that allows the material parameters to be derived from experimental data for materials such as pastes that may be described as viscoplastic. The geometry is based on a cylindrical square-ended barrel with variable diameter orifices. A rigid-viscoplastic constitutive relationship was employed that incorporated incompressibility and associated Herschel-Bulkley post-yield flow; the total strains were considered to be sufficiently large that elastic deformations could be ignored. The model provides a closed-form expression that relates the extrusion pressure to the material parameters. In the limit when the flow consistency is set to zero, the expression reduces to the ideal work approximation used to describe the extrusion of rigid-plastic solids. When the yield stress is set to zero, the result reduces to the solution derived by Gibson (Rheological Measurement, Elsevier, Barking, 1988, pp. 49-92) for the extrusion of power-law fluids. The model is used to analyse experimental data for a model paste and is compared to the widely applied empirical correlation of Benbow and Bridgwater (Paste Flow and Extrusion, Clarendon Press, Oxford, 1993).     

EFFECT OF TEMPERATURE ON THE RHEOLOGY OF POLYMERIC LIQUID CRYSTALS

As part of a more general effort to elucidate the flow of polymeric liquid crystals, the effect of temperature on the rheological properties has been investigated. A lyotropic sample of poly(γ-benzyl-L-glutamate) in m-cresol has been used throughout the measurements. Under steady state shear flow the viscosity and the first normal stress difference have been measured. Oscillatory flow after cessation of steady shear flow reveals a time effect which led to the determination of initial and final moduli; both have been measured as a function of temperature. Finally some transients have been considered as well.

The limiting zero frequency value of the dynamic viscosity and the zero shear value of the steady state viscosity have different activation energies. The dynamic moduli can be scaled for temperature effects by means of the zero frequency viscosity. Because of the difference in activation energies this scaling does not hold for the steady state properties. An alternative scaling procedure is suggested. The time scale of the transients is nearly independent of temperature. None of the available theoretical models describes the measured phenomena.     

Modelling non-linear stress–strain behaviour of rubber toughened plastics

Abstract

An elastic–plastic model has been developed for describing the non-linear, stress–strain curves of rubber toughened plastics. Following a linear elastic response at low strains, it is assumed that the material undergoes plastic deformation which, for dilatational stress states, is enhanced by the generation and growth of cavities within the rubber particles. The model is based on Gurson's theory of plasticity in porous materials and follows the developments proposed by Bucknall and co-workers. Parameters are included that allow for the effect of pressure on the yield stress of the matrix material between the cavities and for the influence of void interactions on matrix shear banding. Account is also taken of the change in matrix composition, and hence the matrix yield stress, during void nucleation. The nucleation is assumed to occur over a critical range of volumetric strain ε_V and to involve the replacement of rubber particles by an equal volume of effective cavities. Two different nucleation functions have been investigated to describe the dependence of the effective void fraction on ε_V.

Equations that govern the elastic, yield and flow behaviour under multiaxial stress states have been solved to determine required material parameters and to predict behaviour in tension and compression from shear hardening data. The predicted and observed behaviour show good agreement, indicating that the model may be applied with some confidence to stress analyses using finite element calculations.     

Influence of bentonite clay on the rheological behaviour of fresh mortars

Fine mineral additives are often used in the formulation of ready-mix mortars as thickeners and thixotropic agents. Yet, these attributed fresh state properties are not clearly defined from the rheological point of view. In the present study, we consider the influence of bentonite (montmorillonite-based clay mineral) on the rheological behaviour of mortars, including in particular creep and thixotropy. The mortar pastes are subjected to different shear-rates and then allowed to creep under fixed shear stresses until reaching steady state, which corresponds to either rest if the applied stress is smaller than the yield stress or permanent flow otherwise. The evolution of the creep strain is investigated depending on shear history for different contents of bentonite. The microstructure rebuilding kinetics after shear (thixotropy) is considered by analysing the temporal evolution of the creep strain for different applied shear stresses (lower than the yield stress). As expected, bentonite is found to enhance the mortar creep (or sag) resistance. This enhancement consists of both an increase of the yield stress recovered after shear, and a diminution of the characteristic time for yield stress recovery (related to microstructure rebuilding).