Practical Viscometry — Why can a Brookfield rotational viscometer not directly report true shear stress for non-Newtonian fluids?

Introduction:
Brookfield viscometers are common quality-control tools for paints, foods, and polymer solutions. They measure torque on a rotating spindle immersed in a sample. Although excellent for apparent viscosity trends, they do not directly yield a unique wall shear stress for non-Newtonian fluids without additional assumptions. This question examines why.

Given Data / Assumptions:

• Spindle rotating at a set speed in a cup; torque is measured.
• Sample may be non-Newtonian and/or time-dependent.
• Goal is to obtain true shear stress–shear rate data.

Concept / Approach:

In Brookfield geometries, the shear rate varies spatially around the spindle, and end effects complicate the flow. For Newtonian fluids, conversion factors can relate torque and speed to viscosity. For non-Newtonian fluids, however, the shear rate distribution depends on the constitutive law itself, creating a circular problem. Thus, without an assumed model (e.g., power-law) or empirical calibration, one cannot assign a single true shear stress at a single true shear rate; the instrument provides an apparent viscosity at an indicated speed/spindle setting.

Step-by-Step Solution:

Verification / Alternative check:

Compare with controlled-stress/controlled-rate rheometers using cone-and-plate geometries that deliver nearly uniform shear rate, enabling direct tau–gamma_dot curves. Brookfield devices trade rigor for robustness and simplicity.

Why Other Options Are Wrong:

B: Torque is measured accurately; it is not the limitation. C: Instruments report torque and derived apparent viscosity, not just rpm. D: Many setups include temperature control accessories. E: Shear stress is well-defined in fluid mechanics.

Common Pitfalls:

Assuming QC apparent viscosity equals fundamental rheological viscosity function; always specify spindle, speed, and protocol when reporting Brookfield data.

Final Answer:

Because the shear rate field around the spindle is non-uniform and not uniquely known, so true shear stress cannot be computed without model assumptions/calibration.