Non-Newtonian mixtures

Non-Newtonian mixtures are homogenized considerably more slowly than Newtonian liquids in laminar and transition ranges. This is also due to a shear rate field existing in the tank, which causes strong viscosity differences. 

Opara stated, that it was not to be expected that a correlation between the mixing time and and hence with Rseg, could be realized, because the concept of Metzner and Otto was derived from work on the power characteristic. There was determined from the shear rates, which occured at the largest rate differences, whereas the regions close to the walls, in which the smallest rate differences were to be found, were determining for homogenization times. 

To arrive at a representative viscosity for the mixing process, Tebel and Zehner [539] used the proportionality between the circulation number N s and the mixing effect in a loop reactor driven by a propulsion jet (where qi is the total liquid circulating and qi is the throughput of the propulsion jet). Its circulation characteristic N (Reeff) was due to the purposeful flow direction and momentum 

The m value for the above equation can be determined by bringing into coincidence the predicted and measured circulation characteristics N (Reefr) for different CMC solutions. 

This concept for the determination of the effective viscosity for mixing processes is also transferable to stirred vessels, because in the laminar flow range the above circumstances also apply for propeller loop reactors [351]. This was proved with tanks with pitched-blade stirrers [540]. The nO values could be better correlated with RSefr numbers, which were produced according to expression (3.25), than those which contained ft g according to expression (1.45) after Metzner-Otto. 

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In non-Newtonian mixtures in the laminar and transition range this mixing operation requires considerably longer mixing times than in Newtonian liquids. This is due to the fact that in the catchment area of the stirrer higher shear rates and, there-... 

In the case of non-Newtonian mixtures, which also exert pseudoplastic and viscoelastic behavior, the pi-space is widened by the Weissenberg number, Wi. In addition, it has to be decided which effective viscosity, peffi has to enter the Reynolds number ... 

Mycelial growth and polymeric substrates or metabolities often produce a highly viscous and sometimes pseudoplastic non-Newtonian mixture. 

An interesting observation with some non-newtonian mixtures is that at high shear they appear to violate the zero-velocity boundary condition at the wall. For multiphase fluids such as suspensions and fiber-filled polymers, this effect is believed to be the result of a thin layer near the wall that is depleted of particulates... 

Another aspect of the structural changes observed in these systems is elucidated by the stationary measurements. The surfactant-based gels behave as non-Newtonian mixtures, and their activation energies can be determined with the well-known Arrhenius equation. If a positive activation energy is acquired, there... 

Concepts of non-Newtonian mixtures are reviewed so the reader can understand the principles used to analyze complex homogeneous flows of very fine particles at high volumetric concentration. 

TABLE 3-8 Regimes of Flows for Newtonian and Non-Newtonian Mixtures after Govier and Aziz (1972)... 

FIGURE 3-15 Pseudoshear diagram of a non-Newtonian mixture tested in a capillary tube... 

Equation 4-60 is not applicable at high concentration of fines, as the slurry starts to behave as a non-Newtonian mixture. For particles with dso finer than 74 p,m, the method does not give very reUable results. 

The value of ratio 14 is then calculated from the Molerus diagram (Figure 5-10). The values of Xand APJL are then calculated from Equations 5-59 and 5-60. This step may be repeated for each range of particle size and summed up with other particle sizes to get an overall pressure drop for solids. However for Non-Newtonian mixtures additional procedures are needed. 

A phenomenon encountered with non Newtonian mixtures is a tendency for the low-viscosity constituent to migrate to regions of high shear and to lubricate the flow. One example is the core annular flow of crude oil in water, where the more viscous material is lubricated by the less viscous material. In the case of emulsions and certain non-Newtonian slurries, lubrication occurs by a slip layer of water on the wall. 

Johnson (1982) reviewed some of the problems of pumping non-Newtonian mixtures. In his assessment of fittings for sewage, he indicated important discrepancies in the laminar regime with losses 2-4 times as much as those for water flows. In the turbulent regime, the losses were either of the order of those for water or higher. He recommended that further studies be conducted for laminar flow, but for turbulent flows, the concept of equivalent length be used. 

Stepanoff (1969) reported work hy Japanese investigators who indicated that tests on car-hide slurries tended to show that the head-capacity ratio may increase or decrease depending on whether the soUds concentration tended to cause the slurry to behave as a Newtonian or non-Newtonian mixture. 

Extensive experience has been gained over the years on the pumping of different minerals and tailings. Some particles are ground to a very fine range and flow as non-Newtonian mixtures, and some are as coarse as 50 mm (2 in), as in the coal and oil sand industries. 

