Performance in a stirred tank comes far more from the flow pattern than from the impeller speed. Two different impellers running at the same power can give entirely different mixing times.
The impeller type sets the pattern
Radial flow impeller. Throws the flow outwards towards the wall, dividing the tank into an upper and a lower circulation loop. It gives high shear — good for dispersion and gas distribution. But the exchange between the two loops is weak and the mixing time can lengthen.
Axial flow impeller. Produces one large circulation; transport through the tank is strong. Preferred for solids suspension and homogenisation.
The choice depends on what is wanted: shear, or circulation.
Dead zones
What usually sets the mixing time is not the main circulation but the slowest-renewing region: the bottom corners, just below the surface, around the jacket, behind a baffle.
Those regions lengthen the mixing time; with a reaction present the local concentration drifts, and in a heated tank local overheating occurs. The presence of a dead zone is seen not from the mean velocity but from the residence time distribution.
Fitting baffles is the classic remedy: in an unbaffled tank the liquid rotates with the impeller (a vortex forms) and real mixing almost stops — power is consumed and no work is done.
Worse with non-Newtonian fluids
In a shear-thinning fluid the viscosity is low near the impeller and high away from it. The result can be a rotating "cavern" around the impeller with an almost stationary region outside it. See the non-Newtonian note.
Modelling
The impeller region is solved as a rotating zone. Mixing time is measured by injecting a tracer and following the homogenisation of the concentration — a quantity that can both be measured in the field and computed in the model, which makes it convenient for validation.
If the free-surface vortex matters, the problem becomes multiphase.
References
- Ferziger, J. H., Perić, M. & Street, R. L. (2020). Computational Methods for Fluid Dynamics, 4th ed. Springer. DOI: 10.1007/978-3-319-99693-6
- Launder, B. E., Reece, G. J. & Rodi, W. (1975). Progress in the development of a Reynolds-stress turbulence closure. Journal of Fluid Mechanics, 68(3), 537–566.