Non-Newtonian rheological behaviour

A number of publications have appeared in the literature describing simulation models for pol3rmer flooding (1-8). The transport properties of the polymer, the interaction with the rock matrix, possible chemical reactions and the non-Newtonian rheological behaviour of polymeric liquids combine to make polymer flow through porous media very complex The main features which should be included in a polymer simulator for both field and laboratory use are as follows ... 

Several methods have been su ested for measuring the non-Newtonian rheological behaviour of surfadant and polymer films. For example, Haydon et al. [61] constructed a special apparatus to measure the two-dimensional creep and stress relaxation of adsorbed protein film at the 0/W interface. In creep experiments, a constant torque (in mN m ) was apphed and the resulting deformation (in radians) was recorded as a fimction of time. In the stress relaxation experiments, a certain deformation y was produced in the film by applying an initial stress, and the deformation was kept constant by gradually decreasing the stress. 

Many (semi-)empirical relationships have been proposed to describe non-Newtonian suspension behaviour. For more information the reader is referred to Ref. [15] or other textbooks on suspension rheology. 

Similarly, since much has been written about the importance of the measurement of rheological data in the same range of shear or deformation rates as those likely to be encountered in the envisaged application. Table 1.3 gives typical orders of magnitudes for various processing operations in which non-Newtonian fluid behaviour is likely to be significant. 

Multiphase flow is encountered in many chemical and process engineering applications, and the behaviom of the material is influenced by the properties of the components, such as their Newtonian or non-Newtonian characteristics or the size, shape and concentration of particulates, the flowrate of the two components and the geometry of the system. In general, the flow is so complex that theoretical treatments, which tend to apply to highly idealised situations, have proved to be of little practical utility. Consequently, design methods rely very much on analyses of the behaviour of such systems in practice. While the term multiphase flows embraces the complete spectrum of gas/liquid, liquid/liquid, gas/solid, liquid/solid gas/liquid/solid and gas/liquid/liquid systems, the main concern here is to illustrate the role of non-Newtonian rheology of the liquid phase on the nature of the flow. Attention is concentrated on the simultaneous co-current flow of a gas and a non-Newtonian liquid and the transport of coarse solids in non-Newtonian liquids. 

The rheological model for Newtonian fluids contains just one constant, T n. Many models have been proposed to describe the non-Newtonian flow behaviour of fluids, although the majority of these are of little value for engineering design applications and serve more as theoretical analyses. 

The non-Newtonian rheological model briefly discussed above was used with the assumption of isothermal behaviour of the oil. The test case used by Glovnea and Spikes [1] is moderately loaded in numerical terms having Moes and Bosma non-dimensional parameter values of M= 211 and L = 5.02 at their stated conditions. The computing domain used is -2.5a [Pg.80]

The branch of science which is concerned with the flow of both simple (Newtonian) and complex (non-Newtonian) fluids is known as rheology. The flow characteristics are represented by a rheogram, which is a plot of shear stress against rate of shear, and normally consists of a collection of experimentally determined points through which a curve may be drawn. If an equation can be fitted to the curve, it facilitates calculation of the behaviour of the fluid. It must be borne in mind, however, that such equations are approximations to the actual behaviour of the fluid and should not be used outside the range of conditions (particularly shear rates) for which they were determined. 

An understanding of non-Newtonian behaviour is important to the chemical engineer from two points of view. Frequently, non-Newtonian properties are desirable in that they can confer desirable properties on the material which are essential if it is to fulfil the purpose for which it is required. The example of paint has already been given. Toothpaste should not flow out of the tube until it is squeezed and should stay in place on the brush until it is applied to the teeth. The texture of foodstuffs is largely attributable to rheology. 

Because concentrated flocculated suspensions generally have high apparent viscosities at the shear rates existing in pipelines, they are frequently transported under laminar flow conditions. Pressure drops are then readily calculated from their rheology, as described in Chapter 3. When the flow is turbulent, the pressure drop is difficult to predict accurately and will generally be somewhat less than that calculated assuming Newtonian behaviour. As the Reynolds number becomes greater, the effects of non-Newtonian behaviour become... 

These flow features are of importance in a great number of technical processes, especially for high process velocities when extremely high shear rates can be observed. For polymeric systems this can lead to a so-called non-Newtonian behaviour, i.e. the rheological material functions become dependent on the shear or elongational rate. 

Investigations of the rheological properties of disperse systems are very important both from the fundamental and applied points of view (1-5). For example, the non-Newtonian and viscoelastic behaviour of concentrated dispersions may be related to the interaction forces between the dispersed particles (6-9). On the other hand, such studies are of vital practical importance, as, for example, in the assessment and prediction of the longterm physical stability of suspensions (5). 

M. M. Cross, Rheology of Non-Newtonian Fluids a New Flow Equation for Pseudoplastic Systems, J. Colloids Sci., 20, 417 137 (1965) also M. M. Cross, Relation Between Viscoe-lasiticity and Shear-thinning Behaviour in Liquids, Rheological Acta, 18, 609-614 (1979). 

An understanding of the rheological behaviour is necessary as PVC pastes are classified as non-Newtonian liquids and can be dilatent (shear thickening), pseudoplastic (shear thinning) or thixotropic (viscosity reduces with time under constant shear). Each process requires specific rheological characteristics and this is achieved by formulation of appropriate PVC grades and knowledge of the influence of shear rate and time under constant shear. 

This lesson is an introduction to the flow behaviour (rheology) of pastes and gels. Examples of such non-Newtonian liquids are ... 

The sedimentation results obtained with the structured suspensions, are consistent with the predictions from rheological investigations. In the absence of any bentonite clay, the pesticidal suspension exhibits Newtonian behaviour with unmeasurable yield value, modulus or residual viscosity. In this case the particles are free to settle individually under gravity forming a dilatant sediment or clay. On the other hand, at bentonite concentrations above the gel point (> 30 g dm the non-Newtonian behaviour of the suspensions and in particular their viscoelastic behaviour results from the formation of a "three-dimensional" network, which elastically supports the total mass. After 21 weeks standing in 100 ml measuring cylinders, no separation was observed when the bentonite concentration was >37.5 g dm corresponding to a modulus > 60 Nm. Clearly the modulus value required to support the mass of the suspension depends on the density difference between particle and medium. 

The yield point is lowered by gradual increase in water content in the raw material mix, until the range of liquid suspension is reached. If the system contains so much liquid that the particles of solids are mutualy separated by thick liquid layers, these suspensions behave like Newtonian liquids. Deviations from this simple rheological behaviour arise when the particles come into mutual contact. The yield point will arise or various types of non-linear dependence of deformation rate on stress will occur. 

In practice coating fluids are often non-Newtonian dispersions. The complete rheological behaviour is then of importance. 

Many attempts have been made to obtain (semi-)analytical descriptions for non-Newtonian coating flows. These are necessarily approximate and the approximations made to obtain tractable mathematics are sometimes non-physical [58]. These models do not predict the coating behaviour very well from the rheological parameters. The thickness is usually considerably overestimated. It seems more advantageous to simulate non-Newtonian coating flows by computational fluid dynamic methods (see also Ref. [58]). 

Figure 8.3 Basic types of rheological behaviour (a) Newtonian, (b)—(c) non-Newtonian /(b) shear thickening, (c) shear thinning, A) pseudoplastic. (e) plastic (Bingham plow), in which o0 is the yield stress and On is the Bingham yield stress/.

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