Liquids non-Newtonian

The liquids that are Newtonian in their flow behaviour include water, true solutions and simple organic liquids. For all these, a graph of shear strain rate (or 7) against shear stress r (known 

Many other liquids, however, do not show this behaviour and are known as non-Newtonian or anomalous liquids. For all these liquids the quantity r/7 varies with 7 and sometimes with time as 

time-dependent liquids, for which 7 depends on both r and the duration of its application and 

viscoelastic liquids that possess elasticity as well as viscosity. Many real liquids show a combination of properties from these basic types, and such liquids are termed complex rheological liquids. 

Some shear-thinning materials deform like elastic solids until a certain stress, known as the yield stress, is reached, after which they deform as normal shear-thinning liquids. These materials are described as shear thinning with yield value, and have a consistency curve like curve 2 of Fig. 6.3. Flow ceases when the stress falls below the yield stress. Materials which show this behaviour include toothpaste and muds. These substances also tend to be thixotropic. 

The effects of broth viscosity on k a in aerated stirred tanks and bubble columns is apparent from Equations 7.37 and 7.41, respectively. These equations can be applied to ordinary non-Newtonian liquids with the use of apparent viscosity as defined by Equation 2.6. Although liquid-phase diffusivity generally decreases with increasing viscosity, it should be noted that at equal temperatures, the gas diffusivities in aqueous polymer solutions are almost equal to those in water. 

Some fermentation broths are non-Newtonian due to the presence of microbial mycelia or fermentation products, such as polysaccharides. In some cases, a small amount of water-soluble polymer may be added to the broth to reduce stirrer power requirements, or to protect the microbes against excessive shear forces. These additives may develop non-Newtonian viscosity or even viscoelasticity of the broth, which in turn will affect the aeration characteristics of the fermentor. Viscoelastic liquids exhibit elasticity superimposed on viscosity. The elastic constant, an index of elasticity, is defined as the ratio of stress (Pa) to strain (—), while viscosity is shear stress divided by shear rate (Equation 2.4). The relaxation time (s) is viscosity (Pa s) divided by the elastic constant (Pa). 

Values of kj a for viscoelastic liquids in aerated stirred tanks are substantially smaller than those in inelastic liquids. Moreover, less breakage of gas bubbles in the vicinity ofthe impeller occurs in viscoelastic liquids. The following dimensionless equation [8] (a modified form of Equation 7.37) can be used to correlate kj a in sparged stirred tanks for non-Newtonian (including viscoelastic) liquids  

Correlations for k a in bubble columns such as Equation 7.41 should hold for non-Newtonian fluids with use of apparent viscosity To estimate the effective shear rate (s ), which is necessary to calculate jMj, by Equation 2.6, the 

Values of in bubble columns decrease with increasing values of liquid vis- 

In general the viscosity of a liquid can depend upon three parameters  

In non-Newtonian liquids, p is not only a physical constant which is dependent upon temperature, but also depends upon y and under certain circumstances upon t. Such liquids are classified according to their flow behavior (seeTable 1.4and DIN 1342/1 2 DIN 13 342)  

The viscosity is dependent upon the duration of the shear stress. 

The graphic representation of the flow behavior in the form is known as a flow curve and in the form /z(y) as a viscosity curve. The two forms of representations are compared in Fig. 1.28 for two Newtonian liquids of different viscosities ( / i) and for two non-Newtonian fluids of material class 1. 

The first material class consists of three sub-classes  

With particularly simple networks, some rearrangement of equations sometimes can be made to simplify the solution. Example 6.7 is of such a case. 

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Flow behaviour of polymer melts is still difficult to predict in detail. Here, we only mention two aspects. The viscosity of a polymer melt decreases with increasing shear rate. This phenomenon is called shear thinning [48]. Another particularity of the flow of non-Newtonian liquids is the appearance of stress nonnal to the shear direction [48]. This type of stress is responsible for the expansion of a polymer melt at the exit of a tube that it was forced tlirough. Shear thinning and nonnal stress are both due to the change of the chain confonnation under large shear. On the one hand, the compressed coil cross section leads to a smaller viscosity. On the other hand, when the stress is released, as for example at the exit of a tube, the coils fold back to their isotropic confonnation and, thus, give rise to the lateral expansion of the melt. 

