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Paper coating fluids also called colors are concentrated aqueous suspensions composed mainly of mineral pigments, thickeners, binders and dispersing agents. They are applied onto moving paper web for improving the optical and printing properties. Roll coating is one of the most used technologies for paper coating, however jet coating is currently a promising technology for high-speed processes. Coating colors are submitted to high strain rates in both roll or jet coaters, therefore the extensional viscosity plays a major role in the process. An orifice flowmeter was used for measuring the extensional properties of complex rheology fluids such as coating colors. The principle of this flowmeter is based on the relationship between pressure drop and the flow rate of fluid passing through a small orifice. The flowmeter was firstly calibrated in terms of a dimensionless Euler number as a function of the Reynolds number with Newtonian fluids. The calibration curve was then used to determine the apparent extensional viscosity of coating colors. Results of extensional properties of paper coating colors are presented and compared to shear viscosity. The ratio of extensional to shear viscosity (Trouton ratio) for some coating colors was shown to exceed considerably the theoretical value of 3 expected for Newtonian fluids.Copyright © 2003 by ASME

This paper describes an original on-line video device developed in order to study bubble instabilities occurring in the film blowing process, taking into account their three-dimensional behavior. For a linear low-density polyethylene, two forms of instabilities and combination have been observed: draw resonance and helical instability. These instabilities could be quantitatively described and differences in behavior could be assessed using real objective measurements and criteria. The influence of key processing conditions was investigated and the results showed that the instabilities are enhanced by increasing the draw ratio, blow up ratio and frost line height. These first results are in agreement with the majority of the results reported in the literature, but allow for a more accurate analysis of the phenomena.

Dynamic perturbations and off-centered single impeller configurations have been investigated to reduce mixing time with shear thinning fluids. The use of a color-decolorization technique based on a fast acid-base reaction allowed to measure mixing times and to reveal the presence of both segregated and dead zones. A statistical design approach has been used to evaluate the effect of the impeller position as well as the dynamic conditions and their interactions. Mixing times and flow patterns for shear thinning fluids were presented and compared to conventional operating modes. Homogenization was significantly enhanced when a radial flow impeller was used under both off-centered and dynamic perturbation conditions. In the case of an axial flow impeller, a combination of a large axial displacement with long clockwise times and short counter-clockwise times gave better mixing times.Copyright © 2002 by ASME

Publisher Summary This chapter discusses various aspects related to the rheological behavior of concentrated suspensions. Concentrated colloidal suspensions are characterized by yield stresses, shear thinning and thixotropic behavior, and for small amplitude shear flow, the elastic moduli could be significantly larger than the loss moduli. The rheological behavior of a concentrated suspension is the result of various contributions that are very difficult to measure and accurately describe. When dealing with industrial suspensions, other complications may arise from uncontrollable parameters, such as purity and technical specifications of the various components. The continuum concept is no longer valid for highly concentrated suspensions. Hence, in modeling the rheological properties of such materials, the assumption of affine deformation embedded needs to be relaxed. This can be done empirically using the Gordon- Schowalter derivative with a slip parameter instead of the usual upper convected derivative. A better and probably more successful route is to use computer (direct) simulations of the dynamics of particles injected in a suspending fluid. Such (2-D) computer simulations are carried out for a few hundred long rigid fibers and the qualitative results are shown.

Plasticized starches (PLS) are materials of current interest either for food or non-food purposes. Their processability and the control of their end-properties require a good knowledge of their rheological properties measured under physical conditions similar to the ones encountered in industrial processes, like extrusion. In preceding works, stability and linearity conditions and water content have been found for reliable results on PLS viscoelasticity. Semi crystalline structure has been shown tot be partly responsible for their gel-like viscoelastic behavior (Delia Valle et al. 1998). Due to this structural feature, rheological properties during processing, i. e. under large deformation, may not be deduced straightforwardly from the linear viscoelastic properties.

The linear viscoelastic behavior of starches from various origins, blended with different amounts of a plasticizer using a twin screw extruder, has been investigated. Conditions of stability for reliable measurements and linearity domain have been determined. At low strain, the plasticized starch is found to behave as a viscoelastic gel-like material. This behavior is partially explained by its semicrystalline structure, as evidenced by x-ray diffraction patterns. Crystallites are assumed to participate in the formation of an elastic network, embedded in a viscoelastic amorphous phase. Additional thermomechanical treatment reduces crystallinity and leads to a decrease of the storage and loss moduli. The plasticizing role of water is found to be important. The higher molecular weight of the potato starch is responsible for its larger moduli. In the case of maize starch, the highly branched amorphous amylopectin softens the structured behavior, resulting in lower moduli compared to those of rich-content amy...

Three forces will continue to provide incentive for the industry to produce new polymer blends: the ability to tailor product properties to a particular performance cost balance; fast entry into new markets; and it is easier to develop products for small or niche markets than by synthesizing new polymers. The utilization of polymer blends in commerce represents some 16% of all plastics and the sector is growing at a rate of approximately 10% per year. We expect that polymer blends will grow at a much faster pace in the next decade. The most important class of blends from the commercial viewpoint are the so-called immiscible blends, where the presence of a distinct minor phase may be observed. The minor phase in an immiscible polymer blend is deformable and a wide range of sizes and shapes can thus be obtained for this dispersed phase during processing [1]. Both the size and the shape of the minor phase can influence a multiplicity of physical properties. At present the processing/ morphology/ property relationships in immiscible and partly miscible blends remain poorly understood and a given processing strategy may result in high value added blends. Rheological methods are powerful tools to elucidate such relationships. The morphology of blends is strongly dependent on the rheological properties of the components and rheological properties are needed to understand the processing of blends and changes occurring during processing. Conversely, the blends’ morphology affects the rheological properties.

The importance of the interface to the properties of multicomponent polymer systems is gaining wider recognition. The subject has been investiga- ted in our laboratories for some time, so as to show the consequences arising from interfacial phenomena (1,2,3). In the present investigation attention has turned to the mechanical properties of filled, drawn polyethylene structures, to the thermal stability of these and to the probable part played by polymer/filler interfaces in determining these responses. Implied in the objectives is an experimental ability to express quantitatively the surface interactions of the materials used in the compounds. The recent evolution of inverse gas chromatography (IGC) (4), represents that experimental capability. It has been applied to determine acid/base interaction parameters for the fillers as well as for the polymer host. The present note reports preliminary results of the study; a fuller account is in preparation.

The outline of a model is presented to depict the entanglement states of polymers. Polymer melts are regarded in the model as composed of two components. Free macromolecular chains form the first component and the network of the entangled macromolecular chains the second. The state variables chosen to describe the internal structure of the polymer melt are: two conformational tensors (each describing one component) and another scalar that represents the relative proportion of each component (i.e., related to the entanglement density). The equations governing the time evolution of the state variables and the corresponding formula for the extra stress tensor are suggested with the help of recently developed diffusion‐convection equations. The model provides a convenient framework for the study of changes in the entanglement structure due both to different types of preparation of the polymers and to flow. Rheological data for two types of polyolefins either modified or unmodified are used to make preliminary...

A systematic study of conformation tensor rheological models is presented in this paper. The approach unifies and extends results obtained previously by Hand, Giesekus, and Maugin and Drouot. Rheological properties that are independent of details of the conformational dependence of the intrasegmental force and the mobility are identified. A closed form solution is found for rigid-in-average dumbbell models.

