Hi, I have been struggling with the conversion of raw data T-N plot into the plot of shear stress and shear rate, based on which I can get values of yield stress and viscosity. I understand that modern rheometers could automatically convert raw data, but I am interested in the fundamental methods behind it.
From online sources, I have found three ways to do so
1. Conversion scale factor
2. Reiner–Riwlin equation
3. Conversion equations for (T to shear stress) and (N to shear rate)
My questions are
1. Which way is the common one and what are their limitations. Under what circumstances do we use each of them?
2. Are these methods all dependent on the geometries of a rheometer?
I will appreciate getting some systematic explanations and/or textbook recommendations.
Great thanks in advance.
For almost any kind of rheometer, the equations to do this are either easily derived from the equations of motion or can be found in any basic textbook on rheology
To add a little to Leon Levine's bare bones explanation: You need two factors: the shear stress factor converts torque to stress and the shear rate factor converts rotation rate to shear rate. These depend on the measurement geometry. They are only strictly applicable for Newtonian fluids or linearly elastic solids.
To add a little more: If you use a Taylor-Couette geometry (concentric cylinders), the torque to shear stress conversion is independent of the fluid and therefore gives you a reliable value of the shear stress. Its essentially torque divided by the radius of the inner cylinder to give you the force on the surface of said cylinder and then divided by the submerged surface area to give you the stress.
The shear rate at the inner cylinder, however, can indeed only be determined by assuming a given rheological model (Newtonian fluid is one of those) and is actually quite tricky (e.g., there could be shear bands). So the viscosity is most likely not easy to determine in your case.
Given that you can get stress values, I think a reasonable approach to determine the yield stress would be to plot stress as a function of rotation rate and extrapolate that to zero rotation rate. Even though, the mapping between rotation rate and shear rate is unknown, it should still be monotonic and zero rotation rate certainly corresponds to zero shear rate.
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