Volume 47, Issue 6, November 2003
Index of content:
47(2003); http://dx.doi.org/10.1122/1.1619376View Description Hide Description
Recent theoretical work has investigated incipient failure of a cylinder of yield stress material under gravitational loading [Chamberlain et al., Int. J. Mech. Sci. 43, 793–815 (2001); 44, 1779–1800 (2002)]. This theoretical work, using the slip-line field method of plasticity, suggests that the height of incipient failure increases as the radius increases. In contrast, a simple heuristic model, the “uniform stress model,” predicts that the height of incipient failure is independent of the radius. We present detailed quantitative comparison of the slip-line and uniform stress models with experimental measurements, verifying the predictions of the slip-line model.
Comparison of measured centerplane stress and velocity fields with predictions of viscoelastic constitutive models47(2003); http://dx.doi.org/10.1122/1.1608951View Description Hide Description
High-resolution laser Doppler velocimetry and flow-induced birefringencemeasurements were used to determine velocity and stress fields and to calculate a transient planar elongation viscosity profile for viscoelasticflow on the shear-free centerplane of a planar contraction geometry. A novel, two-component Boger fluid was developed that enabled Weissenberg numbers, We, as high as 2.9 to be attained and allowed the stress-optical coefficients of the fluid components to be measured. The experimental apparatus was designed to subject the fluid traveling on the centerplane to Hencky strains, ε, as great as 3.5. Despite the high We and ε, the flow induced only a weakly nonlinear viscoelastic stress response in the fluid. A spectral decomposition of predictions of linear and nonlinear constitutive equations was used to demonstrate that the weakly nonlinear response was a result of the nonhomogeneous form of the centerplane strain-rate profile in conjunction with the finite response time of the individual relaxation modes. The degree of nonlinear stress response in this experiment cannot be increased by increasing the contraction ratio to increase the total Hencky strain experienced by a fluid element traveling along the centerplane, increasing the flow rate to increase the strain rate at a given point along the centerplane, or introducing a taper to the contraction geometry to change the strain rate profile. Thus, the experimental configuration of flow through a contraction appears to be of limited value in evaluating the accuracy of nonlinear constitutive models in predicting the stress response of a viscoelastic polymer solution to a generalized elongational flow.
Fourier-transform rheology experiments and finite-element simulations on linear polystyrene solutions47(2003); http://dx.doi.org/10.1122/1.1608954View Description Hide Description
Large amplitude oscillatory shear strain was applied to anionically synthesized linear polystyrene solutions in dioctylphthalate. The resulting torque was analyzed in Fourier space with respect to frequency, magnitude, and phase (Fourier-transform rheology). The concentration of the solutions was varied to achieve different degrees of entanglement. In addition, numerical simulations were performed using the Giesekus constitutive equation fitted on the basis of linear viscoelastic data. We found a good qualitative agreement between experiments and predictions; a quantitative agreement was reached for intermediate strain amplitudes. Some deviations were observed at very low strain amplitudes. We present a descriptive relation for the relative magnitude of the third harmonic as a function of strain amplitude using a modified damping function. From this relation we obtained a universal parameter that describes the scaling behavior law for the increasing non-linearity (e.g., measured by the relative intensity of the third harmonic with respect to the response at the excitation frequency) as a function of the strain amplitude. We found that the scaling exponent for the investigated linear polymer systems was independent of various factors. In addition, we analyzed the strain dependence of the relative phase of the higher harmonics. For vanishing strain amplitudes we define a property that should reflect the contribution of the different relaxation modes to the viscoelastic response, and thus, a potential correlation to polymer topology.
Effect of the orientation of the magnetic field on the flow of a magnetorheological fluid. I. Plane channel47(2003); http://dx.doi.org/10.1122/1.1619377View Description Hide Description
Shear flow and Poiseuille flow of magnetorheological fluids in a plane channel under an inclined magnetic field are studied. The proposed theoretical model is based on stabilityanalysis of chain-like clusters of dipolar magnetic particles. Hydrodynamic and magnetic torque acting on aggregates balances each other such that some misalignment between orientations of chains and the field takes place. Two magnetic field directions symmetric relative to the velocity gradient influence the aggregate behavior in different ways. In one case, the aggregates tend to turn along the flow whereas in the other case, they tend to turn transverse to the flow. The predicted peak value of the yield stress arises for (where is the clockwise angle between the velocity gradient and the direction of the field) and is 1.8 times the value for If we consider Poiseuille flow between two parallel plates, the velocity gradient, being positive on one side and negative on the other, the stress is no longer symmetric relative to the center of the gap if Nevertheless we show that the velocity profile remains symmetric and that we just have to consider the average yield stress In this case the flow rate is almost constant for a field angle between 0 and π/4 and increases steadily for larger angles, that is to say, when the field becomes aligned with the flow. Expressions are given which allow one to calculate the flow rate in planar Poiseuille flow for any inclination angle of the magnetic field.
Effect of the orientation of the magnetic field on the flow of magnetorheological fluid. II. Cylindrical channel47(2003); http://dx.doi.org/10.1122/1.1619378View Description Hide Description
We consider the flow of a magnetorheological (MR)fluid in a cylindrical channel in the presence of a magnetic field inclined relatively to the channel axis The stress tensor in the MR fluid is derived by assuming that chain structures are located in the planes parallel to the velocity and the magnetic field (plane We show that the velocity field has two orthogonal axes of symmetry, and in the plane perpendicular to and that the plug zone can be approximated by an ellipsoid of major axis The plug zone is not defined in the usual way since inside the plug each line perpendicular to the axis is moving at a different velocity. The experiments in a cylindrical capillary at high Mason numbers are compared for different angles between the flow and the field to theoretical predictions. We still recover Bingham behavior and all the pressure versus flow rate curves obtained at different field angles gather on a single straight line when represented against an average normalized yield stress. The slope of this master curve (−0.69) differs slightly from the prediction of the model (−0.85) but is closer than the prediction of the usual model (−4/3) for axial-symmetric flow. The channel hydraulic resistance is maximum for field perpendicular (θ=0) to the axis of the channel and decreases drastically when the angle θ of inclination of the field is larger than 45°; this behavior is reproduced well by our model.
47(2003); http://dx.doi.org/10.1122/1.1608953View Description Hide Description
Recent “tack” experiments on Newtonian liquids have shown that the force versus gap measurements obtained by pulling apart two surfaces separated by a thin liquid film result from a complex and dynamic balance between the viscous force resisting the separation and the spring force exerted by the compliant load cell of the instrument [Tirumkudulu et al. Phys. Fluids 15(6), 1588–1605 (2003)]. Here, we present similar experiments with waterborne adhesives that are colloidal dispersions of soft polymer spheres dispersed in water. By employing a simple power law to describe the complex rheology of the waterborne adhesives and a lubrication approximation for the viscous force, we predict pull-off forces in close agreement with those observed experimentally. However, experiments with high particle concentration adhesive and/or large separation rates cause cavitation in the gap, resulting in forces that are lower than predicted. Finally, a simple analysis for adhesives of two different rheologies shows that the tack test may result in contradictory conclusions, since the forces are sensitive to small variations in the instrument settings.
Texture evolution of sheared liquid crystalline polymers: Numerical predictions of roll-cells instability, director turbulence, and striped texture with a molecular model47(2003); http://dx.doi.org/10.1122/1.1621420View Description Hide Description
In the present work, we study the textural evolution of liquid crystal polymer (LCP) systems under planar shear at high shear rates, based on computational simulations using a recently developed molecular model with distortional elasticity [Feng etal. (2000)]. We concentrate our attention on the final striped texture that is observed in real LCP systems and on the secondary flow instability characterized by the formation of cross-sectional roll cells that is believed to represent the starting point of the orientational evolution. We verify that the theoreticalmodel is capable of predicting a texture evolution that captures many of the essential features of the interplay between shear flow and LCP microstructure that are observed in experiments. We identify the mechanisms at play and the relative roles of the various forces in determining the evolution of texture at moderate shear rates and how they depend on the Deborah number, which is the characteristic parameter that defines the different regimes at moderate and high values of shear rate.
Thermorheological properties of self-assembled dibenzylidene sorbitol structures in various polymer matrices: Determination and prediction of characteristic temperatures47(2003); http://dx.doi.org/10.1122/1.1619379View Description Hide Description
Self-assembling of low molecular mass molecules based on a sugar derivative, namely dibenzylidene sorbitol, was studied in different polymeric matrices experimentally. The characteristic temperature at which the supramolecular organization of these materials sets in was determined by rheological means. The investigations revealed a crucial role of interactions between the structure forming agent and the polymer matrix. An equation was derived which correlates the characteristic temperature at which the structure formation sets in with the strength of enthalpic interactions expressed by the Hildebrand solubility parameter. The agreement between experimental data and calculations is satisfactory. Based on our experiments and calculations we are able to formulate necessary criteria for self-assembly in order to predict the behavior of unknown systems.
47(2003); http://dx.doi.org/10.1122/1.1621421View Description Hide Description
The unstable capillary flow of the micellar system formed by cetylpyridinium chloride 100 mM/sodium salicylate 60 mM (CPyCl/NaSal) in tridistilled water was studied in this work using a combination of particle imagevelocimetry(PIV) and rheometrical measurements. The experiments were run in a pressure controlled capillary rheometer at a temperature of 26 °C and covered all the different flow regimes occurring in the nonmonotonic flow curve characteristic of micellar solutions. First, we show the suitability of the PIV technique to study the unstable capillary flow of this micellar system. Then, and more important, we provide evidence of the development of shear banding and the velocity profiles for the different flow regimes, including the transition to the high shear branch because of spurt. The velocity profiles at low shear rates exhibited a Newtonian behavior, followed by a still Newtonian with apparent slip up to the onset of spurt. There was a jump of one order of magnitude in the shear rate with a transient of a few minutes once spurt was triggered. The velocity profiles obtained during the transition to the high shear rate branch were plug-like, with a large increase in the velocity close to the capillary wall. When the transition was completed, the velocity profiles corresponding to the high shear rate branch showed the development of a shear band close to the capillary wall, whose thickness increased along with the shear rate. Finally, the true flow curve reconstructed from the velocity profiles provided additional evidence of the existence of a shear band that grows from the capillary wall.
