Showing papers in "Journal of Non-newtonian Fluid Mechanics in 1985"
TL;DR: In this paper, the fracture zone around a four-bladed vane rotating in a Bingham liquid has a diameter D c which is significantly larger than the vane diameter.
Abstract: The fracture zone (or shearing surface) around a four-bladed vane rotating in a Bingham liquid has a diameter D c which is significantly larger than the vane diameter. In typical plastic liquids D c / D ≈ 1.00–1.05. We have measured D c and the rheology of some automotive greases. We have also photographed the fractural surface in a transparent Bingham liquid and have found it to be approximately cylindrical. Computer simulations of a four-bladed vane rotating in a Bingham liquid have produced a value of D c / D = 1.025 which agrees well with experimental data on two viscoelastic automotive greases. We have not been able to obtain agreement between experiment and theory on the dependence of D c / D on τ y /η p . The experimental and theoretical data presented here support the use of the vane for yield stress measurements if the diameter correction is applied. The present experimental data suggests the vane diameter has little or no effect on D c / D .
109 citations
TL;DR: In this paper, the authors used finite-element programs to estimate the drag on an unbounded fluid in an (inelastic) power-law fluid and showed that wall effects are negligible forn ⩽ 0.5.
Abstract: Using a finite-element program, the drag on an unbounded fluid in an (inelastic) power-law fluid is estimated. Comparison with upper and lower bounds, and with experimental data is given. Some remarks on wall effects are also made, and it is shown that wall effects are negligible forn ⩽ 0.5.
108 citations
TL;DR: In this paper, the steady flow of an upper convected Maxwell fluid through a pipe with wavy walls was considered, and it was shown that the vorticity at the center of the pipe becomes hyperbolic when the centerline velocity is larger than the speed of shear waves into rest.
Abstract: We consider the steady flow of an upper convected Maxwell fluid through a pipe with wavy walls The analysis is an extension to round pipes of the methods introduced by Yoo and Joseph [1] to study the same problem in plane channels As in the channel problem, the vorticity in a small cylinder at the center of the pipe becomes hyperbolic when the centerline velocity is larger than the speed of shear waves into rest The region of hyperbolicity is smaller, but the decay of vorticity is less, when the elasticity parameter is larger
70 citations
TL;DR: In this article, the authors established a parallel between these theorems and observations made in the numerical calculation of such flows by means of a mixed method, and showed that numerical errors in the evaluation of the extra-stress tensor have dramatic consequences upon the other field variables for the flow of a Maxwell fluid, and the damage is limited with an Oldroyd-B fluid.
Abstract: Having recalled some theorems pertaining to strong solutions of the viscoelastic flow problem, the authors establish a parallel between these theorems and observations made in the numerical calculation of such flows by means of a mixed method. Numerical errors in the evaluation of the extra-stress tensor have dramatic consequences upon the other field variables for the flow of a Maxwell fluid, and the damage is limited with an Oldroyd-B fluid.
69 citations
TL;DR: In this article, it was shown that the creeping cone-and-plate flow of an Oldroyd-B fluid is unstable with respect to an infinitesimal disturbance.
Abstract: It is shown that the creeping cone-and-plate flow of an Oldroyd-B fluid is unstable with respect to an infinitesimal disturbance. The critical Weissenberg number for the case of the Maxwell fluid is about 2.
69 citations
TL;DR: In this article, a comparison is made between the behaviour of a variety of different viscoelastic models when applied to the die swell problem, and a wide range of elongational and shear behaviour is exhibited by the models examined.
Abstract: Numerical studies of die swell have until now dealt perimarily with the Maxwell or Oldroyd-B viscoelastic models. However, these models exhibit features that often make them unsuitable for numerical work. Furthermore, they are not realistic representations of actual viscoelastic fluids. In this report a comparison is made between the behaviour of a variety of different viscoelastic models when applied to the die swell problem. A wide range of elongational and shear behaviour is exhibited by the models examined. Both types of behaviour are shown to be important in the die swell problem, and the observed swelling is related to these characteristics of the models.
