It would be easier if you would have a transparent liquid.
Also, you, I hope, understand that what you will measure in small
container will not transfer simply to a larger container.
There are some 'scaling laws' which define similar conditions, but
they involve more then just size of the vessel, but also viscosity,
speed of rotations and size of the mixing blade. Problem is more complex
then $10 question would indicate, but I can give you some references which
I hope will be useful - at least useful for asessing the scope of the problem.
There are shear-rate meters - and whole science of Rhaology dealing
with these issues. Even though you did not indicated the size of your
budget, I am guessing that you are intending to give it some time and energy.
So, lets starts with an overview:
People do study complex flows - it is a demeanding discipline,
normally needing a well eqipped laboratory and expertise.
Shear rate is not same at different parts vessel, it changes
with position, and in your case with time (as viscosity is changing).
Typical velocity field looks like this:
Even if liquid is not transparent, you can imbed markers and track
those near surface optically, other by complex telemetry (Xrays,
magnetic sensors ..)
Markers could be small rods (rather then balls) - and then their rate
of rotation will be proportional to shear rate at that time and place,
Here are references to the scaling laws and Reynolds number
To measure rheology of a material, it needs to deform over a period of
time, ... Scaling Laws. Strain rates in earth versus experiment are
orders of ...
Basicaly Same number means 'similar flow' (turbulent or laminar)
I suspect you want something more simple:
I would try to estimate the shear rate from the force needed to mix the paste
at different rotation rates.
The viscosity of the paste is non-newtonian, and so the torque needed
to rotate the blades will depend on the shear rate.
You will have to measure fast (electronic recording) to differentiate
effect of speed and of hardening.
Here you will find more references: