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Journal of RheologyVolume 47, Issue 3 (May-June 2003) |
Contents
On the shear thickening flow of dilute CTAT wormlike micellar solutionsE. R. Macías, F. Bautistaa), J. F. A. Soltero,
J. E. Puig P. Attané O. Manerob) AbstractDilute solutions of wormlike micelles exhibit shear thickening caused by microstructural changes under specific flow conditions. In this work, for the first time, shear thickening in parallel plate and Poiseuille flows is investigated using simultaneously Particle Image Velocimetry (PIV) and rheometry. Four distinctive zones of flow behaviour have been identified in parallel plates as the shear rate increases, namely, a Newtonian region, a transition regime where inhomogeneous nucleation of the shear-induced structures (SIS) is followed by homogeneous nucleation of SIS, and an apparent second-Newtonian regime at high shear rates, where rapid temporal fluctuations of the viscosity are smoothed out by inertia of the moving plate. In pipe pressure flow, PIV results reveal a flow pattern consisting, of a superposition of two parabolic regions of the velocity profile located near the centre and close to the pipe walls, and a transition region where again strong fluctuations in the velocity profile are observed. The experimental results are compared with predictions of a convected-Maxwell constitutive equation coupled to a kinetic equation that accounts for increasing dissipation of the system due to the presence of the SIS. The model accounts for the average steady values of the viscosity in the structured thickened state. b) Author to whom correspondence should be addressed. E- mail: manero@servidor.unam.mx A model for large deformation of an ellipsoidal droplet with interfacial tensionNancy E. Jackson and Charles
L. Tucker IIIa) AbstractA model is developed to predict the transient shape evolution of an ellipsoidal Newtonian droplet with interfacial tension, suspended in another Newtonian fluid with a different viscosity. Using the Eshelby equivalent inclusion theory (Eshelby, 1957), this model adds an approximate interfacial tension term to the exact deformation model of Wetzel and Tucker (2001) for droplets with zero interfacial tension. The model can predict large deformations and rotations of the ellipsoid, it allows any value of viscosity ratio, and it admits arbitrary far-field flows. The model does not incorporate breakup or coalescence. At viscosity ratios less than 0.1, the model blends the Eshelby model (for compact shapes) with a classical slender-body model (for thread-like shapes), providing a smooth transition between these two limits. The model accurately matches many experimental results from the literature, including steady shapes in simple shear, transient shapes during shear reversal, widening in simple shear, relaxation after step shear, and the critical capillary number for breakup in both shear and planar elongation. The model also compares favorably to the ellipsoidal droplet model of Maffettone and Minale (1998). a) Author to whom correspondence should be addressed; E-mail: c-tucker@uiuc.edu
Large strain time dependent behaviour of cheeseS. M. Goh, M. N. Charalambides, and J. G. Williams AbstractThis study is aimed at characterising the non-linear viscoelastic behaviour of hard cheeses using mild Cheddar and Gruyere as examples. The constitutive model consists of the Van der Waals hyperelastic function and the Prony series. The material constants were calibrated using data from monotonic compression and stress relaxation tests. Based on these constants, finite element simulations of three point bend and wire cutting tests were performed. The finite element predictions were compared with experimental data and good agreement was observed. In addition, successful predictions of the steady-state cutting force in the wire cutting tests have been made through the use of a critical fracture strain criterion. Cyclic generation of wall slip at exit of plane Couette flowHiroshi Mizunuma and Hideyuki Takagi AbstractSharkskin-type melt fracture is generally produced by a discontinuous boundary condition at a die exit. In order to investigate this flow instability, a shear flow having a negative