65 citations
TL;DR: In this article, a numerical method for finitely extensible nonlinear elastic (FENE) dumbbells in a dilute suspension undergoing steady-state shear flow has been improved by assuming a form of the distribution function that removes the singularity at R = 0.
Abstract: Warner's numerical method for finitely extensible nonlinear elastic (“FENE”) dumbbells in a dilute suspension undergoing steady-state shear flow has been improved by assuming a form of the distribution function that removes the singularity at R = 0 and improves the behavior of the weight function in the Galerkin expression for large b . The comparison of the results of the present method to those of Christiansen and Bird's extrapolation and Warner's numerical solution indicates the success of this method. The material functions, the dumbbell elongation, and the distribution function for steady-state shear flow are given. In addition the newly obtained results are used to assess the accuracy of two approximate methods referred to as the FENE-P model and the FENE-P-B model.
54 citations
TL;DR: In this article, the authors used the kinetic theory of nonlinear elastic dumbbells, with bead friction coefficients that depend linearly on the interbead distance, to obtain the elongational viscosity and the dumbbell stretching as a function of elongation rate.
Abstract: The kinetic theory of nonlinear elastic dumbbells, with bead friction coefficients that depend linearly on the interbead distance, is used to obtain the elongational viscosity and the dumbbell stretching as a function of elongation rate. The results are obtained by solving numerically the “diffusion equation” for the configurational distribution function. No S-shaped curves were found for the elongational viscosity or for the mean-square end-to-end distance. Previous investigators did report S-shaped curves and related “hysteresis” effects. However, their results were based on using mathematical approximations that now appear to be inappropriate.
52 citations
50 citations
TL;DR: In this paper, the authors measured the apparent viscosity and primary normal stress difference for dispersions of fumed silica in poly(dimethylsiloxane) and found that the shape of the hysteresis loops were sensitive to the details of the deformation history.
Abstract: The apparent viscosity and primary normal stress difference were measured for dispersions of fumed silica in poly(dimethylsiloxane). Dispersions with less than 4.75% by weight of filler exhibit hysteresis in both the viscosity and normal stress, when the shear rate was increased and then decreased in discrete steps. The shape of the hysteresis loops were sensitive to the details of the deformation history. By using the appropriate deformation history, the material properties determined during the increasing shear rate part of the hysteresis experiment compare favourably with the steady-state rheological properties. The rheological properties of the dispersion were quite sensitive to the age of the fluid with no hysteresis behaviou exhibited by dispersions less than three days old. For dispersions with at least 4.75% by weight of fumed silica, neither the apparent viscosity nor the primary normal stress coefficient exhibited significant hysteresis behaviour. The relationship between the observed rheological behaviour and the dispersion's microstructure is discussed.
48 citations
TL;DR: In this article, a generalized model is introduced in which the dependence of the mobility tensor on the configuration tensor is given by a relaxation-type functional for steady and transient extensional and shear flows.
Abstract: After a brief outline of the concept of configuration-dependent molecular mobility for the particular case of the one-mode mean-configuration theory, a generalized model is introduced in which the dependence of the mobility tensor on the configuration tensor is given by a relaxation-type functional. This model is analysed for steady and transient extensional and shear flows. In extensional flow it predicts a maximum in the steady-state uniaxial viscosity curves and stress overshoot in the stressing curves, and in shear flow it predicts even larger stress overshoot in the stressing curves. This model bridges the gap between the current molecular models and the most elaborate network models. In an appendix it is shown that for the relaxation-type dependence of the mobility it is only by using the upper Oldroyd derivative that physically acceptable results are predicted.
TL;DR: Theoretical predictions for constant velocity squeezing are compared to experimental observation for well characterized non-shear thinning elastic fluids as mentioned in this paper, and it is shown both theoretically and experimentally that the effect of elasticity in a constant velocity squeeze film flow is to always reduce the load relative to the inelastic (Newtonian) prediction and this load reduction falls between the upper and lower asymptote prediction by the exact solution for the Oldroyd B fluid.
