The basic statement of the problem is fundamentally incorrect.  Creating a vortex in a cylindrical container is inconsistent with achieving the greatest amount of composition and temperature uniformity.  Vortexing the entire contents of a vessel is about the worst possible way of mixing for uniformity.  A vortex in a cylindrical container effectively will cause solid-body rotation of the fluid, which provides almost no radial or vertical flow, both of which are necessary to accomplish mixing.
 
The answer to the seventh question provides some insight into the answers to the other parts of the question:
 
7.    A formula to calculate the impeller size and speed necessary to create a vortex does not exist.  First, a complicated relationship exists between impeller type, size, rotational speed, liquid level coverage, and vortex depth.  Second, such a complicated relationship has little industrial utility.  Any situation showing only circular vortex motion is a sign of poor mixing.  The only situations for which a vortex can be a benefit is in combination with other mixing characteristics associated with axial flow and baffles to achieve vertical and radial mixing motion.  If the only motion fluid motion follows the rotation of the vortex, then any concentration or temperature differences will merely circulate around the vessel.  Some studies of vortexing have been conducted, but the results have not been reduced to a formula.  Most industrial situations benefiting from a surface vortex are tested at full scale and impeller speed or liquid coverage are adjusted to optimize the vortex depth.  At the maximum vortex depth, the amount of surface area can only be about 50% greater than the flat surface area of stationary liquid.
 
6.    All mixers are 100% efficient.  All of the horsepower applied to the fluid in the vessel will be converted into heat.  Insulated vessels will retain that heat, so an estimate of temperature rise can be derived from the power dissipated.  Note: the power dissipated in the fluid will be lower than the motor power, sometimes by a large amount.
 
5.    A liquid is an incompressible fluid, by definition.  So pressure should have no effect of vortex formation.  The only pressure consideration would involve any vapor coming off the liquid, possibly as a result of heating.
 
4.    If ingredients are added to containers with only rotational flow (strong vortexing) mixing and/or suspension will be slow and ineffective.  The rotational motion which forms a vortex is similar to the conditions in a centrifuge, which is designed to separate, not mix, materials of different densities.
 
3.    Impeller blades designed to disperse gas, typically radial-flow disk impellers and wide-blade hydrofoil impellers, can operate above the boiling point the liquid.  The impellers alone will not provide enough heat for boiling the liquid, because of the high heat of vaporization of liquids.  External heat must be applied to the vessel to effectively raise the temperature.
 
2.    Liquid level measurement can be difficult, especially with a vortex and changing liquid level.  With good liquid level measurement and a programmed controller, mixer speed could be adjusted.  However, no such special purpose equipment is commercially available as a standard package.
 
1.    If forming a vortex is sufficient for these applications, then a 0.8 meter diameter pitched-blade turbine operating at 1.13 rps with a 2,200 Watt motor should be sufficient for the 6,000-liter vessel.  For the 200-liter vessel, a 0.4 meter diameter pitched-blade turbine operating at 1.4 rpm with a 380 Watt motor should be sufficient.
 
The effect of viscosity between 1 and 200 cp will have little if any effect on these applications, since whatever mixing does occur will be turbulent.  The effect of fluid properties on power requirements will be in direct proportion to the fluid density and effectively independent of viscosity for this range of conditions.
 
The mistake often made in moving from the laboratory to production is that mixing in a glass beaker with a magnetic stir bar can be scaled geometrically.  A glass beaker with a stir bar will mix effectively for two primary reason, small size and large surface to volume ratio.  Small size means that any mixing will occur quickly, simply because of small distances and high rotational speeds.  While the contents appear to simply vortex, even small vibrations of the stir bar can cause secondary flow that will not occur with a shaft-mounted impeller.  In a beaker, the surface area at sides causes sufficient friction to create secondary motion and mixing.  As the process is scaled-up to production, the surface area increases with the vessel diameter squared, while the volume increases as the diameter cubed.  In the large vessel, friction at the wall has almost no effect on the swirling contents and thus adds no effective mixing.
 
This question is based on several common misconceptions about how mixing takes place and the effect of a vortex.  The best assumption is that the presence of a vortex is an indication of poor mixing.

The answers by this expert are based on the best available interpretation of the information provided.  The consequences of the application of this information are the responsibility of the user.  If clarification is needed, please submit a further question.


 

EDITOR'S NOTE: The questioner offered additional information, to which our expert offered this additional advice:

    This question and answer are quite different, once the objective of the mixing is clear.  The need for a vortex, based on this description is still irrelevant.  The amount of additional surface area provided by a vortex is inconsequential by comparison with the surface renewal provided by turbulent mixing.
 
1)  The following are recommendations for the mixers:
 
First container - Height 2.25 meters, Diameter 1.5 meters top and bottom, 2 meters center, barrel shaped, 4 baffles 0.15 meters wide, contoured to vessel shape, mounted about 0.01 meters off the wall.
Impeller - pitched-blade turbine, 4 blades, 45 degree angle, pumping downward 0.6 meters in diameter, 0.12 meter wide blades, 0.1 meters off the bottom.  Rotational speed 2.08 rps (125 rpm) with a 3.7 kW motor.
 
Second container - Height 1 meter, Diameter 0.5 meters top and bottom, 0.6 meters center, barrel shaped, 4 baffles 0.04 meters wide, contoured to vessel shape, mounted about 0.005 meters off the wall.
Impeller - pitched-blade turbine, 4 blades, 45 degree angle, pumping downward 0.25 meters in diameter, 0.05 meter wide blades, 0.04 meters off the bottom. Rotational speed 5.8 rps (350 rpm) with a 0.75 kW motor.
 
2)    No known variable speed drive specifically programmed for liquid level feedback control.  A programmed logic controller (PLC) with a liquid level sensor could be programmed to provide a form of feedback control.  Control logic would have be developed to match surface motion and mixing intensity.  Manual adjustment or incremental adjustment to liquid level could be more practical.
 
3)    Baffle recommendation is included in the answer to question 1).  Standard baffles are 4 at 90 degrees around the vessel, approximately 1/12 the tank diameter and spaced a small distance from the vessel wall.