Batch mixing of viscous fluids with helical-ribbon agitators in 2.4 liter and 13 liter vessels has been studied for agitator speeds up to 200 RPM. Seven different agitators of different dimensions were employed in this work. Mixing times were measured using a decoloration technique and circulation times were determined by the tracer bead method. In addition, velocity profiles were obtained from streak photographs using selective illumination of the vessel and PVC powder as tracer particles. It was found that the mixing times of Newtonian fluids, which agreed with previously published data, were considerably (3 to 7 times) shorter than those of the viscoelastic fluids. The mixing time was strongly affected by the fluids' elasticity; increasing as the fluid elasticity increased. The velocity profiles were qualitatively similar for all the fluids but showed decreased axial circulation and increased circumferential flow as fluid elasticity increased. However, mixing is not only a function of the axial circulation (impeller pumping rate) but also is a function of the perturbations superimposed on the main flow. A simple, first approximation model based on the impeller geometry and flow patterns is proposed to correlate the circulation capacity and mixing time data for the various geometries studied. On a etudie, en employant des vitesses d'agitation atteignant 200 tours a la minute, le melange discontinu de fluides visqueux assure par des agitateurs a ruban helicoidal dans des vaisseaux de 2.4 litres et 13 litres; on a utilise a cette fin sept agitateurs differents de dimensions variees. On a mesure les temps de melange par une methode de decoloration et determine les temps de circulation au moyen d'une methode a base de perles marquees. On a, en outre, obtenu des profils de vitesse a partir de photographies avec stries, en utilisant un eclairage selectif du vaisseau et de la poudre de chlorure de polyvinyle qui servait pour les particules marquees. On a trouve que les temps de melange des fluides newtoniens, qui correspondaient a ceux qui ont deja ete publies, etaient bien plus faibles (3 a 7 fois) que les temps de melange des fluides visco-elastiques. L'elasticite des fluides a considerablement affecte le temps de melange, qui augmentait avec celleci. Les profils de vitesse se sont averes qualitativement semblables pour tous les fluides, mais ils ont indique une circulation axiale moindre et un ecoulement circonferentiel accru, a mesure que l'elasticite des fluides augmentait. Toutefois, le melange est une fonction non seulement de la circulation axiale, (taux de pompage du rotor), mais aussi des perturbations sur-imposees sur l'ecoulement principal. On propose un modele simple et fournissant une premiere approximation, lequel est base sur la geometrie du rotor et les types d'ecoulement, en vue d'etablir des correlations entre les resultats relatifs a la circulation et aux temps de melange, dans le cas des diverses formes geometriques etudiees.

The use of helical ribbon agitators to mix viscous non-Newtonian fluids has been investigated. A generalized model, based on an appropriate definition of effective viscosity, is proposed to predict power consumption. This model is most successful with fluids that do not have a high degree of elasticity. It was found that the efficiency of mixing of pseudoplastic fluids was about half of that of Newtonian fluids in the same mixer, while the efficiency of mixing viscoelastic fluids was still lower and approximately independent of the mixer geometry. Blade width was the primary variable affecting the mixing efficiency on inelastic fluids.

It has been observed that polymeric fluids exhibit frequently anomalous wall effects in rate-dependent laminar flow. In this work, we propose a new technique to obtain quantitative effects of anomalies observed in the gravity flow of six aqueous polymeric solutions on inclined plane surfaces. Wall effects are determined from departures of the experimental flow rates from the theoretical predictions, assuming Ellis behaviour for the non-Newtonian fluids. In all cases, the experimental flow rates exceed the predicted values, by a factor of four in some cases. The deviations are interpreted in the light of the “separation” phenomenon, ascribable to the formation of a layer of dilute polymer solution at the wall. From determination of the viscosity of the wall, it is shown that the polymer concentration is from 10 to 56% less of that of the bulk fluid.

Velocity-volume data of air bubbles were collected in a Newtonian fluid [40% (wt) glycerol in water], and in two non-Newtonian fluids [1% (wt) carboxymethylcellulose in water and 1% (wt) of polyacrylamide in glycerol and water]. No velocity discontinuity was observed in the case of the log-log plots of velocity versus volume for the three fluids. Also, there was no appreciable effect of injection period of the air bubbles upon their terminal velocities. Preliminary data on the coalescence phenomena were examined for two and three air bubbles injected simultaneously in the 1% CMC and the 1% PAA solutions. In both cases, coalescence followed a regular sequence. First the trailing bubble(s) enter the wake of the leading bubble, then the bubble(s) accelerate towards the leading bubble until collision occurs. This action results in a thin film separating each, continuing with a film thinning process until complete coalescence. Some experiments were performed relating the bubble volume required to coalesce with a 1.0 × 10−6 m3 bubble as a function of orifice separation, illustrating the effect of elasticity upon bubble coalescence.

