Pierre J. Carreau

Rheological Equations from Molecular Network Theories

Lodges molecular network theories are quite successful in describing the linear viscoelastic behavior of polymer solutions and melts, but cannot account for the rate‐of‐strain dependence of various material functions. By allowing the junction‐creation rate and the probability of loss of junctions to depend on the second invariant of the rate‐of‐strain tensor, more realistic constitutive equations were obtained. Two rheological models are proposed by assuming two different mechanisms for the effect of the rate of strain on the kinetics of the network. The experimental data on three fluids (representative of eight viscoelastic fluids) are used to test the models in various flow situations. For steady simple shearing and small‐amplitude, sinusoidal simple shearing, both model A and model B are capable of fitting the four functions η, −(τ11−τ22), η′, and G′ rather well over many decades of shear rate or frequency. For suddenly changing flow experiments model A is inadequate. Model B however appears to be the...

Influence of elastic properties on drop deformation and breakup in shear flow

In this article we report experimental results on the deformation and the critical breakup conditions of a single drop in a medium under simple shear flow. The role played by both drop and matrix elasticities is quantified by using constant viscosity elastic (Boger) fluids. The experiments were conducted using two transparent parallel disks mounted on a R-18 Weissenberg rheogoniometer. The critical shear rate was determined by imposing successive small changes in shear rate from lower to higher values until the drop breakup was observed. The results show remarkable differences in the mode of deformation and breakup for Newtonian and elastic fluid systems. It is also found that the drop resistance to deformation and breakup increases with increasing elasticity ratio. The contribution of the drop and matrix elasticities is quantified by using an empirical relation established between the drop deformation and the capillary number, Ca. The critical breakup conditions, such as a dimensionless breakup time, tb*...

Morphological stability, interfacial tension, and dual-phase continuity in polystyrene-polyethylene blends

The morphological stability of polystyrene high-density polyethylene (PS/PE) blend is investigated in the region of dual-phase continuity. The effect of the addition of a triblock SEBS copolymer to the blends on the stability of these morphologies, is examined. The results show that the morphology of the unmodified blends changes from co-continuous to droplet matrix for PS-rich blends whereas the morphology of a 50/50 blend maintains continuity but coarsened significantly upon annealing at 200°C. In the presence of the copolymer, these morphologies are much more stable. Selective solvent extraction of polystyrene in di-ethyl ether reveals that the level of PS continuity in the 50/50 blend is higher for the unmodified system than for the modified one. Upon annealing, the level of PS continuity significantly increases for the unmodified 50/50 PS/PE blend. The effect of the copolymer content in the blend on the interfacial tension between the two components is also investigated using the breaking thread method. The interfacial tension is found to be reduced from 5.6 to 1.1 mN/m by the addition of 20 parts of the copolymer to the blend.

Relationships between rheology and morphology for immiscible molten blends of polypropylene and ethylene copolymers under shear flow

The linear and nonlinear viscoelastic properties of immiscible polymer blends polypropylene/ethylenevinylacetate–ethylenemethylacrylate [PP/(EVA–EMA)] have been investigated. The transient shear flow experiments reflect the structural changes of the blends during the flow. Overshoots in stress growth experiments are observed when the dispersed phase is deformable. In this case, a good description of these transient rheological data is obtained using modified versions of the Lee and Park [J. Rheol. 38, 1405 (1994)] and the Grmela and Ait-Kadi [J. Non-Newtonian Fluid Mech. 55, 191 (1994)] models. Predictions of the morphological evolution of the blend under transient shear flows were calculated from the modified models which are shown to describe the breakup and coalescence phenomena under moderately large deformation shear flow. When the dispersed phase is undeformable, these models, which are either based on the original Doi and Ohta [J. Chem. Phys. 95, 1242 (1991)] theory or derived to retrieve an extens...

Properties of PETG/EVA blends : 1. Viscoelastic, morphological and interfacial properties

Abstract The linear viscoelastic properties of molten polyethylene terephthalate glycol/polyester-ethylene vinylacetate (PETG/EVA) immiscible blends were measured as a function of frequency for different compositions and temperatures. The morphology of the blends was determined by scanning electron microscopy and the rheological behaviour of the blends is described by the Palierne emulsion model. The behaviour is typical of homogeneous molten polymers except for the appearance of a shoulder in the storage modulus data at low frequencies. This corresponds to an increase in elasticity in the terminal zone and longer relaxation time compared to the matrix. The model describes correctly the experimental data, and the model predictions are used to determine the interfacial tension between PETG and EVA. The interfacial tension is shown to vary between 4.5 MnM−1 and 7 mNm−1, depending on composition and temperature. These values are in the range of interfacial tension values determined for other similar polymer systems. No comparison with literature data was possible and an attempt to use the breaking thread method to verify the interfacial tension value for this system was not successful.

