Practical Viscometry — Why can a Brookfield rotational viscometer not directly report true shear stress for non-Newtonian fluids?
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ABecause 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.
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BBecause the instrument cannot measure torque.
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CBecause such viscometers only display rpm and cannot be used on liquids.
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DBecause temperature control is impossible in Brookfield tests.
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EBecause shear stress is not defined for liquids.
Answer
Correct 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.
Explanation
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:
Recognize what the instrument measures directly: torque and rpm.Note that non-uniform shear rate exists across the gap and near spindle ends.Understand that mapping torque–rpm to tau–gamma_dot requires a constitutive assumption.Conclude that true shear stress cannot be directly determined for non-Newtonian fluids without a model or calibration.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.