A culture broth is described as both pseudoplastic and thixotropic. What does this combined rheology imply about how apparent viscosity changes with increasing stirrer speed and with mixing time at roughly constant shear?

Introduction:
Bioprocess broths often deviate from ideal Newtonian behavior. Two common non-Newtonian features are pseudoplasticity (shear-thinning) and thixotropy (time-dependent structural breakdown under shear). When a culture fluid is both pseudoplastic and thixotropic, process engineers must interpret how viscosity responds to both the magnitude of shear and its duration in order to select agitation and aeration settings that protect cells while maintaining mass transfer.

Given Data / Assumptions:

• Pseudoplastic: apparent viscosity decreases as shear rate increases.
• Thixotropic: apparent viscosity decreases with time under sustained shear and recovers when shear is removed.
• Mixing conditions are typical for bioreactors (moderate impeller tip speeds and gas rates).

Concept / Approach:
Shear-thinning arises because polymeric or flocculated microstructures align and offer less resistance at higher shear rates. Thixotropy adds a temporal component: microstructures progressively break down during mixing, lowering viscosity further at a fixed shear rate. Together, these behaviors decrease viscosity both when the stirrer speed is raised and when mixing is continued over time at a given speed.

Step-by-Step Solution:

Verification / Alternative check:
Rheometer tests with up- and down-shear ramps and time sweeps show hysteresis loops and time-dependent decay of viscosity, confirming both pseudoplasticity and thixotropy. Process torque measurements during start-up similarly decline with time at fixed rpm.

Why Other Options Are Wrong:

• Increases with speed: Opposite of pseudoplastic behavior.
• Increases with time: Opposite of thixotropic breakdown (that would suggest rheopecty).
• Decreases with speed but increases with time: Conflicts with thixotropy.

Common Pitfalls:
Confusing thixotropy with simple shear-thinning only. Ignoring time dependence can lead to overestimating required power input after the broth relaxes to a lower viscosity during a run.

Final Answer:
decreases with stirring speed and decreases with mixing time