Primary normal stress difference data of some 32 different polymer solutions have been examined and correlated to the shear stress by a simple power-law model. The normal stress at constant shear stress is shown to increase with the molecular weight of the polymer, but decreases with the polymer concentration. The method proposed by Abdel-Khalik, et al., for predicting the primary normal stress difference from viscosity data for these polymer solutions is inadequate. The FENE-P dumbbell model is used to obtain master curves combining normal stress and viscosity data as a function of a dimensionless shear rate. It is found that this presents several drawbacks. It predicts shear-thinning effects with a power-law slope of −2/3, which is found to be too restrictive. The model fails to predict shear-thinning effects for dimensionless shear rates λEγ lower than approximately 0.5. It also fails to predict satisfactorily the low shear rate value of the dimensionless combination of viscosity and first normal stress coefficient Ψ1/λE(η − ηs). An empirically modified correlation is proposed. The fit for a series of polyacrylamide (Dow Separan AP-30) solutions is very good. In the case of a series of monodisperse polystyrene solutions, the fit is not as good, as the data show a more pronounced effect of polymer concentration at high shear rates.

Heat transfer at the inner wall for co-current vertical air-water mixture flow has been investigated in a 161.5 mm diameter pumping tube of an air-lift system. The experimental heat transfer coefficients were found to be significantly higher than those calculated from a single liquid phase correlation for the same liquid flow rate. The enhancement of heat transfer was found to be related to the flow pattern. A decrease of the heat transfer coefficient was observed in the transition region from slug flow to churn flow. Hydrodynamic and heat transfer models have been used to describe heat transfer during the slug flow regime and a correlation is proposed for the heat transfer coefficient in the liquid plug behind the gas bubble. On a etudie le transfert de chaleur a la paroi du tube de pompage de 161.5 mm de diametre d'un systeme d'entraǐnement d'un liquide par un gaz, pour un ecoulement ascendant air-eau. On a observe que les coefficients de transfert de chaleur experimentalement mesures etaient bien superieurs a ceux que l'on peut calculer, pour un měme debit liquide, avec une correlation s'appliquant a un ecoulement liquide monophasique. L'influence du regime d'ecoulement sur le transfert de chaleur a ete mis en evidence et on a observe une decroissance des coefficients de transfert de chaleur dans la region de transition separant les regimes d'ecoulement par poches et turbulent baratte. Dans le cas de l'ecoulement par poches, et a partir de modeles de l'hydrodynamique et du transfert thermique, on propose une correlation pour le coefficient de transfert de chaleur dans le bouchon liquide.

The hydrodynamic behavior of a bubble column has been studied for various Newtonian and non-Newtonian liquids (water, glycerol, carboxymethylcellulose and polyacrylamide solutions). The mixing time, the power consumption, the circulation time and the gas hold-up have been measured in a cylindrical column (diameter: 0.254 m, height: 0.9 m) for three air sparger plates with different numbers and distributions of 1 mm diameter orifices. It is shown that the mixing efficiency decreases as the viscosity or the shear-thinning and elastic properties of the liquid increase. The viscosity of the liquid has little influence on the gas hold-up which is, however, strongly affected by the sparger plate characteristics and increases as the liquid phase becomes more elastic. A model for predicting gas hold-up is proposed. Le comportement hydrodynamique d'une colonne a bulles utilisant differents liquides newtoniens et non-newtoniens (eau, glycerol, solutions de carboxymethylcellulose et de polyacrylamide) a ete etudie. Le temps dc melange, la puissance dissipee, le temps de circulation et le taux de vide ont ete determines dans une colonne cylindrique (diametre: 0.254 m, hauteur: 0.9 m). Trois differents types de distributeur d'air ont ete utilises. Tous possedent des orifices de I mm de diametre, mais le nombre et la repartition des orifices different de l'un a l'autre. On constate que l'efficacite de l'action de melange decroit lorsque la viscosite du liquide augmente ou lorsque ses proprietes rheofluidisantes et elastiques deviennent plus importantes. La viscosite du liquide a peu d'influence sur le taux de vide observe qui, par contre, varie beaucoup selon le type de plaque distributrice utilise et augmente avec le caractere elastique du liquide. Un modele pour la prediction du taux de vide est propose.

Rheological measurements of polyisobutylene solutions are presented. A mineral oil of low viscosity has been used as solvent. The combined effects of concentration, molecular weight and temperature were studied. It is found that the rheological data, when plotted as N1λE/(η-ηs) versus λEγ fall on a master curve over several decades of the dimensionless shear rate, irrespective of temperature, polymer concentration and molecular weight. The findings of this work can be used to address the problem of hydrodynamic lubrication of a journal bearing using a viscoelastic lubricant.

