K. Walters

The yield stress myth

New experimental data obtained from constant stress rheometers are used to show that the yield stress concept is an idealization, and that, given accurate measurements, no yield stress exists. The simple Cross model is shown to be a useful empiricism for many non-Newtonian fluids, including those which have hitherto been thought to possess a yield stress.

Flow characteristics associated with abrupt changes in geometry in the case of highly elastic liquids

Consideration is given to the influence of small changes in corner geometry on flow characteristics in the case of elastic liquids flowing in various contraction geometries. Both Boger fluids and aqueous solutions of polyacrylamide are used to show that it is very difficult to make generalizations from one geometry to another or from one type of non-Newtonian fluid to another. Of major importance is the observation that the precise mechanism of vortex enhancement varies with the contraction ratio. For large contraction ratios, a re-entrant corner vortex (not present in a 4:1 contraction) is shown to have an important influence on the development of vortex enhancement.

On the use of flow through a contraction in estimating the extensional viscosity of mobile polymer solutions

Abstract We consider the use of pressure measurements in contraction flows in the determination of the extensional viscosity behaviour of polymer solutions. The experimental data are interpreted on the basis of the recent theory of Binding. The resulting extensional viscosities are compared with those obtained from a commercial Spin Line Rheometer. We conclude that contraction flows provide a convenient means of determining the extensional viscosity of shear-thinning polymer solutions. The case is not so clear for constant viscosity Boger fluids. In the course of the experiments, it is shown that excess pressure losses in the contractions can be brought about by two distinct flow mechanisms in the case of Boger fluids. In the axisymmetric case, both vortex enhancement and excess pressure loss are observed, although there is not a strict one-to-one correlation between these phenomena. In the planar case, vortex enhancement is not conspicuously present, although there is still a substantial excess pressure loss at high flow rates. This excess must be associated with the ‘bulb’ flow field which essentially replaces the vortex-enhancement regime of the axisymmetric case.

Further remarks on the lip-vortex mechanism of vortex enhancement in planar-contraction flows

Abstract Aqueous solutions of polyacrylamide are investigated in various planar-contraction flows in an attempt to answer some unresolved questions from an earlier paper of the present authors. It is concluded that a lip-vortex mechanism can be responsible for vortex enhancement for any planar-contraction ratio, provided the polymer concentration is chosen carefully or, alternatively, the contraction angle is varied.

On pulsatile flow of non-Newtonian liquids

We consider the behaviour of non-Newtonian liquids as they are made to flow through straight pipes of circular cross section under the action of a pressure -gradient which oscillates sinusoidally about a non-zero mean. The theory for such a situation is developed in detail and certain predictions, some quantitative some qualitative, are made. Quite a substantial increase in mean flow rate due to the fluctuation in the pressure-gradient is predicted under some conditions. The theoretical predictions are shown to be in good agreement with experimental results and a method for locating the “optimum conditions” is outlined which makes use of the experimentally determined apparent viscosity of the fluids only.The possible relevance of the work to blood flow in the human body is discussed.ZusammenfassungWir betrachten das Verhalten nicht-Newtonischer Fl:ussigkeiten, die unter der Wirkung eines Druckgradienten, der sinusförmig nur einen von Null verschiedenen Mittelwert oszilliert, durch gerade Rohre mit kreisförmigem Querschnitt strömen. Hierf:ur wird in Einzelheiten eine Theorie entwickelt und es werden einige Voraussagen, die zum einen qualitativ und zum andern quantitativ sind, gemacht. Es wird ein wesentlicher Anstieg der mittleren Strömungsgeschwindigkeit aufgrund der Schwankungen der Druckgradienten unter bestimmten Bedingungen vorhergesagt. Theorie und Experiment stimmen gut überein. Es werden „optimale Bedingungen“ aus einer Methode abgeleitet, die sich allein auf die experimentell bestimmte scheinbare Viskosität bezieht. Die möglichen Beziehungen dieser Arbeit zum Blutflien im menschlichen Körper werden diskutiert.