When water (a Newtonian liquid) is in an open-ended pipe, pressure can be applied to move it. Doubling the water pressure doubles the flow rate of the water. Water does not have a shear-thinning action. However, in a similar situation but using a plastic melt (a non-Newtonian liquid), if the pressure is doubled the melt flow may increase from 2 to 15 times, depending on the plastic used. As an example, linear low-density polyethylene (LLDPE), with a low shear-thinning action, experiences a low rate increase, which explains why it can cause more processing problems than other PEs. The higher-flow melts include polyvinyl chloride (PVC) and polystyrene (PS). 

Chapter 3 Flow of Newtonian and non-Newtonian Liquids Chapter 4 Flow of Compressible Fluids (Gases)... 

For streamline flow of non-Newtonian liquids, the situation is completely different and the behaviour of two-phase mixtures in which the liquid is a shear-thinning fluid is now... 

Chhabra, R. P. and Richardson, J. F. In Encyclopedia of Fluid Mechanics, Volume 3, Gas-Liquid Flow Cheremisinoff, N, P. eds (Gulf Publishing Co. 1986). Co-current horizontal and vertical upwards flow of gas and non-Newtonian liquid. 

In many instances, two or more miscible liquids must be mixed to give a product of a desired specification, such as, for example, in the blending of petroleum products of different viscosities. This is the simplest type of mixing as it involves neither heat nor mass transfer, nor indeed a chemical reaction. Even such simple operations can however pose problems when the two liquids have vastly different viscosities. Another example is the use of mechanical agitation to enhance the rates of heat and mass transfer between the wall of a vessel, or a coil, and the liquid. Additional complications arise in the case of highly viscous Newtonian and non-Newtonian liquids. 

At the other extreme, in the formation of composite materials, especially filled polymers, fine particles must be dispersed into a highly viscous Newtonian or non-Newtonian liquid. The incorporation of carbon black powder into rubber is one such operation. Because of the large surface areas involved, surface phenomena play an important role in such applications. 

Dynamic similarity occurs in two geometrically similar units of different sizes if all corresponding forces at counterpart locations have a constant ratio. It is necessary here lo distinguish between the various types of force inertial, gravitational, viscous, surface tension and other forms, such as normal stresses in the case of viscoelastic non-Newtonian liquids. Some or all of these forms may be significant in a mixing vessel. Considering... 

At low values of the Reynolds number, less than about 10, a laminar or viscous zone exists and the slope of the power curve on logarithmic coordinates is — 1, which is typical of most viscous flows. This region, which is characterised by slow mixing at both macro-arid micro-levels, is where the majority of the highly viscous (Newtonian as well as non-Newtonian) liquids are processed. 

A simple relationship has been shown to exist, however, between much of the data on power consumption with time-independent non-Newtonian liquids and Newtonian liquids in the laminar region. This link, which was first established by Metzner and Otto 1 2 for pseudoplastic liquids, depends on the fact that there appears to be an average angular shear rate y mt, for a mixer which characterises power consumption, and which is directly proportional to the rotational speed of impeller ... 

The flow patterns for single phase, Newtonian and non-Newtonian liquids in tanks agitated by various types of impeller have been repotted in the literature.1 3 27 38 39) The experimental techniques which have been employed include the introduction of tracer liquids, neutrally buoyant particles or hydrogen bubbles, and measurement of local velocities by means of Pitot tubes, laser-doppler anemometers, and so on. The salient features of the flow patterns encountered with propellers and disc turbines are shown in Figures 7.9 and 7.10. 

Molecularly motivated empiricisms, such as the solubility parameter concept, have been valuable in dealing with mixtures of weakly interacting small molecules where surface forces are small. However, they are completely inadequate for mixtures that involve macromolecules, associating entities like surfactants, and rod-like or plate-like species that can form ordered phases. New theories and models are needed to describe and understand these systems. This is an active research area where advances could lead to better understanding of the dynamics of polymers and colloids in solution, the rheological and mechanical properties of these solutions, and, more generally, the fluid mechaiucs of non-Newtonian liquids. 

