Showing papers by "Pierre J. Carreau published in 1979"

An analysis of the viscous behaviour of polymeric solutions

Abstract: 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.

Mixing with helical ribbon agitators: Part II. Newtonian Fluids

Abstract: 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.

Review of some useful rheological equations

Abstract: 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.

A constitutive equation derived from Lodge's network theory

Abstract: A constitutive equation is presented, derived from Lodge's molecular network theory. The equation is of a form similar to the one presented previously by Carreau. The rate of creation of junctions and the probability of loss of junctions depend here also on the second invariant of the rate-of-strain tensor. The dependence, however, is through simple exponential functions, resulting in easy-to-use equations. Material functions are presented for the viscosity, the primary normal stress coefficient, the complex viscosity, the stress relaxation after cessation of steady simple shear, the stress growth after onset of steady simple shear and for elongational flow. The usefulness of the simplified (series truncated) equations is discussed and the model is evaluated with typical viscoelastic data.

Wall effects in polymer flow on inclined plane

Abstract: 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.