Three forms of mixing can be considered: macromixing, micromixing and mesomixing. The latter can have a large impact on fast chemical reactions and precipitations taking place at the reactant or anti-solvent feed point. An improperly designed feed can result in variable and high local levels of supersaturation, producing high nucleation rates and a small CSD.
Macromixing refers to the overall mixing performance and involves bulk fluid movement and blending. It is dictated by the type of agitator, agitator speed and vessel geometry. Macromixing is generally measured as the overall circulation, residence-time distribution (RTD), turnovers and degree of solid suspension. For turbulent flow, the macromixing time increases with vessel diameter and decreases with average power per unit volume, (P/V)avg, with P/V defined as the energy dissipation rate.
For a given agitator design and vessel geometry, (P/V)avg is a key measure of the degree of macromixing, which determines the relative flow rates and blending efficiency. Macromixing reduces local differences in temperature, concentration, supersaturation, suspended solids density and other parameters.
Micromixing, or turbulent mixing at the molecular level, can have a significant impact on precipitations resulting from fast chemical reactions or anti-solvent addition. It can dictate the level of supersaturation, influencing the nucleation and growth rate of particles.
The local P/V will affect the degree of micromixing, and values can vary by more than two orders of magnitude at different locations within a crystallizer. With (P/V)avg defined as the overall power input from the agitator divided by the total slurry volume, the local P/V equals about 70 (P/V)avg at the mixer impeller swept volume, 3.5 (P/V)avg in the discharge stream and 20 (P/V)avg in the overall impeller region but only one-fifth of that value at the liquid surface, baffles and corners. As a result of this hundred-fold difference, the relative importance of micromixing and reaction rates for precipitation can vary greatly within a vessel. One must take these variations into account when specifying feed-point location, vessel design and the type of agitator.
Generally, to be effective in crystallization, an agitator must be capable of the following:
Full crystal off-bottom suspension to maintain growth.
Sufficient mixing and solids availability to eliminate local excessive levels of supersaturation at feed points, cooling surfaces and evaporation surfaces
Adequate heat transfer, allowing for operation within the metastable zone.
Product removal via isokinetic discharge.
Acceptable levels of secondary nucleation and breakage, yielding desired CSD and shape.
Table 2 presents turbulent-flow parameters for five typical agitators. (Q/P)R is the ratio of flow for that particular agitator design for the same power input and diameter vs. the PBT as the standard. NQ, defined as the agitator flow number, varies less among mixer types than does the agitator power number, NP.
* 2,000 gallon glass lined vessel, diameter @ 44" and NRe>2.4 x 106
**2,000 gallon glass lined vessel, diameter @ 33" and NRe>2.4 x 106
These values are for turbulent flow and specific geometric configurations. They are independent of scale, assuming geometric similarity. For a given power input, the hydrofoil produces 51 percent more flow than the PBT, while the radial flow Rushton turbine produces only 18 percent of the flow generated by the standard PBT. Note that, for the same flow, the hydrofoil requires about 34 percent less power than the PBT while the radial, high-shear 90 Degrees pitch Rushton requires approximately 450 percent more power than the PBT. The increased power and shear can have a negative impact on secondary nucleation and crystal breakage.
Using the agitator parameters in Table 2, one can calculate the primary impeller pumping capacity and power draw as follows:
Q=NQND3x7.48 (in gpm) (5)
Where N is rotational speed in rpm , D is impeller diameter in feet, and Q is the flow just off the blade.
Where D is impeller diameter in inches and sg is specific gravity.
The Rushton turbine, due to its high power number, is a high-torque impeller requiring a relatively low speed for a given power and size. Torque is defined as power divided by speed. Low Np agitators such as a hydrofoil, when operated at the same power and diameter as the Rushton, run at higher speed. Thus, they require less torque and are cheaper to install since they have smaller shaft diameters, seals and gear boxes. Due to their favorable flow-vs.-power characteristics, hydrofoil impellers are often used for solids suspension.
Note that the values of NP and NQ for glass-lined agitators are measured at different configurations than those employed for metal agitators. For example, the baffling and the impeller-to-tank diameter ratio is different for the GL vessel. Thus, a direct comparison between the performances of these agitators would not be entirely accurate.
Wayne Genck, principal of Genck International, is an industrial consultant in the field of crystallization and precipitation. He can be reached at (708) 748-7200.