Experimental work by Sundararaj and Macosko, nicely contrasted the competing effects of droplet breakup and droplet coalescence in both Newtonian and non-Newtonian mixtures. They concluded that the extent of interfacial tension reduction due to the presence of block copolymer was insufficient to be the primary reason for the reduction of the droplet size, and the primary effect of the copolymer was to prevent droplet coalescence through steric stabilization of the droplets. Sundararqj and Macosko also noted that the droplet size as a function of shear rate for a pure blend decreased to a minimum value, then increased at higher shear rates. No data was given for the compatibilized blend and they referred to this shear rate dependence of the dispersed phase size for the pure blend as "anomalous". Sundararaj and Macosko noted that this anomalous behavior has been observed previously by... 

A separator is fed with a condensate/gas mixture. The condensate leaves the bottom of the separator, passes a flowmeter and is followed by a choke valve, after which the condensate is boiling. The flow can not be measured using the transit time method, due to the combination of short piping, the absence of a suitable injection point and the flow properties of the condensate, which is non-newtonian due to a high contents of wax particles The condensate can not be representatively sampled, as it boils upon depressuratioh... 

Heat Exchangers Using Non-Newtonian Fluids. Most fluids used in the chemical, pharmaceutical, food, and biomedical industries can be classified as non-Newtonian, ie, the viscosity varies with shear rate at a given temperature. In contrast, Newtonian fluids such as water, air, and glycerin have constant viscosities at a given temperature. Examples of non-Newtonian fluids include molten polymer, aqueous polymer solutions, slurries, coal—water mixture, tomato ketchup, soup, mayonnaise, purees, suspension of small particles, blood, etc. Because non-Newtonian fluids ate nonlinear in nature, these ate seldom amenable to analysis by classical mathematical techniques. 

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... 

Mixtures of liquids with gas or vapour, flow 181 Modified Reynolds number, non-Newtonian flow 124 Molar units 8 Mole 8... 

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. 

All the above methods which make use of the passage of light through the liquid-gas mixture are applicable only when the liquid transmits light. For opaque systems like fluidized beds and some non-Newtonian fluids, methods based on different principles have to be employed. 

The 3 1 C12- or C24-DAO/SDS mixture exhibits non-Newtonian fluid characteristics its viscosity decreases with Increased shear rate. At high pH (A<12), the mixture is still non-Newtonian and its viscosity is enhanced by about an order of magnitude (at high shear rate) to two orders of magnitude (at low shear rate) compared to the values at its natural pH (AylO). The... 

In addition to temperature, the viscosity of these mixtures can change dramatically over time, or even with applied shear. Liquids or solutions whose viscosity changes with time or shear rate are said to be non-Newtonian, that is, viscosity can no longer be considered a proportionality constant between the shear stress and the shear rate. In solutions containing large molecules and suspensions contain nonattracting aniso-metric particles, flow can orient the molecules or particles. This orientation reduces the resistance to shear, and the stress required to increase the shear rate diminishes with increasing shear rate. This behavior is often described by an empirical power law equation that is simply a variation of Eq. (4.3), and the fluid is said to be a power law fluid ... 

In the in situ consolidation model of Liu [26], the Lee-Springer intimate contact model was modified to account for the effects of shear rate-dependent viscosity of the non-Newtonian matrix resin and included a contact model to estimate the size of the contact area between the roller and the composite. The authors also considered lateral expansion of the composite tow, which can lead to gaps and/or laps between adjacent tows. For constant temperature and loading conditions, their analysis can be integrated exactly to give the expression developed by Wang and Gutowski [27]. In fact, the expression for lateral expansion was used to fit tow compression data to determine the temperature dependent non-Newtonian viscosity and the power law exponent of the fiber-matrix mixture. 

It should be noted that for relatively dilute solid-liquid mixtures, except for fibrous solids, the power to agitate at a given speed is essentially the same as for the clear liquid (Treybal, 1980). Concentrated slurries and suspensions of fibrous solids are likely to be non-Newtonian in character. 

Specific correlations of individual film coefficients necessarily are restricted in scope. Among the distinctions that are made are those of geometry, whether inside or outside of tubes for instance, or the shapes of the heat transfer surfaces free or forced convection laminar or turbulent flow liquids, gases, liquid metals, non-Newtonian fluids pure substances or mixtures completely or partially condensable air, water, refrigerants, or other specific substances fluidized or fixed particles combined convection and radiation and others. In spite of such qualifications, it should be... 

In 1959 Dodge s thesis under the supervision of Metzner was published at the same time as Shaver s findings under the supervision of Merrill. Both noticed unusually low friction factors for certain non-Newtonian solutions like those of sodium carboxy-methylcellulose in water. At around the same time, industrial researchers made similar observations with certain additives, the most prominent being guar gum, which is a polysaccharide derived from a plant. The gums were used to suspend sand in the sand-water mixtures utilized in oil-well fracturing operations. 

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