Let's take your problem statement, assumptions and questions a step at a time:

Dimensions: Impeller diameter [D] 2" (50.8 mm) diameter

Vessel diameters [T] 130mm D/T = 0.39 140mm D/T = 0.36 Impeller to tank diameter ratios [D/T] look reasonable for high-shear dispersion with sawtooth impeller

Aspect ratios 1.3 to 1.4 (liquid height to vessel diameter ratios (?)

Aspect ratios between 0.8 and 1.0 would give better mixing in most applications.

However, high impeller speed in a small vessel is likely to form a deep vortex and draw air into the impeller.

Gas dispersion through the impeller destroys flow, reduces power, and hurts liquid-liquid dispersion. Operating assumptions:

Impeller power: P_imp = Np * rho * N^3 * D^5

Correct description for impeller power, Np is impeller power number which will depend on sawtooth design.

Impeller pumping: Q = Nq * N * D^3

Description for impeller pumping capacity, if Nq (pumping number) is known.

Pumping capacity has limited value, since it does not tell about flow direction, impact on fluid volume, or effect on mixing and shear.

Head: H related to N^2 * D^2

Head is an attempt to define pressure force on fluid in impeller region. Tells almost nothing about effective shear.

Other important assumptions:

Heat = P * t All power input by the impeller adds heat to the fluid.

So heat input (temperature increase) equals power times time.

Tip speed = pi * N * D

Ultimate drop diameter in typical liquid-liquid dispersions is roughly inversely proportional to impeller tip speed.

Ultimate drop diameter may take different amounts of time to achieve in different systems.

Times should be very short in very small vessels. Shorter dispersion time will reduce heat input and may not change drop size.