Rheological modeling of concentrated colloidal suspensions

Abstract The use of concentrated colloidal suspensions is common in several industries such as paints, foodstuffs and pulp and paper. These suspensions are generally composed of strongly interactive particles. If the attractive forces dominate the repulsion and Brownian forces, the particles aggregate to form a three-dimensional network yielding a gel structure. Under flow, the micro-structure of suspensions can be drastically modified and the rheological properties are then governed by structure breakdown and build-up. In this work, we propose a structural network model based on a modified upper convected Jeffreys model with a single relaxation time and a kinetic equation to describe the flow-induced micro-structure evolution. Three distinct kinetic equations are tested for this purpose. The proposed model describes yield and thixotropic phenomena, nonlinear viscoelastic behavior and output signal distortions observed for relatively small strain amplitude during oscillatory measurements, and overshoots observed in stress growth experiments. A comparison of model predictions and experimental data for fumed silica and coating colors is also presented. However, different model parameters must be used to correctly predict the different flow properties indicating that a more versatile or generalized kinetic equation must be proposed.

Influence of elastic properties on drop deformation in elongational flow

We report experimental results on the deformation of a single drop suspended in a medium under uniaxial elongational flow along the central axis of a converging conical channel made of Plexiglas. Both the drop and the continuous phases consist of constant viscosity elastic fluids, so-called Boger fluids. This study reveals several interesting features about the role played by both the drop and matrix elasticities on the drop deformability. In a given matrix fluid, the drop deformation decreases as its elasticity increases. For a given drop fluid, the matrix elasticity has the opposite effect: the drop deformation increases with increasing matrix elasticity. An empirical relation between the drop and matrix deformations is established as a function of the drop and matrix characteristic elastic times.

Linear viscoelastic behavior of molten polymer blends: A comparative study of the Palierne and Lee and Park models

The linear viscoelastic properties of several molten blends with immiscible components of different viscosity ratio have been investigated. All the blends show a morphology of emulsion type. At low frequencies, the behaviors of these blends are essentially governed by the interface. The Palierne (1990) model is shown to well predict the linear behavior of all the blends. The Lee and Park model (1994), developed to take into account the relationship between the rheological behavior and morphological changes under large strain flows, is also shown to well describe the storage and loss moduli of the blends by adjusting a single fitting parameter. Based on the weighted relaxation spectra, a comparison of both model predictions is made focussing on the time associated to the interface. An approximate method is then proposed to evaluate the interface parameter introduced in the Lee and Park model. At high frequency, discrepancies are observed for the Lee and Park predictions when the viscoelastic properties of both components are considerably different. The description of the bulk properties of the blend, i.e., the mixing rule used by Lee and Park, is modified to obtain a better description of the high frequency data.

Rheological properties of short fiber model suspensions

The rheological behavior of two series of model suspensions containing the same glass fibers in a Newtonian polybutene and in a Boger fluid has also been investigated. The steady-state shear viscosity of both supensions increased with fiber content, but the suspensions in the Boger fluid became shear thinning. Both types of suspension exhibited non-negligible normal stresses. The steady-state viscosity and normal stress difference of the supensions in the polybutene are well predicted by the Lipscomb (1987) equation coupled with the Folgar–Tucker (1984) model. Both types of fiber suspensions were shown to exhibit shear and normal stress overshoots in stress growth experiments. Under flow reversal, a shear stress overshoot was observed at a larger deformation compared to the primary overshoot. The reverse overshoot has been attributed to tumbling of fibers that are not totally aligned in the flow direction even after a very long time. When the flow was reversed, the normal stress difference took initially ...

Modeling of ultrafiltration: Predictions of concentration polarization effects

Abstract This paper essentially deals with modeling of the concentration polarization effects on solute separation in ultrafiltration. Laminar tangential flow in a rectangular section channel is considered. The concentration polarization phenomenon in ultrafiltration has been studied by different authors who used different approaches for the finite-difference discretization of the mass transport differential equation. Two of those approaches are examined in detail. It is shown how numerical convergence can be reached, with a small number of increments, when an appropriate choice of the discretized mass transport equation is done. It is also shown why erroneous results have been obtained even with a large number of increments. Parametric studies show a strong influence of the true separation and of the permeation velocity on the separation profile along the tangential flow channel. A comparison between a finite-difference solution and an analytical solution for the mass transport differential equation is presented. Good agreement between the two methods is shown for the limiting case of high separation.