Experimental studies on the effect of viscous heating on the hydrodynamic stability of viscoelastic Taylor–Couette flow47(2003); http://dx.doi.org/10.1122/1.1621423View Description Hide Description
Experimental results on the hydrodynamic stability of three dilute polymer solutions (polyisobutylene-based Boger fluids) in Taylor–Couette flow are presented. We demonstrate that viscous heating causes significant destabilization relative to the isothermal viscoelastic case, and we quantify the effect of viscous heating on the critical conditions. Experiments in which the shear rate was stepped to a steady value indicate that the onset time for instability scales with the product of the polymeric relaxation time and the time for the fluid to reach a steady temperature profile under the influence of viscous heating. This time scale was used to perform quasistatic ramp tests to determine the critical Deborah number (De) as a function of the Nahme number, or the magnitude of viscous heating. At low Nahme and Peclet numbers, the critical De remains essentially constant and the disturbance flow is nonaxisymmetric and oscillatory. As the Nahme number (Na) and Peclet number (Pe) are increased, the disturbance flow changes to an axisymmetric and stationary vortexflow similar to Taylor vortices, and the critical De decreases dramatically. At and corresponding to a maximum temperature increase in the gap of 1.6 K, the critical Deborah number decreases to a value that is 12% of the plateau value of observed at low Na and Pe. These observations are in agreement with linear stability predictions by Al-Mubaiyedh and co-workers (1999, 2000) of viscoelastic Taylor–Couette flow for a multimode Oldroyd-B fluid in which viscous heating is present.
47(2003); http://dx.doi.org/10.1122/1.1608952View Description Hide Description
Steady and transient shear flows have been used to study the nonlinear behavior of aqueous, very concentrated suspensions of plate-like particles interacting mainly through excluded volume and electrostatic interactions. These interactions lead to an ordered structure corresponding to regions of aligned plates with very small interparticle gaps, as shown by cryomicroscopy. The transient shear behavior, observed at different shear rates, in terms of the shear stress τ and the first normal stress difference shows that the time required to reach steady state values is relatively short, probably in relation to the high degree of packing of these highly concentrated suspensions. However, changes from positive to negative values with time, and finally reaches a negative steady state value. Moreover, it is shown that the second normal stress difference compared to takes significant steady state values, the sign of which depends on the applied shear rate. The steady shear stress (or viscosity) versus shear rate curve resembles in shape the three-region flow curve observed in a number of liquid crystalline polymers, the intermediate region (II) corresponding to the transition between two shear-thinning regions. The versus shear rateflow curve shows a negative minimum, which takes place in the intermediate region. These flow curves are analyzed in terms of shear induced structural changes, on different length scales. Possible interplate friction resulting from lubricated contacts is also considered.
47(2003); http://dx.doi.org/10.1122/1.1621422View Description Hide Description
The linear viscoelastic properties of two families of metallocene-catalyzed polyolefins were determined in the “plateau” and terminal regions. Low values of the plateau modulus were observed for linear polyethylene relative to values cited for conventional and model hydrogenated polyolefins in several studies. This diminished value is discussed in terms of a possible decrease in entanglement density compared to that of other polymers synthesized through different polymerization processes [Aguilar et al. (2001)]. For atactic polypropylene the situation becomes more complex, but the values obtained are within the broad range observed in the literature for isotactic and atactic species (0.30–0.86 MPa) [Aguilar et al. (2003)]. When the viscoelastic response is inferred from molecular data, the result may vary depending on the physical entanglement state. It would thus appear that great care should be taken to ensure that measurements are performed on samples in suitably entangled reference states. The viscoelastic variables determined here, were verified according to the different molecular dynamic models available, all based on reptation concepts. Results showed exceptional agreement when the effect of polydispersity was modeled either through an average relaxation time for each molecular species or through the double reptation concept.
Flow induced coating of fluoropolymer additives: Development of frustrated total internal reflection imaging47(2003); http://dx.doi.org/10.1122/1.1619375View Description Hide Description
In the extrusion of linear low-density polyethylene (PE), fluoropolymer processing additives (PPAs) are used to eliminate the surface defect known as “sharkskin” by coating the die wall and inducing slip at the PPA/PE interface. We describe an in situ optical method for measurement of the coating thickness by exploiting the phenomenon of frustrated total internal reflection. By correlating the optical and pressure measurements, extrudate appearance and auxiliary experiments, we can elucidate the kinetics of the coating process. The PPA droplets first adsorb in the entrance region of the die and migrate under shear stress towards the capillary exit where they act to suppress sharkskin. We find that a uniform coating in the range of 25–60 nm is sufficient for sharkskin elimination. The steady state coating thickness near the exit ranges from 200 to 400 nm depending on the shear rate and concentration. We develop a mass balance model for calculation of the steady state coating thickness which compares well with our experimental data.