Laminar/transitional flow dispersions

Agitated dispersions at low impeller speeds or high continuous phase viscosities are in a state of laminar or transition flow. At low impeller Reynolds number, (NRe)T < 15, the flow is laminar around the impeller... 

What models should be used either for scaleup or to correlate pilot plant data Section 9.1 gives the preferred models for nonisothermal reactions in packed beds. These models have a reasonable experimental basis even though they use empirical parameters D, hr, and Kr to account for the packing and the complexity of the flow field. For laminar flow in open tubes, use the methods in Chapter 8. For highly turbulent flows in open tubes (with reasonably large L/dt ratios) use the axial dispersion model in both the isothermal and nonisothermal cases. The assumption D = E will usually be safe, but do calculate how a PFR would perform. If there is a substantial difference between the PFR model and the axial dispersion model, understand the reason. For transitional flows, it is usually conservative to use the methods of Chapter 8 to calculate yields and selectivities but to assume turbulence for pressure drop calculations. 

Flow field in agitated dispersions(laminar/transitional dispersions,turbulent dispersions)... 

Mixing processes involved in the manufacture of disperse systems, whether suspensions or emulsions, are far more problematic than those employed in the blending of low-viscosity miscible liquids due to the multi-phasic character of the systems and deviations from Newtonian flow behavior. It is not uncommon for both laminar and turbulent flow to occur simultaneously in different regions of the system. In some regions, the flow regime may be in transition, i.e., neither laminar nor turbulent but somewhere in between. The implications of these flow regime variations for scale-up are considerable. Nonetheless, it should be noted that the mixing process is only completed when Brownian motion occurs sufficiently to achieve uniformity on a molecular scale. 

A comparison of the measured pressure drops and those calculated using the intermittent and annular/disperse-wave/mist flow models is shown in Figure 11 for each tube considered. In the overlap zone (Figure 7), the flow exhibits both the adjoining mechanisms (intermittent and annular/disperse-wave/mist flow). Therefore, for calculating the pressure drops in the overlap zones in Figure 11, the four-point interpolation scheme described above in connection with the transition between laminar and turbulent data was applied to the pressure drops calculated using the intermittent and annular/disperse-wave/mist flow models. This combined model for the... 

Here t is given by Eq. (48) and G is given by either Eq. (50) or (51), depending on whether the range of flow is laminar or transitional. Thus, he obtained the following expression for the coalescence efficiency between rigid drops in dispersions under laminar and transition range flows... 

After a complete structure disintegration, the disperse system behaves as a Newtonian fluid under the laminar flow conditions (Fig. IX-24, region IV). The viscosity r mm of such relatively concentrated system is higher than that of dispersion medium by the amount exceeding the one predicted by Einstein s equation. In this case the concentration of dispersed phase is sufficiently high, and the particles interact with each other. Further increase in the applied shear stress results in deviations from Newton s equation due to the appearance of turbulence. Early transition of the flow to turbulent behavior sometimes results in the absence of region IV (Fig. IX-24). 

Reynolds dye experiment on transition to turbulence in pipe flow and G. I. Taylor s experiments on axial dispersion in laminar flow represent the early use of tracers in flow visualization and transport parameters evaluation in chemical engineering. A more widespread use in chemical reactors dates to the work of Danckwerts (1). He realized that the performance of process equipment depends on the residence time distribution of process fluid, and that this information can be obtained by tracer methods. Residence time distributions are now discussed in standard chemical reaction engineering texts (2,3) and are well summarized in a recent excellent monograph by Nauman and Buffham (4). Tracer methods. 

In the region 1 < Re < 10, a transition occurs from laminar (Fa oc v) to turbulent flow (Fa oc v ) and the relationship between Fa and v becomes more complex. Also, since drag forces actually apply only to the relative velocity of the particle to the medium, the effects of drag or viscous resistance to flow for a dispersed particle must be adjusted to account for the flow of the medium. 

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