Shear-thinning behaviour

Figure l.l Shear thinning behaviour of pseudoplastic fluids... 

This equation is based on the assumption that pseudoplastic (shear-thinning) behaviour is associated with the formation and rupture of structural linkages. It is based on an experimental study of a wide range of fluids-including aqueous suspensions of flocculated inorganic particles, aqueous polymer solutions and non-aqueous suspensions and solutions-over a wide range of shear rates (y) ( 10 to 104 s 1). 

Clearly, shear thinning behaviour corresponds to nshear thickening behaviour to n> 1. The special case, n = 1, is that of Newtonian behaviour and in this case the consistency coefficient K is identical to the viscosity fx. Values of n for shear thinning fluids often extend to 0.5 but less commonly can be as low as 0.3 or even 0.2, while values of n for shear thickening behaviour usually extend to 1.2 or 1.3. 

Under conditions of steady fully developed flow, molten polymers are shear thinning over many orders of magnitude of the shear rate. Like many other materials, they exhibit Newtonian behaviour at very low shear rates however, they also have Newtonian behaviour at very high shear rates as shown in Figure 1.20. The term pseudoplastic is used to describe this type of behaviour. Unfortunately, the same term is frequently used for shear thinning behaviour, that is the falling viscosity part of the full curve for a pseudoplastic material. The whole flow curve can be represented by the Cross model [Cross (1965)] ... 

Equation 3.29 is helpful in showing how the value of the correction factor in the Rabinowitsch-Mooney equation corresponds to different types of flow behaviour. For a Newtonian fluid, n = 1 and therefore the correction factor has the value unity. Shear thinning behaviour corresponds to < 1 and consequently the correction factor has values greater than unity, showing that the wall shear rate yw is of greater magnitude than the value for Newtonian flow. Similarly, for shear thickening behaviour, yw is of a... 

As the behaviour becomes more complicated, more parameters are required to fit the experimental curves. To illustrate this, consider two common equations used to describe the shear-thinning behaviour observed in viscometers. Figure 1.5 shows these two responses. 

However, we should seek a more reliable solution that will describe the full range of volume fractions at which flow can occur and give some guidance as to the shear thinning behaviour. 

Variants to this expression and alternative models have also been proposed to describe shear thinning behaviour of concentrated suspensions [12,13]. 

Examples include oil-well drilling muds, greases, lipstick, toothpaste, and natural rubber polymers. An illustration is provided in Figure 6.13. Here, the flocculated structures are responsible for the existence of a yield stress. Once disrupted, the nature of the floe break-up process determines the extent of shear thinning behaviour... 

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). 

When n < 1, shear-thinning behaviour is represented n > 1, shear-thickening behaviour is represented n = 1, the behaviour is Newtonian. 

For shear-thinning fluids, // —> oo a I zero shear stress and fi 0 at infinite shear stress. Paint often exhibits shear thinning behaviour as its apparent viscosity is very high while in the can and when just applied to a wall but its apparent viscosity is very low as the brush applies it to the surface when it flows readily to give an even film. Toothpaste remains in its tube and on the brush when not subjected to shear but when sheared, as it is when the tube is squeezed, it flows readily through the nozzle to the brush. 

In other cases, several discrete relaxation times or distributions of relaxation times can be found [39]. This is typically the case if the stress relaxation is dominated by reptation processes [42 ]. The stress relaxation model can explain why surfactant solutions with wormlike micelles never show a yield stress Even the smallest applied stress can relax either by reptation or by breakage of micelles. For higher shear rates those solutions typically show shear thinning behaviour and this can be understood by the disentanglement and the orientation of the rod-like micelles in the shear field. 

In Sect. 15.4 it was shown how the shear thinning behaviour of the viscosity could be described empirically with the aid of many suggestions found in literature. It was not mentioned there that the first normal stress coefficient also shows shear thinning behaviour. In this Sect. 15.5 it became clear that also the extensional viscosity is not a constant, but depending on the strain rate upon increasing the strain rate qe the extensional viscosity depart from the Trouton behaviour and increases (called strain hardening) to a maximum value, followed by a decrease to values below the zero extensional viscosity. It has to be emphasised that results in literature may show different behaviour for the extensional behaviour, but in many cases this is due to the limited extensions used,... 

However, although it has some thermodynamic consistency, the latter model failsto describe the non linear viscoelastic behaviour properties, especially in shear, wherein the shear-thinning behaviour of the viscosity and of the normal stress coefficients are not predicted. As a consequence, more complex... 

Results. In general, the glass fibre slurries exhibited slight shear thinning behaviour, which became more marked with increase in fibre length and with concentration. This is illustrated in Figure 4 with a series of flow curves for different w/w concentrations of 1.5mm, CSG dispersed in PRA1478, (see (1)) measured with a 3° annular cone. 

Many systems show a dynamic yield value followed by a shear thinning behaviour [9]. The flow curve can be analysed using the Herschel-Bulkley equation ... 

Figure 3.66 shows the steady-shear viscosity for a polymer system at three molar masses. Note the plateau in viscosity at low shear rates (or the zero-shear viscosity). Also note how the zero-shear viscosity scales with to the power 3.4. (This is predicted by Rouse theory (Rouse, 1953).) Figure 3.67 shows the viscosity and first normal-stress difference for a high-density polyethylene at 200 C. Note the decrease in steady-shear viscosity with increasing shear rate. This is termed shear-thinning behaviour and is typical of polymer-melt flow, in which it is believed to be due to the polymer chain orientation and non-affine motion of polymer chains. Note also that the normal-stress difference increases with shear rate. This is also common for polymer melts, and is related to an increase in elasticity as the polymer chain motion becomes more restricted normal to flow at higher shearing rates. 

Van der Werff and de Kruif (1989) examined the scaling of rheological properties of a hard-sphere silica dispersion (sterically stable monodisperse silica in cyclohexane) with particle size, volume fraction and shear rate. The shear-thinning behaviour was found to scale with the Peclet number Pe = 6nt]sa yl k-QT), or the ratio of shear time to structure-build-up time, where a is the particle radius, is the viscosity of the solution, y is the shear... 

Shear-thinning behaviour is the result of either droplet distortion and alignment with the flow, or due to increasing shear stress causing breakdown of weak floes with a consequent decrease in effective phase volume (Figure I4.2b). 

Figure I4.A.I shows how for a pseudoplastic emulsion product the apparent viscosity, (I3 and shear thinning behaviour expressed as a power law fluid, altered during ten operations during its manufacture ...

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