This second paper of a series continues the examination of the tensile properties of two series of linear low density polyethylene/polypropylene, (LLDPE/PP) blends. The blends were prepared using a twin-screw extruder and cover the whole concentration range, An Instron Universal Tensile Tester was used to measure the tensile properties of the blends between 10 and 70°C, and the temperature and composition dependences of the modulus were examined. A comparison is established between the solid state and melt properties to underline the behavior in the PP rich region. Results of dynamic mechanical experiments and differential scanning calorimetry on the same materials are also given, and the mechanical behavior is discussed in terms of the variation of the system's crystallinity.

L'hydrodynamique d'un ecoulement air-eau, vertical ascendant a ete etudiee dans un dispositif original d'entrainement d'un liquide par un gaz developpe par Atara connu sous le nom de «canon a bulles». On observe deux types d'ecoulement: l'ecoulement bouchon et l'ecoulement turbulent baratte. Les mesures de pertes de charge ont mis en evidence l'importance de l'effet de l'entree des bulles d'air dans le tube. On a mesure les capacites de pompage du dispositif et une modelisation basee sur l'equation de quantite de mouvement a permis d'obtenir une relation entre les debits de liquide et de gaz

The exit flow from a capillary is analyzed with the help of macroscopic mechanical energy and momentum balances. The analysis shows that primary normal stress differences cannot be determined from the exit pressures under the assumption that the flow is viscometric down to the exit. This assumption and the second one (made by Han [9]) that both slit and capillary exit pressures are the same would lead to unacceptable results. Published exit pressure data for polyethylene melts are shown to be unreliable because of large hole-pressure errors in the pressure measurements. Pressure profiles obtained with a thin tube technique for the flow of a poly(isobutylene) solution indicate that the flow does not remain fully developed near the exit. Moreover, it is shown that for this polymer solution the excess viscous dissipation at the exit contributes to approximately 90 percent of the exit pressure.

The rheological properties of three types of fluids that exhibit large normal stresses are examined and compared. These fluids have a constant or nearly constant viscosity and can be used as model viscoelastic fluids, covering a range of viscosity from 0.1 to 124 Pa.s. One lubricant, Emkarox FC 31-45000, is shown to have the characteristics of a second-order fluid. Series difficulties encountered in measuring the rheological properties of the Separan—corn syrup solutions (Boger fluids) are reported. The Emkarox and solutions of polyacrylamide (Pusher 700) in mixtures of glycerine and water are proposed as better model fluids.

The mechanical and rheological properties of high density polyethylene filled with carbon black have been examined. Two sources of carbon black (one commercial and other obtained from a pyrolysis process) and various treatments have been studied. The rheological measurements in the melt state has been performed on a Rheometrics stress rheometer and a capillary rheometer. These materials possess outstanding hardness and toughness showing great potential for structural application. Comparison of carbon black from two sources showed that the carbon from the pyrolysis process has a good potential as a reinforcing agent. It was found that surface treatment reduces the particle-particle interactions and improves the filler dispersion. The relationship between the yield stresses, filler percentage, surface modification by the coupling agents and mechanical properties is discussed.

Excess pressure losses in a slit are reported for the flow of viscous fluids under a large range of the Reynolds number. Four types of fluids were used: Newtonian, inelastic shear-thinning, elastic shear-thinning and approximately second-order fluids. The excess pressure losses were obtained from pressure measurements with ten flush-mounted transducers, hence eliminating hole errors and differentiating between entrance and exit losses. The contribution of the viscous dissipation to the excess pressure losses was calculated from a macroscopic energy balance, correcting for the kinetic energy losses and the normal stresses arising in the fully developed flow region. Entrance losses are very important when the fluid exhibits both elastic and shear-thinning properties. In the absence of shear-thinning properties, the entrance losses are smaller or close to values obtained with Newtonian fluids. The exit losses present the same patterns as the entrance losses, but their magnitudes are only 20—40% of the entrance losses. Our results confirm that the assumption of fully developed flow down to the exit is unacceptable, in consequence the exit pressure cannot be used to evaluate the primary normal stress difference.

