Newtonian fluids, mixing

When choosing a mixer for gel preparation, the common approach is to test available mixers until one is found which adequately performs the tasks described previously. Although this is largely a hit-or-miss approach, it is apparently not too critical, and many suitable candidate fuel slurries have been prepared. Similar end products can be obtained with different mixing devices. At present non-Newtonian fluid mixing remains more of an art than a science, and the outlook is that it will remain as such in the near future. 

Some concerns directly related to a tomizer operation include inadequate mixing of Hquid and gas, incomplete droplet evaporation, hydrodynamic instabiHty, formation of nonuniform sprays, uneven deposition of Hquid particles on soHd surfaces, and drifting of small droplets. Other possible problems include difficulty in achieving ignition, poor combustion efficiency, and incorrect rates of evaporation, chemical reaction, solidification, or deposition. Atomizers must also provide the desired spray angle and pattern, penetration, concentration, and particle size distribution. In certain appHcations, they must handle high viscosity or non-Newtonian fluids, or provide extremely fine sprays for rapid cooling. 

Computational fluid dynamics (CFD) emerged in the 1980s as a significant tool for fluid dynamics both in research and in practice, enabled by rapid development in computer hardware and software. Commercial CFD software is widely available. Computational fluid dynamics is the numerical solution of the equations or continuity and momentum (Navier-Stokes equations for incompressible Newtonian fluids) along with additional conseiwation equations for energy and material species in order to solve problems of nonisothermal flow, mixing, and chemical reaction. 

Topics that acquire special importance on the industrial scale are the quality of mixing in tanks and the residence time distribution in vessels where plug flow may be the goal. The information about agitation in tanks described for gas/liquid and slurry reactions is largely apphcable here. The relation between heat transfer and agitation also is discussed elsewhere in this Handbook. Residence time distribution is covered at length under Reactor Efficiency. A special case is that of laminar and related flow distributions characteristic of non-Newtonian fluids, which often occiu s in polymerization reactors. 

Figure 3-56. Viscosity performance correction chart for centrifugal pumps. Note do not extrapolate. For centrifugal pumps only, not for axial or mixed flow. NPSH must be adequate. For Newtonian fluids only. For multistage pumps, use head per stage. (By permission. Hydraulic Institute Standards for Centrifugal, Rotary, and Reciprocating Pumps, 13th ed.. Hydraulic Institute, 1975.)...

The following treatment of agitation is restricted to fluids that approximate to Newtonian fluids. As mixing is a complex process, the variables involved are considered together in a... 

Hah, K. R. and Godfrey, J. C. Trans. Inst. Chem. Eng. 46 (1968) 205. The mixing rales of highly viscous Newtonian and non-Newtonian fluids in a laboratory sigma blade mixer. 

Equation (6-37) represents the friction factor for Newtonian fluids in smooth tubes quite well over a range of Reynolds numbers from about 5000 to 105. The Prandtl mixing length theory and the von Karman and Blasius equations are referred to as semiempirical models. That is, even though these models result from a process of logical reasoning, the results cannot be deduced solely from first principles, because they require the introduction of certain parameters that can be evaluated only experimentally. 

This method can be easily used to show the logic behind the scale-up from original R D batches to production-scale batches. Although scale-of agitation analysis has its limitations, especially in mixing of suspension, non-Newtonian fluids, and gas dispersions, similar analysis could be applied to these systems, provided that pertinent system variables were used. These variables may include superficial gas velocity, dimensionless aeration numbers for gas systems, and terminal settling velocity for suspensions. 

Smith JM. The mixing of Newtonian and non-Newtonian fluids. J Soc Cosmet Chem 1970 21 541-552. 

Unsteady state phenomena have been stated to be of greater importance for non-Newtonian than for Newtonian materials and therefore warrant experimental investigation. The prediction of pressure drop for two-phase flow of a gas and a non-Newtonian fluid seems to be in a well-perfected state but requires extension to situations in which the liquid flow is laminar. Apparently no information is yet available on the problems of mixing, entrainment, and other similar relationships which are of importance if such contactors are to be designed for chemical rather than mechanical purposes. 

The table below illustrates this using the example chosen at the beginning of this chapter, namely the heat transfer characteristics of a mixing vessel or a smooth straight pipe, Eq. (27). It shows the complete set of pi numbers for a temperature independent (a) and temperature dependent (b) viscosity of a Newtonian and a non-Newtonian fluid. 

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