Abstract: An exact solution is presented for the squeeze film flow of an Oldroyd B. fluid. The solution demonstrates that the flow kinematics is similar to the Newtonian (or Maxwellian) one. Theoretical predictions for constant velocity squeezing are compared to experimental observation for well characterized non-shear thinning elastic fluids. It is shown both theoretically and experimentally that the effect of elasticity in a constant velocity squeeze film flow is to always reduce the load relative to the inelastic (Newtonian) prediction and that this load reduction falls between the upper and lower asymptote prediction by the exact solution for the Oldroyd B fluid. The upper load asymptote is given by the Stefan solution for the viscosity of the polymer solution and the lower asymptote is given by the Stefan solution for the viscosity of the solvent. Experimental observations agree with the theoretical prediction for the Oldroyd B fluid at low shear rates where it is shown that the steady and dynamic flow properties of the test fluids used in the experimental program are well represented by the Oldroyd B constitutive equation. With the exception of the work of Lee et al. [6] for constant load squeezing of a Maxwell fluid, this work represents one of the few cases where experimental observation of large effects due to elasticity are indeed predicted with a constitutive equation which actually describes the steady and dynamic shear properties of the fluids used in the experimental program.
TL;DR: In this article, the authors developed an algorithm for calculating the steady flow of viscoelastic fluids of the integral type based on a simple integration of the strains along the streamlines.
Abstract: In the present paper, we develop an algorithm for calculating the steady flow of viscoelastic fluids of the integral type. The calculation is based upon a simple integration of the strains along the streamlines, and the method remains valid for arbitrary elements. The technique is applied to the flow of a Maxwell fluid through a wedge and to the calculation of the hole-pressure error for the Doi-Edwards fluid.
TL;DR: In this article, the flow patterns in the entrance region of dies with various entrance geometry configurations have been investigated for low density polyethylene filled with carbon black, and the results showed that all longitudinal sections of these systems showed streamline motion directed towards the die entrance.
Abstract: Flow patterns in the entrance region of dies with various entrance geometry configurations have been investigated for low density polyethylene filled with carbon black. The experiments were carried out using samples with titanium dioxide markers in the barrel of an Instron capillary rheometer using dies with varying entrance geometries. The material in the barrel was cooled under pressure, removed and longitudinally sectioned. Samples with 0–5 volume percent carbon black exhibited in 180° entrance angle dies corner vortices typical of low density polyethylenes. At higher volume loadings, no vortices were observed. All longitudinal sections of these systems showed streamline motion directed towards the die entrance. This was found to be the case for blacks of varying particle size and different die entrance geometries. Purging experiments using initially white (CaCO 3 or TiO 2 ) filled regions at the die entrance revealed only very small stagnant regions in the corners of 180° entrance angle dies, 270° diverging entrance angle dies were also shown to exhibit small stagnant regions in the diverging parts of the die.
TL;DR: In this paper, a three-dimensional Boundary Element formulation for elastostatics including zero-Reynolds number viscous flow with free surfaces is presented, and numerical results are presented for the flow of an incompressible Newtonian fluid out of a long square die.
Abstract: The paper reports a three-dimensional Boundary Element formulation for elastostatics including zero-Reynolds number viscous flow with free surfaces. Numerical results are presented for the flow of an incompressible Newtonian fluid out of a long square die. The method is ideal for this type of problem.
TL;DR: In this paper, the steady-state viscosity, stress relaxation, and stress growth function were measured for a 3.0% by weight dispersion of fumed silica in poly(dimethylsiloxane); using a two-step shear rate history.
