Specific power input

Eigure 6 enables a comparison to be made of kj a values in stirred bioreactors and bubble columns (51). It can be seen that bubble columns are at least as energy-efficient as stirred bioreactors in coalescing systems and considerably more so when coalescence is repressed at low specific power inputs (gas velocities). 

The rotor speed of the scaled up tower is based on maintaining the same specific power input number as used on the pilot column it can be determined by substituting the specific values into the relationship ... 

Figure 2.15 Local specific power input to agitated vessels for several stirrers (after Mersmann and Geisler, 1991)...

For plant cell suspensions cultivated in shake flasks, Huang et al. [45] used the energy dissipation rate as a correlating parameter for system response. Specific power input was calculated using the empirical correlation proposed by Sumino et al. [46] and subsequently employed in other applications [47,48] ... 

Such spatial variations in, e.g., mixing rate, bubble size, drop size, or crystal size usually are the direct or indirect result of spatial variations in the turbulence parameters across the flow domain. Stirred vessels are notorious indeed, due to the wide spread in turbulence intensity as a result of the action of the revolving impeller. Scale-up is still an important issue in the field of mixing, for at least two good reasons first, usually it is not just a single nondimensional number that should be kept constant, and, secondly, average values for specific parameters such as the specific power input do not reflect the wide spread in turbulent conditions within the vessel and the nonlinear interactions between flow and process. Colenbrander (2000) reported experimental data on the steady drop size distributions of liquid-liquid dispersions in stirred vessels of different sizes and on the response of the drop size distribution to a sudden change in stirred speed. 

P/Vis the specific power input into the fermenter via the impeller (P = power [W],... 

In these equations, x and x2 denote the particle sizes of the colliding particles, T the absolute temperature, k the Boltzmann constant, q the dynamic viscosity of the fluid, j> the density of the fluid, pp the density of the particle, y the local shear rate and e the local mass-specific power input due to turbulence. 

Fig. 3. Time scales in precipitation calculated for BaSC>4 precipitated from 0.5 m BaCl2- and 0.33 m H2S04-solutions at 25 °C. To quantify mixing, a specific power input typical for the applied T-mixer (s = 103 W/kg) was used.

Clearly, the power input and the specific power input both vanish at a pressure-to-drag flow ratio of 1/3, when the shear stress at the wall is zero. It is also worth noting that the specific power input is proportional to viscosity and plate velocity, and inversely proportional to the... 

Thus, for Newtonian fluids, the pressurization capability of the optimized JMP is eight times that of the SMP, and for non-Newtonian fluids, the ratio exhibits a minimum at n = 0.801 and rises to 11.59 at it — 0.25 whereas, the flow rate at fixed pressure rise for Newtonian fluids is 81 2 — 2.83 times in JMP as compared to SMP, and for non-Newtonian fluids with n = 0.25 it rises to 7.25. Clearly, the JMP configuration is about an order of magnitude more efficient then the SMP one. Moreover, the specific power input in a JMP configuration for Newtonian fluids is one-half that of the SMP, and for n — 0.25, it is one-fifth the corresponding ratios for specific power dissipated into heat are, one-quarter and 1/25, respectively. 

At first sight, based on the results we have, any of these extruders would be able to do the job. The 8-in extruder would need 7.5 turns to build up the required pressure, whereas the 16-in one will only need 3.75 turns. We note that both mean shear rate and specific power input per... 

A typical task is the milling of minerals in the pm-range with power consumption of approximately 50 Wh kg-1. A tumbling ball mill would need 1 hour of milling time at a specific power input of 50 W kg-1 for the comminution, a stirred media mill would need 2 min at 1400 W kg-1, a vibration mill 40 s at 4500 W kg-1, and a planetary mill 5 s at 36,000 W kg-1 (Fig. 14.4). 

This is still a low power level of 6.2/1.74 = 3.55 HP/1,000 gal. With this agitator, a reasonable upper hmit for agitator speed would be 100 rpm, for which the impeller power would be 22 HP with a specific power input of 13HP/l,000gal and Npe = 9. This change would move up into the Reynolds number near the lower limit recommended by Hemrajani and Tatterson (in Paul (2004), 345). This example illustrates the great impact of fluid viscosity on (1) the power requirement of a 6BD and (2) the choice of an impeller style between a turbine and a helical ribbon impeller. 

Thermochemical Equilibrium Predictions. As described in the Plasma Composition section, above, a full range of composition calculations were made assuming thermochemical equilibrium. These calculations predicted that the plasma composition within the RF. coil would be dominated by atomic species for the specific power input used in this study. Perhaps the following additional consideration of these theoretical predictions can elucidate the processes occurring during rapid quench. 

A typical example for a stirred two-phase system with a volume fraction of 30 vol.% organic phase dispersed in water, an interfacial tension of 25 mN m-1 and a specific power input of 0.5 W L 1 shows a droplet diameter in the range of 250 pun and a specific interface of about 10 m2 L 1. These dimensions maybe estimated from simple empirical correlations between the Sauter mean diameter of the dispersed phase (zf2.3) and the characteristic Weber number (We). In case of turbulent mixing the following correlation is proposed in the literature for calculation of the mean diameter of dispersed droplets [24]... 

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