Impeller region

Obviously shear rate in different parts of a mixing tank are different, and therefore there are several definitions of shear rate (/) for average shear rate in the impeller region, oc V, the proportionaUty constant varies between 8 and 14 for all impeller types (2) maximum shear rate, oc tip speed (%NU), occurs near the blade tip (3) average shear rate in the entire tank is an order of magnitude less than case / and (4) minimum shear rate is about 25% of case 3. 

The time required to pass through the high shear zone will be proportional to the volume of the vessel divided by the flow from the turbine. This will be porportional to 1/ND. With a turbine in turbulent flow, turnover is relatively rapid and all the fluid will pass through the impeller region in a relatively short period of time. The flow regime in an anchor or helically agitated vessel can be inferred from the flow studies by Smith and Peters (], 13j. These indicated... 

Breakup will occur due to high turbulence and high shear rate. This will occur in the impeller region and close to the walls. In a stirred tank, almost all breakup of the bubbles occurs in the impeller region. According to Eq. (15.3), the energy required to break up a 5-mm bubble is on the order of 1W m 3, while 35 W m-3 is required to break up a 1-mm air bubble in water. A high rate of bubble breakup... 

Hydrodynamic effects on suspended particles in an STR may be broadly categorized as time-averaged, time-dependent and collision-related. Time-averaged shear rates are most commonly considered. Maximum shear rates, and accordingly maximum stresses, are assumed to occur in the impeller region. Time-dependent effects, on the other hand, are attributable to turbulent velocity fluctuations. The relevant turbulent Reynolds stresses are frequently evaluated in terms of the characteristic size and velocity of the turbulent eddies and are generally found to predominate over viscous effects. 

For the same bioreactor mentioned above (operating at an impeller tip speed of 1.4 ms ), Dunlop et al. [57] predicted maximum Reynolds stresses in the impeller region of 32.4 Nm. However, if the energy is assumed to be uniformly dissipated throughout the vessel contents, then Eq. (5) will yield lower values. As calculated, the Reynolds stresses involve a length scale and the stress experienced by a particular entity will depend on its size. 

Heuristically, the recirculation time is the average time required for a fluid element to return to the impeller region after leaving it. 

Liquid-liquid mixing has been widely used in chemical industries. The state of dispersion is determined by the balance of the break-up and coalescence of droplets. In the case of liquid-liquid mixing, the breakup of the droplet is accelerated in the impeller region. Although the droplet size distribution in the operation has been expressed by various PSD functions, the PSD function that is utilized the most is the normal PSD function. However, there is no physical background to apply the normal PSD function to the droplet size distribution. Additionally, when the droplet size distribution is expressed by various PSD functions, it becomes difficult to discuss the relationship between the parameters in PSD and operation conditions. This is one of the obstacles for developing particle technology. 

Fio. 8. Theoretical size distribution and experimental histograms impeller region (solid line), circulation region (dashed line), N = 310 rpm, d) = 0.10, Osj = 0.255 mm (experiment) versus 0.250 mm (calculation), on, = 0.980 min- (experiment) versus 1.026 min (calculation) [from Coulaloglou and Tavlarides (C12)]. 

Using the assumption of cyclically repetitive flow within the impeller region, the first term on the right-hand side of Eq. (10.3) can be approximated as... 

Such a value for the average density is only approximately correct for power calculations (although it is appropriate in most cases), as the solids fraction in the impeller region may differ from 0 depending on N, i.e., on the solids suspension state. 

Placek J., Tavlarides L.L., Turbulent Flow in Stirred Tanks. Part I Turbulent Flow in the Turbine Impeller Region, AIChE J. 31 (1985) 7, p. 1113-1120... 

To validate the predicted results only one time dependent simulation has to be carried out to achieve time and impeller region average values for comparison with experimental data and the steady-state results obtained by the IBC, lO and snapshot methods. 

A plot of the predicted turbulent kinetic energy at the disc axial level is shown in Fig 7.27. The turbulent kinetic energy values are questionable because the energy level is quite low in the impeller region where the velocity gradients are the largest. 

Zhou and Kresta [2] have determined the energy distribution for different impellers. They reported the dissipation rates in the impeller region to be 38.1% for the A-310, 43.4% for the Rushton turbine, and 70.5% for the 45° PBT of the total energy input to the impeller. 

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