Abstract: The steady-state viscosity, stress relaxation, and stress growth function were measured for a 3.0% by weight dispersion of fumed silica in poly(dimethylsiloxane); using a two-step shear rate history. For short rest times the stress growth function η+ increased monotonically towards steady-state, while at long rest times η+ exhibited large overshoot followed by a monotonic decrease to steady-state. For intermediate rest times η+ exhibited more complicated transient behaviour. The effect of both shear rates in the two-step shear-rate history on η+ have been studied, and the resulting rheological behaviour is discussed in terms of phenomenological microstructural models.
TL;DR: In this article, the birefringence and pressure drop measurements were carried out in working cells of planar geometry having different contraction angles and contraction ratios, and a reasonable agreement between theory and experiment has been obtained, which shows the usefulness of the Leonov model in describing actual flows.
Abstract: Extensive experimental data on the birefringence in converging and diverging flows of a polymeric melt have been obtained. The birefringence and pressure drop measurements were carried out in working cells of planar geometry having different contraction angles and contraction ratios. For investigation of diverging or abrupt expansion flow, the direction of flow in the cells was reversed. The theoretical predictions are based upon the Leonov constitutive equation and a finite element scheme with streamwise integration. In contrast to Newtonian and second-order fluids, viscoelastic fluids at high shear rates show significant differences in pressure drop and birefringence (i.e. stresses) in converging and diverging flows. For a constant flow rate, the pressure drop is higher and the birefringence smaller in diverging flows than in converging flows. This difference increases with increasing flow rate. Further, for the same contraction ratio but different contraction angles, the birefringence maximum increases considerably with contraction angle. In addition, an increase in contraction ratio has the same effect. The viscoelastic constitutive equation of Leonov has been shown to describe all the above viscoelastic effects observed in the experiments. In general, a reasonable agreement between theory and experiment has been obtained, which shows the usefulness of the Leonov model in describing actual flows.
TL;DR: In this article, an instrument is described in which steady planar orthogonal stagnation flows of the type proposed by Winter [1] are achieved with lubrication, from pressure readings on steady results acceptable Trouton ratios are achieved for a Newtonian sample and results are obtained for a Boger fluid showing high levels of extensional viscosity with Trouton ratio approaching 4 in the limit of zero stretch rate.
Abstract: An instrument is described in which steady planar orthogonal stagnation flows of the type proposed by Winter [1] are achieved with lubrication. From pressure readings on steady results acceptable Trouton ratios are achieved for a Newtonian sample and results are obtained for a ‘Boger’ fluid showing high levels of extensional viscosity with Trouton ratios approaching 4 in the limit of zero stretch rate.
TL;DR: In this article, a single simple geometry, a blade over a rotating roll, is considered, and a perturbation solution to the Navier-Stokes equations yields a lubrication theory with first order corrections for curvature and inertia.
Abstract: Coating of viscous and viscoelastic liquids is examined both theoretically and experimentally. A single simple geometry, a blade over a rotating roll, is considered. A perturbation solution to the Navier-Stokes equations yields a lubrication theory with first order corrections for curvature and inertia. A numerical solutions by the Finite Element Method (FEM) is compared to the analytical solutions. For Newtonian fluids, agreement between these mathematical models, and data on blade loading, is quite good. The effect of a non-Newtonian viscosity is explored by adopting a purely viscous power law model. The zeroth-order (lubrication) equations are solved by the method of Steidler and Horowitz, and predictions for coating thickness and blade loading agree quite well with those obtained from a FEM solution of the full equations of motion for a power law fluid. Data on blade loading, obtained using a strongly elastic polymer solution, are compared to these mathematical models, and discrepancies are noted.
TL;DR: In this article, an experimental fiber-spinning device has been built in order to study the draw-resonance phenomenon in nearly isothermal conditions The influence of the output rate, of the take-up speed and of the spinning length was studied for four different polyesters.
Abstract: An experimental fiber-spinning device has been built in order to study the draw-resonance phenomenon in nearly isothermal conditions The influence of the output rate, of the take-up speed and of the spinning length was studied for four different polyesters The experimental results are in accordance with non-isothermal and viscoelastic computations
TL;DR: In this article, the dynamics of a macromolecule are considered on the basis of the fundamental model of the polymer chain, e.g., the bead-spring model.