Mechanical and rheological properties of blends of a thermotropic liquid crystalline polyester with a polycarbonate have been investigated. The blends are fibrillar in character and exhibit great hardness and toughness due to high degree of molecular orientation which develops during the melt blending and processing steps. Increases of the Young modulus by 100 percent are observed for blends containing only 10 percent of liquid crystalline polymer, LCP. Time-dependent behavior of the blends was investigated by performing solid state relaxation measurements and the relaxation modulus was also found to increase by the addition of LCP. The effect is relatively small in the glassy zone of viscoelastic response, but increases through the transition and viscous flow regions. The melt viscosity of the polycarbonate is slightly shear thinning whereas that of the unblended LCP increases rapidly with decreasing shear rate at low shear rate. This suggests the presence of yield stresses as confirmed by measurements on the Rheometics RSR in the stress sweep mode. The melt viscosity of the blends was found to be similar to that of the unblended polycarbonate, but more shear-thinning and less viscous. Preliminary results of scanning electron microscopy (SEM) and differential scanning calorimetry (DSC) are also presented.

Three generalizations of classical hydrodynamic theories that are compatible with equilibrium thermodynamics and that are suitable for an appropriate macroscopic dynamical theory of polymeric liquids are considered. The strain tensor, the stress tensor and the chain segment distribution function (introduced in the network theory of polymeric liquids) are accepted as new state variables. We find that the generalized hydrodynamic equations are compatible with equilibrium thermodynamics provided certain conditions restricting the freedom of choice of constitutive relations are satisfied. In some particular cases the conditions are known from other considerations. We say that a dynamical theory is compatible with equilibrium thermodynamics, or equivalently, that it obeys the entropy principle if the properties listed in section 2.1 are satisfied.

A novel approach to phase space kinetic theory of dense polymer systems and to the study of their equilibrium and nonequilibrium properties is proposed. Phase space kinetic equations are constructed as continuity equations of the time evolution equation of a representative dumbbell subjected to an averaged field force. A thermodynamic equation of state, an expression for the pressure tensor involving the configuration space distribution function and an equation governing the time evolution of the configuration space distribution function are obtained as three consequences of a single phase space kinetic equation.

La dynamique des bulles d'air dans deux fluides viscoelastiques (solutions aqueuses :de polyacrylamide et de carboxymethyle cellulose) et un fluide newtonien (huile de silicone) a ete etudiee pour des volumes de bulles variant entre 0,1 et 11 cm3. La vitesse et la forme des bulles ont ete determinees par techniques photographiques avec stroboscope. Le volume des bulles a ete mesure avant chaque injection a l'aide d'une seringue calibree.

A mathematical model based on the diffusion-convection equations is used to describe the rheological properties of dilute polymer solutions. The model uses a second-order conformation tensor as a measure of the internal strain; this avoids the mathematical complexity resulting from the use of a more detailed description of the macromolecules and also avoids the necessity of introducing additional ad-hoc assumptions (closure approximations) commonly used in other molecular theories. The rheological equation is obtained in terms of the rate-of-deformation tensor\(\dot \gamma \) and a scalar functionf(σ) relating the extra stress tensorσ to the internal strain tensorc. The functionf(σ) depends on the physical insight introduced in the Helmholtz free energyA(c) of the solvent-polymer system.

In the light of a new interpretation, we have studied the end effects for highly elastic-constant viscosity fluids commonly called Boger fluids. In terms of entrance effect only, the presence of primary normal-stress differences in absence of shear-thinning properties results in a decrease of the entrance correction below the Couette (Newtonian) value, whereas the total end correction can be substantially increased by an amount which is strongly dependent on the Weissenberg number or recoverable shear.

The friction factors and heat transfer coefficients have been determined for the turbulent flow of water and 100 ppm aqueous solutions of polyacrylamide in circular, square and rectangular pipes. The heat transfer reduction in the circular and square pipes was found to be larger than the drag reduction: 30% as compared to 20%. In the rectangular pipe, the reduction of the heat transfer was about equal to the drag reduction (≃ 15%) and much less than in the other geometries. The Colburn analogy between heat and momentum transfer was found to be valid for the circular pipe but not for the other geometries.

A selection of kernel functions is given to be used in a new integral constitutive equation proposed by Piau whereby the deviatoric stress is calculated from the integral of the history of the past intrinsic rate of rotation and rate of deformation tensors through a representation theorem. Piau has demonstrated the objectivity of a frame moving with a given particle whose axis are directed along the eigenvectors of the rate of deformation tensor. The use of such a framework provides a new approach in the attempt to reduce the computational difficulties associated with conventional constitutive equations written in co-deformational or co-rotational reference frames.

