Non-Newtonian Media

Both phenomena can be understood if the local shear rate in the fluid around the particles is considered. Local rates increase more with concentration than the average shear rate does and thus reduce the apparent medium viscosity. The resulting shift in the curves can be partially compensated if the relative viscosities are calculated from medium and suspension viscosities at equal values of the shear stress, rather than at equal shear rates. 

The elastic properties of a viscoelastic medium also change when particles are added. These changes are qualitatively similar to those of the viscosity (Mewis and de Bleyser, 1975). In the non-Newtonian region, elasticity increases less than viscosity. Hence filled polymers are always less elastic than the suspending polymers under processing conditions. Reviews available on suspensions in non-Newtonian media include Metzner (1985) and Kamal and Mutel (1985). 

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Chhabra. R. P. and Richardson, J. F. Chem. Eng, Res. Des. 63 (J 9S5J 390. Hydraulic transport ol coarse particles in viscous Newtonian and non-Newtonian media in a horizontal pipe. 

The results of the latest research into helical flow of viscoplastic fluids (media characterized by ultimate stress or yield point ) have been systematized and reported most comprehensively in a recent preprint by Z. P. Schulman, V. N. Zad-vornyh, A. I. Litvinov 15). The authors have obtained a closed system of equations independent of a specific type of rheological model of the viscoplastic medium. The equations are represented in a criterion form and permit the calculation of the required characteristics of the helical flow of a specific fluid. For example, calculations have been performed with respect to generalized Schulman s model16) which represents adequately the behavior of various paint compoditions, drilling fluids, pulps, food masses, cement and clay suspensions and a number of other non-Newtonian media characterized by both pseudoplastic and dilatant properties. 

Newtonian fluids such as water, and most bacterial and yeast fermentation broths. Non-Newtonian media such as polysaccharide fermentations and broths of Streptomyces, Aspergilli, and Penicillia. 

The scalar functions p and e determine various rheological models of non-Newtonian media. For example, the case p = const and s = 0 corresponds to the... 

Naidenov, V. I., On integral equations describing the temperature distribution in plane flow of non-Newtonian media, J. Appl. Mech. Techn. Phys., No. 5,1983. 

The only study relating to the use of class II impellers for non-Newtonian media is that of Peters and Smith [1967] who reported a reduction in mixing and circulation times for visco-elastic polymer solutions agitated by an anchor... 

Gas dispersion in agitated tanks may be described in terms of bubble size, gas hold-up, interfacial area and mass transfer coefficient. While gas dispersion in low viscosity systems [Smith, 1985 Tatterson, 1991 Hamby et al., 1992] has been extensively studied, little is known about the analogous process in highly viscous Newtonian and non-Newtonian media, such as those encoim-tered in polymer processing, pulp and paper manufacturing and fermentation applications. 

Kawase, Y, and Moo-Young, M. (1986b), Mixing and mass transfer in concentric-tube airlift fermenters Newtonian and non-Newtonian media, Journal of Chemical Technology and Biotechnology, 36(11) 527-538. 

The influence of viscosity on Et was studied by Hikita and Kikukawa (73). Only a small effect was found, i.e. ELa/i"0 2. Liquid phase dispersion coefficients in aerated non-Newtonian media were not yet measured directly. When matching experimental profiles of liquid phase oxygen concentrations with the predictions of the dispersion model, Schumpe et al. (18) obtained higher Ejj values than for low viscous media. However, these preliminary results need further clarification by direct measurements. 

By assuming that heat transfer data in aerated Newtonian and non-Newtonian fluids follow the same dependencies Nishikawa, Kato, and Hashimoto (84) have proposed valueible correlations for the average shear rate as a function of the gas velocity. With the shear rate known, the effective viscosity of non-Newtonian media in the tower reactor can be obtained from the shear stress vs. shear rate curve. 

Equation 10.26 incorporates all important parameters that characterize a gas-liquid dispersion such as variation of with and, in particular, It should therefore be applicable to other gas-liquid dispersions, such as for coalescing, noncoalescing, Newtonian/non-Newtonian media, etc. In view of this, Equation 10.26 is recommended for estimation of The insignificant effect of T on recorded in Section 10.9.5.5 is also obvious from Equations 10.25 and 10.26, which do not contain any term related to the column diameter. 

Gauthier, F., Goldsmith, H.L., and Mason, S.G. (1971) Particle motions in non-Newtonian media I Couette flow. Rheol. Acta, 10 (3), 344-364. 

