Scale constant blend time

Fig. 10. Log—log plot scale-up by power per unit volume where for A, constant blend time, = 2/3 B, same vortex, y = 1/6 C, dispersion, = 0 D,...

Where T/D is held constant on scale-up, this result reduces to 1/(N N). There are many different ways to make the scaling arguments (see, e.g., Grenville et al., 1995 Grenville and Tilton, 1996, 1997 or Nienow, 1997). The point is that the end result agrees well with Corrsin s approach. The most important thing to recognize is that Lj/e, however it is estimated, must be constant on scale-up to maintain constant blend time. If the dissipation (e) is held constant on scale-up, the blend time will always increase. 

The models presented correctly predict blend time and reaction product distribution. The reaction model correctly predicts the effects of scale, impeller speed, and feed location. This shows that such models can provide valuable tools for designing chemical reactors. Process problems may be avoided by using CFM early in the design stage. When designing an industrial chemical reactor it is recommended that the values of the model constants are determined on a laboratory scale. The reaction model constants can then be used to optimize the product conversion on the production scale varying agitator speed and feed position. 

Common violations of this approach that can immediately cause problems include the attempt to scale from one geometry to another (e.g., V-blender to in-bin blender), changing fill level without concern to its effect, and keeping blending time constant while changing blender speed. 

Some processes are governed by the maximum impeller zone shear rate. For example, the dispersion of a pigment in a paint depends upon the maximum impeller zone shear rate for the ultimate minimum particle size. However, when constant tip speed is used to maintain this, the other geometric variables must be changed to maintain a reasonable blend time, even though process results on full scale will probably take much longer than those on small scale. 

These results are consistent with a scaleup from the pilot-scale operation. Although power per volume is reduced and impeller to tank diameter ratio is increased, torque per volume is about half and tip speed is the same. With any realistic scaleup, some factors unavoidably must change, while the important ones are held constant. In a different situation and process, a different variable, such as power per volume, might be held constant. Other variables, such as blend time, could be calculated, at each step in the scaleup. 

Chang found that the ratio of drop size at a particular time to the equilibrium drop size was a function of the number of revolutions of the impeller. This finding indicates that blend time is the proper scale-up criterion to maintain constant temporal dependence of drop size. 

The concepts of similarity suggest the use of dimensionless groups. There are, however, other process parameters that could be held constant. Such parameters could be, the blending time, the power per unit volume, the superficial gas velocity, the shear rates and the heat transfer coefficient. Which scale-up criteria that should be chosen depends on the actual process, since the sensitivity to each parameter appears to be different for the various processes. 

FIGURE 9.24 Blend time comparisons at constant PIV for different scales. (From Fasano et al., 1991.)... 

The effect of the reactive compadbilizatimi can be observed aheady during mixing by comparing the viscosity (detected e.g. as torque necessary to keep the mixing speed constant) over time curves. Furthermore, the size of the dispersed PA6 particles (mostly the minor phase forms particles dispersed in the major phase) can be analysed in the blends before and after compression moulding. By optical microscopy on thin cuts (or in the reflected light mode on cryo-fractures) in the nonreactive PP/PA6 blend particles in the size of few pm can be detected while in the reactive PP-MA/PA6 blend the PA6 phase is so small (100 nm scale) that... 

Example 2-4a Blend Time. Now that we have ways to estimate s and the characteristic length scale Lg, we return to Corrsin s equations in Table 2-4. Probably the most important practical point is that the time constant of mixing scales with (Lg/e). All the rest of the terms in the equation for (Sc 1) are either constants or relatively minor effects of the Schmidt number. For mixing in a pipe, we take the radius of the feed pipe, ro, as the initial integral length scale, and the fluctuating velocity, u, as a measure of the turbulent energy. Thus we can write... 

We could calculate the bulk blend time in the lab and in the plant, but in this case the process result requires a reaction. The reaction kinetics and molecular diffusivity are constant on scale-up, so we must ensure that the Batchelor scale is also preserved. The Batchelor scale can be defined using an estimate for the dissipation ... 

When scaling-up at constant power per unit mass and geometry, blend time will increase by the scale factor raised to the two-thirds power. 

Scale-up of Batch Mixers While a desirable objective of scale-up might be equal blending uniformity in equal time, practicality dictates that times for blending are longer with larger batches. Scale-up of many processes and applications can be successfully done by holding constant the peripheral speed of the rotating element in the mixer. Equal peripheral speed, often called equal Up speed, essentially means mat the maximum velocity in the mixer remains constant. 

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