Classifying Complex Behavior — If a liquid is both dilatant (shear-thickening) and rheopectic (time-dependent thickening), how does its viscosity respond to speed and to time under shear?

Introduction:
Some complex fluids can thicken both with higher instantaneous shear rate (dilatancy) and with sustained shear over time (rheopexy). Understanding the combined effect is vital for mixing scale-up, pump selection, and quality control to avoid over-torquing or process upsets.

Given Data / Assumptions:

• Dilatant behavior: viscosity rises with shear rate.
• Rheopectic behavior: viscosity rises with time under constant shear.
• Composition and temperature are stable during observation.

Concept / Approach:

When both behaviors are present, the fluid responds to two independent axes: rate and time. Increasing impeller speed elevates shear rate, raising viscosity immediately (dilatancy). Holding the same speed for longer continues to build structure or alignment that further increases viscosity (rheopexy). The net effect is an upward trend with both variables.

Step-by-Step Solution:

Verification / Alternative check:

Rheometer protocols that include rate sweeps and time holds at fixed rates will show increasing curves in both dimensions for such materials.

Why Other Options Are Wrong:

A, C, D: Each contradicts at least one of the two stated behaviors. E: Ignores rate and time effects central to the classification.

Common Pitfalls:

Mislabeling thixotropy (time-dependent thinning) as rheopecty. Always confirm definitions before interpreting plant data.

Final Answer:

Increases with stirring speed and increases with mixing time.