It is customary to account for the non-Newtonian fluid behavior by introducing the so called effective viscosity to define various dimensionless groups. Unlike its constant value for Newtonian liquids, the effective viscosity of non-Newtonian pseudoplastic type fluids depends upon the operating conditions (e.g., gas and liquid velocities) as well as on the geometrical details of the system. Indeed, the lack of a rationed definition of the apparent viscosity or characteristic shear rate appears to be the main impediment in extending the well established predictive correlations for Newtonian media to non-Newtonian media. When we develop correlations for design parameters in bubble columns with non-Newtonian media in an analogous manner to the case of Newtonian media, Newtonian viscosity p is simply replaced by an apparent viscosity for non-Newtonian media. 

The heat transfer rates in bubble columns are much higher than that anticipated from single phase flow considerations. This enhancement is ascribed solely to the bubble-induced turbulence and liquid circulation. Little work has been reported on heat transfer, both at wall and to/from immersed surfaces, in bubble columns employing non-Newtonian media. Nishikawa et al. reported the first set of data on the effect of shearthinning viscosity of CMC solutions on jacket and coil heat transfer coefficients [7]. They reconciled their results for Newtonian and power law liquids by introducing the notion of an effective viscosity estimated via Equation 3, provided the gas velocity was greater than 40 mm/s. For superficial gas velocity lower than this value, the effective shear rate varies as for coil heat transfer... 

Once the process parameters and the rules for scale-up from the model dimensions have been determined by tests at various scales, the next step is to calculate the power rating for the industrial-scale system with the aid of the power characteristic. For Newtonian liquids this is no problem, in total contrast to non-Newtonian media, where the effective viscosity is always a function of agitator shaft speed [4]. 

Buscall R, Goodwin JW, Ottewill RH, Tadros ThF. The settling of particles through Newtonian and non-Newtonian media. J Colloid Interface Sd 85 78-86, 1982. 

Bartram, E., H. L. Goldsmith, and S. G. Mason, Particle motions in non-Newtonian media III. Further observations in elasticoviscous fluids, Rheol Acta 7 776-782 (1975). 

Sharma, M. K. and R. P. Chhabra, A experimental study of free fall of cones in Newtonian and non-Newtonian media drag coefficient and wall effects, Chem. Eng. Proce.ss. 50 61-67 (1991). 

Unnikrishnan, A. and R. P. Chhabra, Slow parallel motion of cylinders in non-Newtonian media wall effects and drag coefficient, Chem. Eng. Process. 25 121-126 (1990). 

A considerable amount of experimental results on the free motion of bubbles and drops in quiescent non-Newtonian media is available in the literature. In most cases, the two-parameter power-law model has been used to model the ambient liquid rheology. It is worthwhile to mention here that in the bulk of the work dealing with the free fall of liquid drops in polymer solutions, the ratio of the viscosity of the dispersed phase to that of the continuous phase is in the range lO -lO" and, hence, these drops may effectively be treated as gas bubbles. At this juncture, it is also important to recall that bubbles in the pretransition region (prior to the abrupt change) behave more like solid spheres and, hence, the drag under these conditions is approximated... 

To date, no analogous results on wall effects are available in non-Newtonian liquids. Some workers (De Kee et al., 1986 Miyahara and Yamanaka, 1993) have minimized wall effects [on the basis of Eq. (16)], whereas others (Calderbank et al., 1970) have corrected their data using Eq. (16). Yet others (Acharya et al., 1977 Haque et al., 1988) have altogether ignored wall effects. Clearly, neither of these procedures is generally justifiable. Based on the behavior of rigid particles (Chhabra, 1993), one can perhaps conjecture that the wall correction is likely to be smaller in non-Newtonian media than in Newtonian liquids. Finally, it should be borne in mind that a 10% error in velocity will lead to a 20% error in drag coefficient ... 

Miyahara, T. and S. Yamanaka, Mechanics of motion and deformation of a single bubble rising through quiescent highly viscous Newtonian and non-Newtonian media, J. Chem. Eng. Jpn. 26 291 (1993). 

For non-Newtonian media with a yield stress some particles do not settle in quiescent conditions, and this observation has led to the concept of stable slurries. However, an externally-applied shear in the medium may initiate particle settling, with possible deleterious effects for pipeline transport. It was decided to add to the rather limited existing data in this area by experimenting with a novel cup-and-bob apparatus in which shear rate decreases with depth. The experimental media were transparent, and approximated Bingham-plastic behaviour. The particles that were used did not settle under quiescent conditions. 

Tharwat s collaborations with Ron Ottewill at Bristol have led to papers on topics as diverse as understanding settling in Newtonian and non-Newtonian media (also with Jim Goodwin and Richard Buscall), and to fundamental studies on microemulsions (also with A.T. Florence). 

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