The presence of a gas in the suspension results in an increase of the stirrer speed required to establish the state of complete suspension. The propeller usually requires a higher speed than the turbine. Furthermore, a critical volume gas flow exists above which drastic sedimentation of particles occurs. Hence, homogenisation of the suspension requires an increase of the rotational speed and/or a decrease of the gas flow rate. The hydrodynamics of suspensions with a solid fraction exceeding 0.25-0.3 becomes very complex because such suspensions behave like non-Newtonian liquids. This produces problems in the scale-up of operations. Hydrodynamics, gas hold-up, mass-transfer coefficients, etc. have been widely studied and many correlations can be found in literature (see e.g. Shah, 1991). 

In equation 5.3, and when calculating the Reynolds number for use with Figure 5.7, the fluid viscosity and density are taken to be constant. This will be true for Newtonian liquids but not for non-Newtonian liquids, where the apparent viscosity will be a function of the shear stress. 

Transition from liquid behavior to solid behavior has been reported with fine particle suspensions with increased filler content in both Newtonian and non-Newtonian liquids. Industrially important classes are rubber-modified polymer melts (small rubber particles embedded in a polymer melt), e.g. ABS (acrylo-nitrile-butadiene-styrene) or HIPS (high-impact polystyrene) and fiber-reinforced polymers. Another interesting suspension is present in plasticized polyvinylchloride (PVC) at low temperatures, when suspended PVC particles are formed in the melt [96], The transition becomes evident in the following... 

For non-Newtonian liquids and suspensions, an apparent viscosity is determined using correlations which include power input and the Reynolds number. Scale-up comparisons based on heat generation data only were determined by comparison of results from RC1 experiments and from a 675-liter reactor [208]. In the experiments, a Bingham plastic fluid was used to determine the film heat transfer coefficient. This presents a worst case because of the low thermal conductivity of the Bingham plastic. Calculated inside film heat transfer coefficients determined in the RC1 tests were about 60% lower than the values determined in the pilot plant reactor, even though substantial effort was made to obtain both geometric and kinematic similarity in the pilot reactor. 

When used with non-Newtonian liquids, this non-uniformity of the shear stress, and therefore the shear rate, is a limitation of the simple type of rotating shaft viscometer that can be placed in a vessel. 

A general time-independent non-Newtonian liquid of density 961 kg/m3 flows steadily with an average velocity of 2.0 m/s through a tube 3.048 m long with an inside diameter of 0.0762 m. For these conditions, the pipe flow consistency coefficient K has a value of 1.48 Pa s0,3 and n a value of 0.3. Calculate the values of the apparent viscosity for pipe flow p.ap, the generalized Reynolds number Re and the pressure drop across the tube, neglecting end effects. 

It is possible to calculate the apparent viscosities of non-Newtonian liquids in agitated tanks from the appropriate power curves for Newtonian... 

Obtain power data using a non-Newtonian liquid and calculate the power number Po from equation 5.13 for various agitator speeds N. 

Nienow and Elson (1988) have reviewed work done mainly by them and their co-workers on the mixing of non-Newtonian liquids in tanks. The above approach for inelastic, shearing thinning liquids has been largely substantiated but considerable doubt has been cast over using this method for dilatant, shear thickening materials. 

Fig. 17. Comparison of the model (S16) with the collected data for bubble formation in non-Newtonian liquids under constant flow conditions.

Dewsbury, K. H., Karamanev, D. G. and Margaritis, A. AIChEJl 46 (2000) 46. Dynamic behavior of freely using buoyant solid sphere in non-Newtonian liquids. 

HOcker, H., Langer, G. and Udo, W. Germ. Chem. Eng. 4 (1981) 51. Mass transfer in aerated Newtonian and non-Newtonian liquids. 

Note 2 For a non-Newtonian liquid (see note 3), a form of the general constitutive equation which may be used is... 

Note 3 For non-Newtonian liquids, when CT12 is not directly proportional toy, q varies withy. The value of q evaluated at a given value of y is termed the non-Newtonian viscosity. 

Note 5 Extrapolation of rj or /app for non-Newtonian liquids to zero y gives the zero-shear viscosity, which is given the symbol rja. 

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