Model viscous mixing

Mixing Models. The assumption of perfect or micro-mixing is frequently made for continuous stirred tank reactors and the ensuing reactor model used for design and optimization studies. For well-agitated reactors with moderate reaction rates and for reaction media which are not too viscous, this model is often justified. Micro-mixed reactors are characterized by uniform concentrations throughout the reactor and an exponential residence time distribution function. 

Sundaraj, U., Dori, Y., and Macosko, C. W., Sheet formation in immiscible polymer blends model experiments on an initial blend morphology. Polymer 36,1957-1968 (1995). Swanson, P. D., and Ottino, J. M., A comparative computational and experimental study of chaotic mixing of viscous fluids, J. Fluid Mech. 213, 227-249 (1990). 

In practice, it is often possible with stirred-tank reactors to come close to the idealized mixed-flow model, providing the fluid phase is not too viscous. For homogenous reactions, such reactors should be avoided for some types of parallel reaction systems (see Figure 5.6) and for all systems in which byproduct formation is via series reactions. 

The TIS and DPF models, introduced in Chapter 19 to describe the residence time distribution (RTD) for nonideal flow, can be adapted as reactor models, once the single parameters of the models, N and Pe, (or DL), respectively, are known. As such, these are macromixing models and are unable to account for nonideal mixing behavior at the microscopic level. For example, the TIS model is based on the assumption that complete backmixing occurs within each tank. If this is not the case, as, perhaps, in a polymerization reaction that produces a viscous product, the model is incomplete. 

For viscoelastic fluids, the formalism of a viscous fluid and an elastic solid are mixed [31]. The equations for the effective viscosity, dynamic viscosity, and the creep compliance are given in Table 12.4 for a viscous fluid, an elastic solid, and a visco-elastic solid and fluid. For the viscoelastic fluid model the dynamic viscosity, >j (tu), and the elastic contribution, G (ti)), are plotted as a function of (w) in Figure 12.31. With one relaxation time, X, the breaks in the two curves occur at co. 

The Rapid Mixing Model. In this model (36, 46) it is assumed that the combined internal convective-diflFusive transports are so rapid that the droplet temperature is maintained spacially imiform but temporally varying. This represents the fastest internal heat transfer hmit and is relevant for less viscous fuels in which internal motion can be easily generated. The model is somewhat artificial in that the existence of nonradial convection, particularly the requirement for the external gas stream to generate internal circulation, invalidates the assumption of spherical S3onmetry. However, by comparing results from the present... 

Viscous dissipation. The mixing efficiency of a viscous fluid is related to the viscous dissipation d> since = t D = 2r] D D where 17 is the dynamic viscosity. Maps of viscous dissipation can, therefore, be used to qualitatively predict the differences in mixing efficiency between different regions of the mantle, or between different models of mantle convection (Figure 10). 

The highly viscous nature of polymeric mesophases could possibly prevent the mixing of the mesophases of polymers and certain model compounds. Therefore, while the miscibility of model compounds with a polymer may be used to identify the type of mesophase, the lack of compatibility does not necessarily suggest that the mesophases are not the same. That is, some model compounds and polymers with the same mesophase may even be inherently incompatible. As a result, some judgment is required in order to make both the proper choice of the model compound and the correct assignment of the mesophase when using this technique. 

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