Viscosity data of an aluminum soap solution, a polyisobutylene solution, a polyacrylamide solution, and ten polystyrene solutions have been analysed using two rheological models: the Carreau model A and the Ellis model. The model parameters were obtained by non-linear regression. The importance of the zero-shear viscosity for design purposes is illustrated by observing the appearance of a master curve in the representation of the dimensionless viscosity versus the product of the zero-shear viscosity by the shear rate. A linear relation is shown to exist between the logarithm of the zero-shear viscosity and the polymer concentration. It is asserted that either model should replace advantageously the commonly used power-law expression. On a analyse, au moyen de deux modeles rheologiques (le modele A de Carreau et celui d'Ellis), les resultats des viscosites d'une solution de savon d'aluminum, une solution de polyisobutylene et dix solutions de polystyrene. On a obtenu les parametres des modeles par regression non lineaire. On illustre l'importance pratique de la viscosite en l'absence de cisaillement, en observant l'apparition d'une courbe principale dans la representation de la viscosite a-dimensionnelle en fonction du produit de la viscosite en l'absence de cisaillement par la vitesse de cisaillement. On montre qu'il existe une relation lineaire entre le logarithme de la viscosite en l'absence de cisaillement et la concentration des polymeres. On soutient que les deux modeles pourraient remplacer avantageusement l'expression de la loi de puissance employee communement.

A variety of constitutive equations have been proposed in recent years to describe the behaviour of polymer solutions and melts. Rather complete reviews of most of the differential and integral equations proposed prior to 1967 have been given by Spriggs, Huppler and Bird(1) and by Bogue and Doughty(2,3). Since then, numerous efforts have been directed towards the development of equations capable of predicting adequately nonlinear and transient properties of polymer solutions and melts. Considerable information can be found in the recently published works by Bird et al.(4,5). Some of the more successful models are presented here in an uniform notation. The models are evaluated in terms of their ability to simultaneously describe some or most of the rheological functions such as the non-Newtonian viscosity, the normal stress difference functions, the components of the complex viscosity, stress growth and stress relaxation. Depuis quelques annees, de nombreuses equations constitutives ont ete proposees pour decrire le comportement des polymeres en solution ou a l'etat fondu. Spriggs, Huppler et Bird(1) de měme que Bogue et Doughty(2) ont resume, dans des articles de revues, la plupart des equations differentielles et integrales publiees avant 1967. Depuis, de nombreux efforts ont ete faits pour developper des equations qui decrivent adequatement les proprietes non-lineaires et transitoires a la fois de solutions de polymeres et de polymeres a l'etat fondu. Dans les articles de Bird et al(4,5) on trouve de nombreux renseignements sur les travaux recents faits dans ce domaine. Dans le present travail sont cites, en utilisant une měme nomenclature, quelques-uns des modeles qui se sont averes les plus efficaces. Ces derniers sont evalues en fonction de leur habilete a decrire simultanement quelques-unes ou la plupart des functions rheologiques telles la viscosite non-newtonienne, les fonctions de contrainte differentielle normale, les composantes de la viscosite complexe, la contrainte de croissance et la relaxation de contrainte.

Measurements of the circulation time during batch mixing of Newtonian and non-Newtonian fluids were used to analyse and compare the performance of six different helical-ribbon impellers and a screw impeller inside a draft coil. The distribution of circulation times obtained from two hundred repeated measurements is shown to depend markedly on the impeller geometry. Mixing time data with the helical-ribbon impellers are correlated with the mean value and the reduced standard deviation of the circulation times. Effective (rapid) mixing corresponds to a large circulation capacity and a wide distribution of the circulation times. The mixing mechanism of Newtonian fluids with the helical-ribbon impellers is qualitatively described by the Voncken model. The helical impellers' circulation capacities are not affected by the shear-thinning properties of non-Newtonian fluids. However, in highly shear-thinning fluids, the presence of important stagnant zones is responsible for much longer mixing times which consequently do not correlate with the circulation parameters. The relative efficiencies of the different impellers in Newtonian fluids are compared using a criterion based on the the total energy required to achieve a certain degree of mixing. The wide blade impeller is the most efficient of the helical-ribbon impellers but is considerably less efficient than the screw impeller in a draft coil.