Characterisation of non-Newtonian fluids

Even the measurement of the steady-state characteristics of shear-dependent fluids is more complex than the determination of viscosities for Newtonian fluids. In simple geometries, such as capillary tubes, the shear stress and shear rate vary over the cross-section and consequently, at a given operating condition, the apparent viscosity will vary with location. Rheological measurements are therefore usually made with instraments in which the sample to be sheared is subjected to the same rate of shear throughout its whole mass. This condition is achieved in concentric cylinder geometry (Fi re 3.37) where the fluid is sheared in the annular space between a fixed and a rotating cylinder if the gap is small compared with the dimneters of the cylinders, the shear rate is approximately 

If it is known that a particular form of relation, such as the power-law mpdel, is applicable, it is not necessary to maintain a constant shear rate. Thus, for instance, a capillary tube viscometer can be used for determination of the values of the two parameters in the model. In this case it is usually possible to allow for the effects of wall-slip by making measurements with tubes covering a range of bores and extrapolating the results to a tube of infinite diameter. Details of the method are given by Farooqi and Richardson. 

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The rheological characterisation of non-Newtonian fluids is widely acknowledged to be far from straightforward. In some non-Newtonian systems, such as concentrated suspensions, rheological measurements may be complicated by non-linear, dispersive, dissipative and thixotropic mechanical properties and the rheometrical challenges posed by these features may be compoimded by an apparent yield stress. 

An alternative procedure, to ensure no external force is applied to the powder bed by the vaned paddle, is to place the compacted sample on a balance and when the paddle is immersed in the powder to raise the vaned head slowly until the balance reading is zero. This dynamic method of bulk powder characterisation is allied to the rheological method for measurement of the viscosity of non-Newtonian fluids and suspensions. Commercial instruments based on the WSL cohesion tester are now available in the form of the FT4 Powder Rheometer (Freeman Technology) and the Stable Micro Systems Powder Flow Analyser (Stable Micro Systems). 

Perhaps the most important and striking features of high internal phase emulsions are their rheological properties. Their viscosities are high, relative to the bulk liquid phases, and they are characterised by a yield stress, which is the shear stress required to induce flow. At stress values below the yield stress, HIPEs behave as viscoelastic solids above the yield stress, they are shear-thinning liquids, i.e. the viscosity varies inversely with shear rate. In other words, HIPEs (and high gas-fraction foams) behave as non-Newtonian fluids. 

The characterisation of the viscosity is difficult for non-Newtonian fluids because the viscosity changes as a result of the flow process, which increases the shear rate. This is further complicated for two-phase fluids because the presence of bubbles will also affect the viscosity. The simpler methods to obtain G for high viscosity fluids make the simplifying assumptions that the fluid viscosity is equal to the liquid viscosity and that the fluid is Newtonian. 

Many modifications of the basic Ostwald geometry are employed in different situations. One example is the Cannon-Fenske routine viscometer (Fig. 6.37b) which is used in the oil industry for measuring kinematic viscosities of 0.02 m2/s and less(4<). As viscosity is sensitive to variations in temperature, these types of viscometer are always immersed in a constant temperature bath. They are not normally suitable for non-Newtonian fluids although FAROOQI and Richardson(47) have employed a capillary viscometer to characterise a power-law fluid. 

The most common type of time-independent non-Newtonian fluid behavioiu observed is pseudoplasticity or shear-thinning, characterised by an apparent viscosity which decreases with increasing shear rate. Both at very low and at very high shear rates, most shear-thinning polymer solutions and melts exhibit Newtonian behaviour, i.e. shear stress-shear rate plots become straight lines. 

Of the techniques used to characterise the linear visco-elastic behaviom displayed by many non-Newtonian fluids, the oscillatory shear technique which involves either an applied stress or shear rate which varies harmonically with time, is perhaps the most convenient and widely used. 

For all fluids, the nature of the flow is governed by the relative importance of the viscous and the inertial forces. For Newtonian fluids, the balance between these forces is characterised by the value of the Reynolds munber. The generally accepted value of the Reynolds number above which stable laminar flow no longer occms is 2100 for Newtonian fluids. For time-independent fluids, the critical value of the Reynolds number depends upon the type and the degree of non-Newtonian behaviour. For power-law fluids (n = n ), the criterion of Ryan and Johnson [1959] can be used. 

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