pressure gradient at the exit was generated by a wedge-shaped slider. A high-resolution DIC (Differential Interference Contrast) microscope was used for simultaneous observation of the inside and outside of the flow cell, which employed linear PDMS. At the cell exit, the spatial distribution and the temporal change in velocity were measured under sharkskin-like instability by use of a particle tracking method and laser Doppler velocimetry. A slip flow and a stick flow appeared alternately at the exit of the sliding plate; the slip flow is associated with cavity penetration from the cell exit. This inner instability was found to be associated with the formation of valleys and ridges on the outer free surface. At the cell exit, a slip flow appeared with a valley, and a stick flow appeared with a ridge. The penetration length of the cavity increases with sliding-plate speed, and this increase in penetration length induces flow stagnation upstream of the cavity. This stagnation relaxes high shear upstream of the cavity and suppresses the increase in penetration length of the cavity. Except for incipient instability, the penetration length has a linear relation with the wavelength of the outer ridges. Quantitative assessment of strain-hardening of LDPE melts by MSF modelM. H. Wagner M. Yamaguchi M. Takahashi AbstractThe elongational viscosity of three tubular and five autoclave low-density polyethylene (LDPE) melts is analysed, and quantitative comparison of the strain-hardening characteristics is made by use of the Molecular Stress Function model. This is based on a new strain-energy function, which assumes that the total strain energy of a branched section of the macromolecule is given by the addition of the strain energies of the individual chain segments contained in this section. The model employs only two nonlinear material parameters: one parameter describes the average number of crosslinked chain segments, which occupy the same tube section, and determines the slope of the elongational viscosity after inception of strain hardening. The second parameter indicates the maximum relative stretch of the chain segments and determines the steady-state (plateau) value of the elongational viscosity. Both parameters depend on the complex branching topology of LDPE melts. While quantitative relations between branching structure and the two nonlinear parameters are not yet available, the results of this comparison seem to indicate that the more tree-like structure of autoclave LDPE leads to a higher density of crosslinked chain segments in the same tube section than in the case of LDPE polymerized in tubular reactors. Wall slip and extrudate distortion of three polymer meltsDilhan M. Kalyona) and Halil Gevgilili AbstractA high-density polyethylene (HDPE), a poly(dimethylsiloxane) (PDMS) and an oxetane based alternating block thermo plastic elastomer (TPE) were subjected to steady torsional and capillary flows. HDPE and PDMS exhibited wall slip in steady torsional flow. The shear stress ranges at which wall slip became apparent during steady torsional flow for HDPE and PDMS coincided with the wall shear stress ranges in capillary flow at which distortions of the extrudates emerging from capillary die were first noted. In contrast, TPE did not exhibit wall slip in steady torsional flow (for shear rates up to 200 s-1 and strains up to 25). None of the three polymers exhibited any overshoots of shear stress or first normal stress difference under steady flow conditions, indicating that the often-reported stress overshoots could be artifacts of wall slip. Furthermore, the extrudates of the TPE were relatively smooth and exhibited only minor and non-periodic surface blemishes. The absence of extrudate distortions under the presumed no-slip condition for TPE emphasizes the intimate link between wall slip and the development of extrudate distortions and strengthens the premise that extrusion flow instabilities can be eliminated under conditions of stable wall slip or stick. c) Corresponding author. E-mail: dkalyon@stevens-tech.edu Simultaneous dielectric and dynamic mechanical measurements on PVDF in the molten state: Study of linear/nonlinear viscoelastic transitionJ-M. Gonneta), J. Guilleta), I.
