Newtonian Fluids — Which statement best describes viscosity behavior during mixing at constant temperature?
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AViscosity remains essentially constant with time and power input (independent of shear history).
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BViscosity increases as power input rises, regardless of time (rate-dependent thickening).
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CViscosity decreases as power input rises, regardless of time (rate-dependent thinning).
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DViscosity drastically increases with power input due to structure build-up.
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EViscosity oscillates periodically with impeller blade passage.
Answer
Correct Answer: Viscosity remains essentially constant with time and power input (independent of shear history).
Explanation
Introduction:A Newtonian fluid has a constant viscosity at a given temperature and pressure, independent of shear rate and mixing time. This is a foundational concept used in pump sizing, pipe flow calculations, and reactor design for simple liquids like water and many light oils.
Given Data / Assumptions:
- Temperature and composition are constant.
- Shear rates fall within the continuum regime where Newtonian behavior applies.
- No time-dependent structural changes occur in the liquid.
Concept / Approach:
Newtonian behavior is defined by a linear relationship between shear stress tau and shear rate gamma_dot: tau = mu * gamma_dot, with constant mu. As such, varying the impeller speed (changing shear rate) changes shear stress proportionally, but does not change mu. Time under shear does not alter mu either.
Step-by-Step Solution:
Identify the defining property: constant viscosity independent of shear rate and time.Relate to mixing: increasing power changes shear rate, but not mu for Newtonian fluids.Exclude structural build-up or breakdown because Newtonian fluids lack microstructure that evolves with shear.Therefore select the option stating constancy with time and power input.Verification / Alternative check:
Viscometry with concentric cylinders shows straight-line tau versus gamma_dot passing through the origin for Newtonian liquids; slope equals mu and is independent of the test duration at constant temperature.
Why Other Options Are Wrong:
B, C, D: Describe non-Newtonian behaviors (shear-thickening, shear-thinning, time dependence). E: Blade-passage pressure fluctuations do not change the intrinsic viscosity.
Common Pitfalls:
Confusing operational power requirements (which do change with speed) with the material property viscosity (which does not for Newtonian fluids).
Final Answer:
Viscosity remains essentially constant with time and power input (independent of shear history).