Abstract: Rheological equations of state for the concentrated solutions and melts of high polymers are derived by applying a structural approach. The dynamics of a macromolecule are considered on the basis of the fundamental model of the polymer chain, e.g., the bead-spring model. The drag forces describing correlations of motion macromolecules are determined by means of the relaxation equations. The oscillatory shearing flow of the melts is studied on the basis of the equations derived. Expressions for the dynamic modulus and relaxation times are determined. As can be judged from the form of the dependence of the dynamic modulus on frequency, the relaxation time distribution is the same as in real materials. The relaxation spectrum of high polymers has a terminal zone with abnormally long relaxation times.
TL;DR: In this article, a linear stability analysis is made for an Oldroyd-type fluid undergoing steady two-dimensional flows in which the velocity field is a linear function of position throughout an unbounded region.
Abstract: A linear stability analysis is made for an Oldroyd-type fluid undergoing steady two-dimensional flows in which the velocity field is a linear function of position throughout an unbounded region. This class of basic flows is characterized by a parameter λ which ranges from λ = 0 for simple shear flow to λ = 1 for pure extensional flow. The time derivatives in the constitutive equation can be varied continuously from co-rotational to co-deformational as a parameter β varies from 0 to 1. The linearized disturbance equations are analyzed to determine the asymptotic behavior as time t → ∞ of a spatially periodic initial disturbance. It is found that unbounded flows in the range 0
TL;DR: The axisymmetric Poiseuille flow of a Johnson-Segalman fluid is selected as a specific one-dimensional example for testing numerical algorithms, while analytical results are also made available as mentioned in this paper.
Abstract: The axisymmetric Poiseuille flow of a Johnson-Segalman fluid is selected as a specific one-dimensional example for testing numerical algorithms, while analytical results are also made available. A particular emphasis is put on the appearance of limit points with some numerical algorithms.
TL;DR: In this article, the authors reported some experimental results on the time development of a Couette flow following the start-up of shear flow using the technique of two-color flow birefringence.
Abstract: This paper reports some experimental results on the time development of a Couette flow following the start-up of shear flow using the technique of two-color flow birefringence. Measurements obtained on collagen solutions are consistent with two theoretical studies which predict that for some viscoelastic liquids, momentum is transferred from the moving Couette cell boundary to the interior of the fluid through a velocity wave propagating and reflecting between the cell boundaries. This non-Newtonian phenomenon, exhibited as an oscillatory response in the measured birefringence and orientation angle, is observed at shear rates above a critical value when the response time of the polymer solution approaches the flow development time in the Couette flow cell.
TL;DR: In this article, the effect of die flow variables on the stability of isothermal melt spinning has been studied, both theoretically and experimentally, both as a steady flow problem and as a linear stability problem.
Abstract: The effect of die flow variables on the stability of isothermal melt spinning has been studied, both theoretically and experimentally. A die flow analysis provides the boundary conditions for a differential treatment of the spinline, both as a steady flow problem and as a linear stability problem. From the latter, one can predict the onset of draw resonance as a function of draw ratio, certain rheological parameters, and the stresses in the die. The experimental materials were two commercial polypropylenes and the apparatus consisted of a short (1.5–6 cm) isothermal spinning chamber; the agreement with theory was quite satisfactory. In most cases, high shear rates in the die (and subsequent high die swells) decrease the spinline stability but the magnitude of this interaction depends on many variables. In general, there is a high propensity for draw resonance (or ductile breakage) when the spinline is operating under conditions of severe thinning in a rheological sense.
TL;DR: In this paper, a method of reduced variables based on the use of a characteristic time τw was proposed τw is defined as the product of zero shear viscosity with the steady state elastic compliance.
