Ostwald-de Waele Law Research Articles

Laminar Power-Law Fluid Flow in a T-Shaped Channel at Given Pressure Differences

The steady laminar flow of an incompressible power-law fluid in a plane T-shaped channel is studied at given pressure differences between the inflow and outflow sections. A non-Newtonian fluid, whose rheological behavior is governed by the Ostwald—de Waele law is called the power-law fluid. The mathematical formulation of the problem includes the equations of motion and continuity. The no-slip condition is imposed on solid walls. The problem solution is obtained using a finite-difference method invoking the SIMPLE procedure. A parametric investigation of the kinematic and dynamic flow parameters is carried out for different values of the relevant parameters of the problem. The flow regime map is constructed for different pressure differences between the inflow and outflow boundaries and different nonlinearity exponents of the rheological model.

Mixing of complex fluids with flat and pitched bladed impellers: Effect of blade attack angle and shear-thinning behaviour

In the present work, results on the mixing of complex fluids by two-bladed stirrers are given; the method used was a numerical analysis. The fluids simulated have a shear thinning behaviour modelled by the Ostwald de Waele Law. The effects of inclined angle on the local and global mixing characteristics have been particularly determined. Also, the effects of Reynolds number and rheological behaviour are checked. To verify our computer simulations, some results have been compared with others experimental data and a satisfactory agreement was found.

Modell zur Beschreibung der rheologischen Eigenschaften von Blends aus HDPE und langkettenverzweigtem linearem Polyethylen niederer Dichte

Die rheologischen Eigenschaften von Blends aus einem Polyethylen hoher Dichte (HDPE) und einem mittels Metallocen-Katalysatoren hergestellten linearen Polyethylen niederer Dichte mit einem Anteil an Langkettenverzweigungen (HBPE) wurden bezüglich der Abhängigkeit der Scherviskosität von der Schergeschwindigkeit über den gesamten Zusammensetzungsbereich der Polymerblends untersucht. Während das reine HDPE einen starken Abfall der Viskosität mit steigender Schergeschwindigkeit aufweist, ist dieses Abfallen beim HBPE wesentlich schwächer ausgeprägt. Bei einer Schergeschwindigkeit von ca. 300 s–1 weisen beide Produkte gleiche Viskositäten auf. Die Viskositäten der Blends zeigen in Abhängigkeit von der Schergeschwindigkeit einen nichtlinearen Übergang zwischen dem Verhalten der reinen Komponenten HDPE und HBPE. Dieses Verhalten konnte mit einem mathematischen Modell beschrieben werden, wobei sich insbesondere rationale Gleichungen neben häufig verwendeten rheologischen Modellgleichungen als geeignet erwiesen. Schließlich wurde im Hinblick auf eine weitere Diskussion als Maß für die Strukturviskosität neben dem Abfall der Viskosität mit steigender Schergeschwindigkeit auch der Exponent im Ostwald-de Waeleschen Gesetz betrachtet. Der Schwellwert, d.h. die Strangaufweitung bei der Extrusion, wurde als Ausdruck für die elastischen Anteile der Polymerschmelze berechnet und ihre Abhängigkeit von der Schergeschwindigkeit und der Zusammensetzung mathematisch dargestellt und diskutiert. Dabei wurde beobachtet, daß der Schwellwert eines Blends eine geringere Veränderung mit der Schergeschwindigkeit erfährt, als ihn die Einzelkomponenten aufweisen. The rheological properties of blends of high-density polyethylene (HDPE) and linear polyethylene of low density with an amount of long-chain branching (HBPE) synthesized with metallocene catalysts were investigated regarding the dependence of the shear viscosity from the shear rate over the whole composition range. While the pure HDPE shows a strong decrease in viscosity with increasing shear rate, the decrease for HBPE is much less distinctive. For a shear rate of about 300 s–1 both products show similar viscosities. The viscosities of the blends, in dependence from the shear rate, show a nonlinear change between the characteristics of the pure components HDPE and HBPE. This behaviour could be described with a mathematical model, for which especially rational functions together with often used rheological model terms gave good results. Finally, besides the decrease of the viscosity with increasing shear rate, the exponent in the Ostwald-de Waele law was discussed as measure for the intrinsic viscosity. The threshold value, i. e. the Merrington effect during extrusion, was calculated as measure for the elastic amounts in the polymer melt, and their dependence from the shear rate and from the composition was expressed mathematically and discussed. It was observed that the treshold value shows a less significant change in dependence from the shear rate than the pure components do.

Laminar and transitional flow of drilling muds and various suspensions in circular tubes

Most suspensions exhibit a rheological behaviour which cannot be represented by either Bingham's or Ostwald–De Waele's law. In studying such cases a very simple expression with only three parameters may be used. Starting with an intermediate law of this sort, this paper gives velocity profiles and head losses in laminar flow, which have been computed and plotted on diagrams in non-dimensional co-ordinates.It has been found that transition flow rates in circular tubes for data taken from the literature and from experiments conducted on drilling muds at the Institut Français du Pétrole, are efficiently predicted by an empirical criterion (Ryan & Johnson 1959) which establishes a relation between a generalized Reynolds number and a generalized Hedström number.