The pressure dependence of the shear and elongational properties of polymer melts

A borderless printing easel comprised of a paper support base having a retaining border formed thereon, and a set of flat sectioned mask plates removably positionable on the base portion, the individual sections of said mask plate being hinged at their center by a pliable strip of adhesive material whereby the mask sections can be successively folded back onto the top of opposing mask sections to reproduce adjacent or nearly adjacent borderless prints on a single sheet of print paper.

The relationship between the linear (oscillatory) and nonlinear (steady-state) flow properties of a series of polymer and colloidal systems

The Cox-Merz empirical relationship between the linear (oscillatory) and nonlinear (steady-state) viscosities has been shown to be valid for many polymeric systems. Here, we present an equivalent expression to relate the linear (G′) and nonlinear (N1) elastic properties of viscoelastic systems. Like the Cox-Merz relationship, it uses a combination of elastic and viscous parameters. The modified form of the storage modulus is then equivalent to the Cox-Merz complex viscosity. It can be used to correlate with (half) the normal force at numerically equal circular frequency and shear rate, respectively.This new expression and the Cox-Merz rule are tested for a range of polymeric and colloidal systems. It is found that both expression work for the polymeric systems considered, but fail for the colloidal systems. In the latter, the steady state values of viscosity and elasticity are consistently low, and replacing them by the complex viscosity and our new elastic expression only makes matters worse.For polymer systems, we suggest this is a general but not universal observation, since we are aware of exceptions to the rule that polymeric systems obey the Cox-Merz rule for viscosity and our rule for elasticity. For colloidal systems we find that neither rule is obeyed for any of our systems.

On Newtonian and Non-Newtonian Flow in Complex Geometries

A flow visualization technique by means of an expanded laser beam and trace amounts of particulate additives is used to study the behaviour of Newtonian and non-Newtonian elastic liquids in a number of complex geometries. Particular attention is paid to the effect of fluid elasticity on the flow characteristics. Attempts are made to simulate numerically the observed flows by using finite-difference techniques. The agreement between theory and experiment is very satisfactory.

The viscoelastic properties of multigrade oils and their effect on journal-bearing characteristics

Abstract In this paper, we readdress the long-standing question as to whether the viscoelastic properties of multigrade oils can have a measurable effect on lubrication characteristics. To facilitate this, we first investigate the rheometrical properties of a number of multigrade oils with similar shear-viscosity responses. Specifically, we employ a Weissenberg Rheogoniometer and a Lodge Stressmeter to provide a measure of the normal stresses. We then investigate the behaviour of the oils in a journal bearing simulator. We find that viscoelasticity does indeed produce a measurable and beneficial effect on lubrication characteristics at the higher eccentricity ratios and that this effect correlates well with a characteristic relaxation time.

The behaviour of polymer solutions in extension-dominated flows, with applications to Enhanced Oil Recovery

The rheometry and flow behaviour of aqueous solutions of polyacrylamide and xanthan gum are discussed, with the expectation that the results will be of use in Enhanced Oil Recovery (EOR). The rheometrical study gives particular prominence to the dramatically high values of extensional viscosity which are possible in aqueous solutions of flexible polymers such as polyacrylamide. The effect of such factors as polymer concentration, salt concentration and mechanical degradation on rheometrical properties is outlined. Reference is also made to the qualitatively-different rheometrical behaviour experienced by comparable solutions of xanthan gum.Further evidence is advanced that some dilute polymer solutions of potential use in EOR experience abnormally high resistance in flows which are dominated by extension. Since flow through a porous medium involves a substantial extensional component, it is argued that there is justification for studying the effect of this high extensional-viscosity behaviour in a number of idealized geometries of relevance to EOR conditions. The resulting experiments indicate that, at low flow rates,shear viscosity is the dominant influence, but that, after a critical set of conditions,extensional-viscosity considerations can become all important and the observed pressure losses are against any expectation based on conventional fluid mechanics.Flow visualization studies support the pressure-drop measurements in emphasising the strong influence of high extensional viscosities in flows through tortuous geometries.