Abstract: Start up from rest and relaxation from steady shear flow experiments have been performed on monodisperse polystyrene solutions with molecular weight ranging from 13 × 105 to 16 × 106 and concentration c ranging from 5% to 40% A method of reduced variables based on the use of a characteristic time τw is proposed τw is defined as the product of zero shear viscosity with the steady state elastic compliance Reduced steady and transient viscometric functions so obtained depend on the ratio M/Me (where Me is the entanglement molecular weight) Limiting forms are obtained when M/Me ⩾ 18 In steady flow, a simple correlation is found between shear and normal stresses In stress relaxation experiments, independent of shear rate, the long-time behaviour can be characterised by a single relaxation time τ1, which is identical for shear and normal stresses τ1 can be simply related to the zero shear rate viscosity and the limiting elastic compliance
TL;DR: In this article, the rigid body motion of an ellipsoid in a second order fluid (SOF) under the action of specified (time independent) external forces and torques has been obtained to first order in the Weissenberg number by inverting the resistance relations for the force and torque under specified rigid body motions.
Abstract: The rigid body motion of an ellipsoid in a second order fluid (SOF) under the action of specified (time independent) external forces and torques has been obtained to first order in the Weissenberg number by inverting the resistance relations for the force and torque under specified rigid body motions. The reciprocal theorem of Lorentz was used to bypass the calculation of the O(W) velocity field. The results agree with known analytic solutions for a SOF with the secondary to primary normal stress ratio of − 1 2 . The solution procedure was also tested by computing the torque on a translating prolate spheroid with aspect ratios ranging from slender bodies to near-spheres. One result is that for a SOF with zero secondary normal stress (Weissenberg fluid), previous asymptotic results for near-spheres were found to be accurate even at fairly large aspect ratios (e.g. 2). New results for non-degenerate ellipsoids suggest that the orientation (as monitored by Euler angles) and trajectory of sedimenting, non-axisymmetric particles such as ellipsoids provide useful information on the rheology of the suspending fluid.
TL;DR: Capillary viscometry was performed on dilute non-Newtonian solutions of monodisperse polystyrene in theta solvents as discussed by the authors, and the results revealed a parametric dependence on the viscosities of poly styrene with styrene.
Abstract: Capillary viscometry was performed on dilute non-Newtonian solutions of monodisperse polystyrene in theta solvents The solvents, blends of low-molecular-weight polystyrene with styrene, had viscosities (η s ) that were varied from 022–27 Pa s Data reduction of the dilute limit, [η]/[η 0 ] vs β = [η 0 ]η s M γ / RT (where γ is shear rate) revealed a parametric dependence on η s that has not before been reported and is not predicted by most molecular theories of polymer dynamics It is suggested that an internal viscosity model can explain such a phenomenon
TL;DR: In this article, the authors examined the effective medium properties of a dilute suspension of spheres in a second-order fluid under linear shear and showed that the term linear in volume fraction increases the corresponding rheological coefficient, just as in the Newtonian case.
Abstract: We examine the effective medium properties of a dilute suspension of spheres in a second-order fluid under linear shear. Since the second-order fluid is the first step toward the general viscoelastic fluid, the results obtained may provide a qualitative feel for the problem in which the suspending fluid obeys a more complicated (and realistic) constitutive relation. The dissipation in the medium is calculated by determining the rate of working by surface forces; this is compared to the dissipation in a homogeneous fluid to give the effective properties. The results show that the term linear in volume fraction increases the corresponding rheological coefficient, just as in the Newtonian case. It is to be noted that the second-order dissipation is zero for simple shear and other weak flows, whereas for strong flows the small correction may increase or decrease the overall dissipation.
TL;DR: In this paper, the effect of high molecular weight polymers on the cavitating flow around a cylinder was investigated and a decrease of the incipient cavitation number and disappearance of the transient cavitation regime were observed when polymers are added to the flow.
Abstract: The present study is concerned with the effect of high molecular weight polymers on the cavitating flow around a cylinder. A decrease of the incipient cavitation number and disappearance of the transient cavitation regime are observed when polymers are added to the flow. Simultaneously, the radiated noise and the drag on the cylinder are substantially reduced for σ values above critical.