Sirakova), R. Fulchironb,c) and G. Seytreb) AbstractSimultaneous dielectric and dynamic mechanical measurements on PVDF in the molten state have been performed by means of a dynamic rheometer equipped with an electrical cell. This device permits the evolution of the dielectric and mechanical properties to be recorded both inside and outside the linear viscoelastic domain (LVD). Dielectric properties during shear experiments inside the LVD are not dependent on the shear rate, according to linear viscoelastic theory and Brownian motion considerations. The linear/nonlinear transition is depicted by a fall of conductivity as well as the presence of a maximum of the real part of the permittivity. The decrease of the specific conductivity results from a modification of the conductive paths, which demonstrates an ionic mobility different in the direction along and normal to the chain, whereas the maximum of real permittivity is correlated to anisotropic dielectric properties. Stopping the dynamic mechanical strain causes a return of the dielectric parameters to a level close to the one obtained inside of the linear viscoelastic domain. c) Author to whom correspondence should be addressed. Rheology of sheared flexible fiber suspensions via fiber-level simulationsLeonard H. Switzer III and Daniel J. Klingenberg AbstractWe employ, particle-level simulation technique to investigate rheology of non-Brownian, flexible fiber suspensions in simple shear flow. The model incorporates a variety of realistic features including fiber flexibility, fiber deformation, and frictional contacts. The viscosity of fiber suspensions is strongly influenced by fiber equilibrium shape, interfiber friction, and fiber stiffness. The suspension viscosity increases as the fiber curvature, the coefficient of friction, or the fiber stiffness is increased. The yield stress of fiber suspensions scales with volume fraction in a manner similar to that observed experimentally. Fiber suspensions that flocculate, exhibit a shear thinning regime that extends to shear rates lower than that observed for homogeneous suspensions. Interfacial slip between polymer melts studied by confocal microscopy and rheological measurementsY. C. Lama), L. Jiang, C. Y. Yue, K. C. Tam,
L. Li X. Hu AbstractInterfacial slip between high density polyethylene (HDPE) and polystyrene (PS) melts was studied. HDPE/PS layered structure was subjected to steady shear in a Cambridge Shearing System. Through thickness melt velocities of the HDPE/PS layered structure were measured in-situ by employing a confocal microscope. Velocity profiles for both HDPE and PS layers were therefore obtained. Velocity discontinuity was observed at the HDPE/PS interface from the velocity profiles, indicating interfacial slip. Slip velocity obtained from the velocity discontinuity is in good agreement with that deduced from independent rheological measurements. a) All correspondence should be directed to Y. C. Lam. Tel: (65) 6790 5866, Fax: (65) 6791 1859, E-mail: myclam@ntu.edu.sg On the definitions of entanglement spacing and time constants in the tube modelR. G. Larsona), T. Sridharb), L. G. Lealc), G. H. McKinleyd), A. E. Likhtmane), and T. C. B. McLeishe) a) Dept. of Chemical Engineering, University of
Michigan, USA AbstractNumerous papers have recently appeared in the literature presenting quantitative comparisons of experimental linear viscoelastic data to the most recent versions of “tube” models for entangled polymer melts and solutions. Since these tube models are now being used for quantitative, rather than just qualitative, predictions, it has become important that numerical pre-factors for the time constants that appear in these theories be evaluated correctly using literature data for the constants (i.e., density, plateau modulus, etc.) that go into the theories. However, in the literature two definitions of the entanglement spacing in terms of plateau modulus have been presented, and confusion between these has produced numerous errors in the recent literature. In addition, two different definitions of the “equilibration time”, a fundamental time constant, have also appeared, creating additional potential for confusion. We therefore carefully review the alternative definitions and clarify the values of the pre-factors that must be used for the different definitions, in the hope of helping future authors to avoid such errors. Separating the effects of sparse long-chain branching on rheology from those due to molecular weight in polyethylenesPhillip J. Doerpinghaus and Donald G. Bairda) AbstractThe effects of sparse (< 1 branch per chain) long chain branching, LCB, molecular weight (M) and molecular weight distribution on the shear rheological properties of commercial polyethylenes are often convoluted. In this paper a method for separating the effects of sparse LCB in metallocene-catalyzed polyethylenes (mPE) from those of molecular weight