Power dissipation, mixing

The above two equations must be solved simultaneously and will require the solution of an equation of cubic form. These correlations are based on the gas phase being sparged into the mixing vessel. Gas dispersion from surface entrainment due to votexing, etc., is not included. The mixing power dissipation must be corrected... 

Thermal conductivity was measured by a steady-state technique the measurements below 1 K (above 1K) were carried out with the mixing chamber maintained at a constant temperature Ts 70 mK (Ts 300mK) by controlling the power dissipated in a heater (Hs) glued to the copper holder. 

Gladki H. Power dissipation, thrust force and average shear stress in the mixing tank with a free jet agitator. In Tatterson GB, Calabrese RV, Penny WR, eds. Industrial Mixing Fundamentals with Applications. New York American Institute of Chemical Engineering, 1995 146-149. 

Eq. (9.32) predicts that the the mass-transfer coefficient for the oxygen dissolution in water 25°C in a mixing vessel is 4.58 x lO m/s, regardless of the power consumption and gas-flow rate as illustrated in the previous example problem. Lopes De Figueiredo and Calderbank (1978) reported later that the value of kL varies from 7.3 x 10"4 to 3.4 x 1CT3 m/s, depending on the power dissipation by impeller per unit volume (Pm/v) as... 

On the other hand, we discussed and presented in physical terms the very powerful melting mechanisms resulting from repeated, large deformations, forced on compacted particulate assemblies by twin co- or counterrotating devices. These mechanisms, which we refer to in Section 5.1, are frictional energy dissipation (FED), plastic energy dissipation (PED), and dissipative mix-melting (DMM). 

Const, (power) dissipation energy per unit vessel volume Const, impeller discharge flow energy Turbulent dispersion Gas-liquid operation Reaction requiring microscale mixing... 

With respect to the consideration of effective viscosity, the concept of Ford and Ulbrecht seems not to be conveniently chosen, in spite of the fact that the results in Fig. 23 are really satisfying. Opara [42] noted that one should not expect to be able to correlate the mixing times using peff and, consequently, Reeff according to the concept of Metzner and Otto, because their concept was founded on power dissipation In this case, ierr is evaluated from shear rates which arise at the highest velocity differences, whereas for the homogenization process those areas are decisive which are dose to the vessel wall, where the smallest velocity differences exist. 

P= mixing power dissipation, kW VL = liquid volume, m3 pL = density of liquid, kg/m3... 

Mechanical agitation and gas-liquid mass transfer are very important in viscous fermentation media. Most recently, Lim and Yoo (1989) and Lee and Wang (1989) have examined mixing effects in the fermentation of Xanthan gum. Aunins-cf al. (1989) evaluated the effects of paddle geometry on power input and mass transfer in small-scale animal cell culture, 500 mL Corning spinner vessels. The results indicate that power dissipation dependency differs from literature correlations and may compromise scale-up at constant power input from these vessels. 

As mentioned before, the power given to the fluid is actually equal to the power dissipated as friction. In any friction loss relationships with Re, such as the Moody diagram, the friction factor has an inverse linear relationship with Re in the laminar range (Re < 10). The power number is actually a friction factor in mixing. Thus, this inverse relationship for % and Re, is... 

Visualize the filament of fluid on the left of Fignre 6.6 composed of several parcels strung together end to end. The motion induced on this filament as a resnlt of the action of the impeller may or may not be uniform. In the more general case, the motion is not uniform. As a result, some parcels will move faster than others. Because of this difference in velocities, the filament rotates. This rotation produces a torque, which, coupled with the rate of rotation produces power. This power is actually the power dissipated that was addressed before. Out of this power dissipation, the criteria are derived for effective mixing. 

The power dissipation must be such that it causes the correct velocity gradient G. The literature have shown the criteria values for effective mixing in the case of rotational mixers. Values of G need to be determined for pneumatic mixers. As an ad hoc measure, however, the values for rotational mixers (Table 6.2) may be used. 

Example 6.2 By considering the criterion for effective mixing, the volume of a rapid-mix tank used to rapidly mix an alum coagulant in a water treatment plant was found to be 6.28 m with a power dissipation of 3.24 hp. Assume air is being provided at a rate of 1.12 m per m of water treated and that the detention time of the tank is 2.2 min. Calculate the pressure at which air is forced into the diffuser. Assume barometric pressure as 101,300 nW, the depth from the surface to the diffuser as 2 m, and the temperature of water as 25°C. 

The power of mixing is simply power dissipation. In any hydraulic process, power or energy is dissipated through friction. Thus, the power of mixing in any hydraulic mixer can be determined if the fluid friction hf can be calculated. The product of rate of flow Q and specihc weight 7 is weight (force) per unit time. If this product is multiplied by hf the result is power. Thus,... 

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