This is an excellent question.

An answer to this question is given in great detail in

Scale Up Study of Retreat Curve Impeller Stirred Tanks Using LDA Measurements and CFD Simulation

https://www.researchgate.net/publication/222660721_Scale_Up_Study_of_Retreat_Curve_Impeller_Stirred_Tanks_Using_LDA_Measurements_and_CFD_Simulation

See, also:

https://www.researchgate.net/publication/27812662_Design_of_Multiple_Impeller_Stirred_Tanks_for_the_Mixing_of_Highly_Viscous_Fluids_Using_CFD

Another very good paper that includes detailed mathematics is given in

https://www.researchgate.net/publication/275719281_Analysis_of_convective_heat_transfer_improved_impeller_stirred_tanks_by_the_lattice_Boltzmann_method

Article Scale Up Study of Retreat Curve Impeller Stirred Tanks Using...

Article Design of Multiple Impeller Stirred Tanks for the Mixing of ...

Article Analysis of convective heat transfer improved impeller stirr...

 Dear Prof 

Many thanks for your prompt reply and the attached manuscript

Regards

Reza

Please check the following article:

W.J. McManame, Sauter mean and maximum drop diameters of liquid-liquid dispersions in turbulent agitated vessels at low dispersed phase hold-up

Chemical Engineering Science, Volume 34, Issue 3, 1979, Pages 432-434