and its distribution based on time-molecular weight superposition is proposed. Four metallocene polyethylenes with degrees of long-chain branching (i.e. M of the arm (Ma) is greater than that for the onset of entanglements, Mc) as determined from dilute solution measurements ranging from zero (linear) to 0.79 LCB/104 CH2, along with a conventional Ziegler-Natta polymerized LLDPE, and a tubular free-radical polymerized LDPE are investigated. In general, it is observed that sparse LCB (for levels < 1.0 LCB/104 CH2) increases the zero shear viscosity, h0 (e.g. by a factor of 7) and decreases, but even to a greater degree, the critical shear rate (g-dotc) for the onset of shear thinning (e.g. by a factor of 100). The breadth of MWD just affects g-dotc but not h0 for the range of data used in this study. Furthermore, the dynamic storage modulus G' shows similar enhancement at low frequencies as viscosity does, while the primary normal stress difference coefficient, Y1,0, exhibits a greater dependence on long-chain branching than hat predicted from the zero-shear viscosity enhancement. The results for the mPE’s are consistent with recent molecular theories for randomly branched molecules in that it is the spacing between branch points and not the number of branches at a point that is important. Furthermore, the results are consistent with the idea that the branches are located on the longest chains and hence have the greatest effects on the longest relaxation modes. a) Author to whom all correspondence should be addressed. Phone: (540) 231-5998; Fax: (540) 231-5022 Strain hardening of various polyolefins in uniaxial elongational flowClaus Gabriela) and Helmut Münstedtb) AbstractIn this contribution correlations between the type of strain hardening of long-chain branched polyethylenes and the level of their zero shear-rate viscosities in comparison to linear polyethylenes are described. For polyethylenes of various branching structures four different types of strain hardening can be observed. Type I: Strain hardening is approximately independent of elongational rate. Type II: Strain hardening decreases with increasing elongational rate. Type III: Strain hardening increases with increasing elongational rate. In addition to that, materials are found which do not show strain hardening within the experimental window (Type IV). Qualitative correlations with the dependence of the zero shear-rate viscosity on the weight average molecular mass can heuristically be deduced. Polyethylenes of Type IV fulfill the well-established relationship h0 ~ MW3.4, samples of Type I and II give higher zero shear-rate viscosities than the linear products, Type III-samples generally exhibit zero shear-rate viscosities lower than the linear relationship. As the dependence of the zero shear-rate viscosities on the molecular mass offers some insight into the branching structure of a polyethylene, the differences in strain hardening can heuristically be related to the molecular structure. These correlations can be transferred to different types of long-chain branched polypropylenes giving some hint to their molecular structure. a) Present address:
Basell Polyolefine GmbH, SPR-CCC, M510, Carl-Bosch-Str. 38, D- 67056
Ludwigshafen, Germany The nonlinear time-dependent response of isotactic polypropyleneAleksey D. Drozdova) and Jesper deC.
Christiansen AbstractTensile creep tests, tensile relaxation tests and a tensile test with a constant strain rate are performed on injection-molded isotactic polypropylene at room temperature. A constitutive model is derived for the time-dependent behavior of semi-crystalline polymers. A polymer is treated as an equivalent network of chains bridged by permanent junctions. The network is modelled as an ensemble of passive meso-regions (with affine junctions) and active mesodomains (where junctions slide with respect to their reference positions with various rates). The distribution of activation energies for sliding of junctions in active meso-regions is described by a random energy model. Adjustable parameters in the stress-strain relations are found by fitting the experimental data. It is demonstrated that the concentration of active meso-domains monotonically grows with strain, whereas the average activation energy for sliding of junctions and the standard deviation of energies suffer substantial down jumps in the vicinity of the yield point. With reference to the concept of dual population of lamellae, these changes in material parameters are attributed to transition from breakage of subsidiary (thin) lamellae in the sub-yield region to fragmentation of dominant (thick) lamellae in the post-yield region of deformations. a) Corresponding author. Present address: Department of Chemical Engineering, West Virginia University, P.O. Box 6102, Morgantown, WV 26506, USA |
Please e-mail suggestions and comments to albertco@umche.maine.edu. Updated 25 January 2004 |