Your questions involve several closely related effects for high-shear dispersion.  Most of the shear created by a rotor-stator impeller is hydraulic shear, not mechanical shear.  Several mechanisms cause high shear in a rotor-stator, with the primary one being the rapid off-center swirling as the gap opens between the rotor and stator opens and again as the gap closes.  Rapid changes in velocity and direction create hydraulic stretching and shear.  The velocity gradients create the forces that cause dispersion.  Additionally, the velocity gradient between the rotor and stator will create shear.  Lesser effects of shear may be caused by impact with the either the rotor or stator.
 
A 3-liter vessel is small, so a laboratory disperser is about the only rotor-stator device available.  Small rotor-stators may have fewer design features than larger rotor-stators.  Baffles may not be needed in a small vessel, since the only rotational flow is at the suction side of the rotor.  Flow out of the rotor-stator mixer is radial, with no rotational velocity.  The liquid height should be less than the vessel diameter, just for good circulation.  The clearance from the bottom should be about the diameter of the rotor, so inward flow sweeps the bottom without restriction.  Vessel geometry usually is not critical, because all of the dispersion occurs in the rotor-stator, the remainder of the vessel just needs to be kept in motion so all of the fluid goes through the rotor-stator frequently.

The most critical factor is tip speed, although the particle size may be different for different rotor-stator designs.  Smaller holes and narrower gaps should give smaller particle sizes.  However, only by testing a particular design can the actual particle size be predicted.  Factors, such as viscosity, surface tension, and viscosity difference all influence liquid-liquid dispersion.  Solid particle size reduction is rarely accomplished with a rotor-stator, although particle agglomerates may be broken, having the effect of particle size reduction.

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The expression P=Po*rho*D^5*RPM^3 may apply to some range of operating conditions for a rotor-stator mixer.  However, the power number (Po) in the expression will depend on the mixer geometry, just as it does to other types of impellers.  I don't have power numbers for rotor-stator mixers, because of the number of geometric variables involved.  I can even imagine that over some ranges, the power number may be a variable, either because of viscosity effects or rotational flow.  I don't think that power calculation is going to be of much help to your for rotor-stator mixers.  The equipment suppliers will need to provide that design information for their specific equipment.

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.