Shear-thinning definition: In a pseudoplastic fluid relevant to fermentation broths, how does apparent viscosity change as stirrer speed (shear rate) increases?

Introduction:
Many biological fluids, including cell suspensions and polymer-rich media, are pseudoplastic. Correctly identifying shear-thinning behavior informs agitator sizing, power draw, and oxygen transfer modeling.

Given Data / Assumptions:

• Pseudoplasticity refers to rate dependence, not necessarily time dependence.
• Shear rate correlates with stirrer speed in a given geometry.
• No yield stress is described.

Concept / Approach:
Pseudoplastic (shear-thinning) fluids show a decrease in apparent viscosity as shear rate increases. Microstructure (entanglements, flocs) aligns or breaks down under shear, providing less resistance to flow. This is distinct from thixotropy (time-dependent) or dilatancy (shear-thickening).

Step-by-Step Solution:
Raise stirrer speed ⇒ higher shear rate in the vessel.Microstructure aligns/breaks ⇒ lower resistance to deformation.Observed effect ⇒ apparent viscosity decreases.Classify ⇒ pseudoplastic (shear-thinning).

Verification / Alternative check:
Flow curves (log viscosity vs. log shear rate) show a negative slope for pseudoplastic fluids; power-law fits exhibit flow index n < 1.

Why Other Options Are Wrong:
Constant viscosity: Newtonian behavior, not pseudoplastic.

Purely time-dependent recovery: thixotropy; rate dependence is not implied.

Increases with speed: dilatant (shear-thickening), opposite of pseudoplastic.

Common Pitfalls:

• Conflating rate-dependent thinning with time-dependent thinning (thixotropy).
• Assuming one measurement at a single speed reveals full rheology; multiple shear rates are needed.

Final Answer:
Decreases with increasing stirrer speed (shear-thinning)