Solutions Newtonian

Rotating cone in non-Newtonian solution See Smith and Greif (S15b) 1 P2a, S15b... 

Chang SH, Parrot EL. Hydrodynamics of dissolution in a new-tonian and a non-newtonian solution. Drug Dev Ind Pharm 1991 17(131 1731-1751. 

No methods appear to be available for the precise prediction of pressure drop when a non-Newtonian fluid is being heated or cooled, but Vaughn (V2) has shown that the procedure recommended most recently by McAdams (M4, p. 149) for Newtonian fluids is slightly conservative when applied to pressure-drop data on the heating of non-Newtonian solutions in laminar flow. McAdams has suggested evaluation of the fluid properties at a film temperature [Pg.116]

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. 

For a power law solution the equation, of motion is non-dimensionalized in a similar manner as with the Newtonian solution, except that dimensionless pressure is defined as... 

The above equations can be used to simulate the flow of non-Newtonian fluids with a shear thinning viscosity. This requires an iterative under-relexation scheme where a Newtonian solution is found first. The initial velocity field is used to compute rates of deformation and viscosity. Next, a corrected velocity field is computed with the updated velocities, at which point an under-relaxation is performed using... 

Figure 11.19 presents the pressure distribution along the x-axis for a Newtonian solution using several bank-to-nip ratios. The solutions are presented with the analytical predictions using McKelvey s lubrication approximation model presented in Chapter 6. The graph shows that the two solutions are in good agreement. Fig. 11.20 presents a sample velocity field for the Newtonian case with a bank-to-nip ratio of 10. As can be seen, the velocities look plausible and present the recirculation pattern predicted by McKelvey s lubrication approximation model and seen in experimental work done in the past [18]. 

Ethylene and propylene into non-Newtonian solution of copolymer 100... 

Finally we comment briefly on weakly elastic fluids. (See [26] and section 3.2.) We assume that the given Newtonian solution v satisfies ] v i < (ciRe), where Ci is some constant depending only on the domain of the flow this condition ensures that v is asymptotically Liapunov stable. (See e.g., [67].) Then, the viscoelastic solution (v ,Tt) close to (v, 0) is linearly (asymptotically) stable for c > 0 small enough. 

Mean flow behaviors and turbulence characteristics of DR solutions differ from those of Newtonian solutions. Topics covered in this section include the maximum DR asymptote (MDRA), mean velocity profiles, diameter scale-up, turbulence intensities, stress balance, and streak spacing in polymer and surfactant DR solutions as well as the HTR-DR relationship for surfactant DR solutions. Numerical simulations for polymer DR are noted and speculations on DR mechanisms are offered. 

Zakin, Myska, and Chara showed that some surfactant DR systems have friction factors over 40% below Virk s MDRA for high polymers and more than 90% below Newtonian solutions (Fig. 11). Their MDRA for surfactants is... 

The model has been tested for its ability to predict Newtonian solution viscosities at polymer concentrations in the range of 30-60 wt % in a number of pure solvents and solvent blends. The calculated results generally agree with the experimental data. 

Indeed, even nonequilibrium systems do not necessarily show measurable excess noise and, thus, deviate from relation 1. An appropriate example that is relevant to the subject is a capillary channel that contains a stream of electrolyte maintained by an external pressure difference. Measurements on several aqueous polymer solutions with added electrolytes performed at up to 5000 dyn/cm2 shear stresses and zero external voltage showed that measurable excess noise can be observed only for non-Newtonian solutions exhibiting elasticity (19, 20). Similar results were obtained for colloid suspensions... 

The 021 calculated using Equation (7-32) is equal for both Newtonian and non-Newtonian solutions because / , r, and L depend on the measuring apparatus only and not on the properties of the liquid being investigated. 021 is proportional to the radius and has a maximum value 021 (max) = pRI2L for capillary radius R. 

Both Mishra et al. [1976] and Ghosh et al. [1986] measmed the rates of mass transfer from glass plates coated with benzoic acid to non-Newtonian solutions of carboxymethyl cellulose (0.88 < n < 1 5 < Rez, < 200), and they foimd a satisfactory ( 25%) agreement between their data and the predictions of equation (7.70). In this narrow range of n values, there is a little difference between the predictions for n = 1 and n = 0.88, however. Thus, the predictive equations developed for Newtonian fluids can be applied without incurring appreciable errors. 

A power-law non-Newtonian solution of a polymer is to be heated from 288 K to 303 K in a concentric-tube heat exchanger. The solution will flow at a mass flow rate of 210 kg/h through the inner copper tube of 31.75 mm inside diameter. Saturated steam at a pressure of 0.46 bar and a temperature of 353 K is to be condensed in the armulus. If the heater is preceded by a sufficiently long unheated section for the velocity profile to be fully established prior to entering the heater, determine the required length of the heat exchanger. Physical properties of the solution at the mean temperature of 295.5 K are ... 

Haque, M.W., Nigam, K.D.P, and Joshi, J.B. (1986), Hydrodynamics and mixing in highly viscous pseudo-plastic non-Newtonian solutions in bubble columns, Chemical Engineering Science, 41(9) 2321-2331. 

As previously stated, generally lower productions of BNC are obtained and higher energy resources are required in agitated systems, and static methods are only widely used for BNC production [34]. One reason for the above is that the fermentation broth with BNC pellets becomes a viscous non-Newtonian solution, which increases the difficulty in mixing the... 

Effect of Physical Properties of the Primary and Secondary Fluids The only available investigation on the effect of the physical properties of the primary hquid on is that of Bhutada and Pangarkar (1988). Newtonian solutions of carboxy-... 

The complete range of power input per unit volume goes from 60 W/m to 2,200 W/m . The effect of u, and polymer concentration on Kj a for all non-Newtonian solutions is shown in Figures 1 to 6. Depending on the conditions and fluids used, K a ranged from 0.0008 to 0.01 s. These values are 1.5 to 15 times lower than those in water (not shown). 

The sedimentation of particles in non-Newtonian fluids, such as aqueous solutions containing high molecular weight compounds (e.g. hydroxyethyl cellulose or xanthan gum), is not simple since these non-Newtonian solutions are shear thinning with the viscosity decreasing with increase in shear rate. As discussed above, these solutions show a Newtonian region at low shear rates or shear stresses, usually referred to as the residual or zero shear viscosity /(0). 

Haque, M. W., K. D. P. Nigam, K. Viswanathan, and J. B. Joshi, Studies on bubble rise velocity in bubble columns employing non-Newtonian solutions, Chem. Eng. Commun. 7i 31 (1988). 

Different mannans have been used in the food industry already for years due to their excellent thickening, binding and stabilizing properties. Guar gum GMs are fairly soluble in water and behave as non-Newtonian solutions. GM solutions... 

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