Combined non-Newtonian behavior — A fluid whose viscosity increases with increasing stirrer speed (shear rate) and also increases with mixing time under constant shear is best described as what?

Introduction:
Some complex fluids display both rate-dependent and time-dependent viscosity changes. Correct classification of combined behaviors is important in diagnosing mixing problems (e.g., overloading agitators or poor dispersion) and choosing appropriate processing conditions.

Given Data / Assumptions:

• Apparent viscosity increases as stirrer speed rises (instantaneous rate effect).
• At roughly constant shear, apparent viscosity also increases with elapsed mixing time (time effect).
• Temperature and composition are stable during the observation window.

Concept / Approach:
Shear-rate thickening is termed dilatancy: viscosity rises with increasing shear rate. Time-dependent thickening under constant shear is called rheopexy. A material exhibiting both simultaneously is therefore dilatant and rheopectic. Pseudoplastic and thixotropic describe rate-thinning and time-thinning, respectively, which contradict the stated trends. Newtonian fluids show neither rate nor time dependence beyond trivial effects.

Step-by-Step Solution:
From the rate effect alone (viscosity ↑ with speed), identify dilatant behavior.From the time effect alone (viscosity ↑ with time at constant shear), identify rheopectic behavior.Combine both to classify the fluid as dilatant, rheopectic.

Verification / Alternative check:
Plot apparent viscosity versus shear rate to confirm thickening; perform a three-interval rheological test at fixed shear to confirm time-dependent increase. Recovery tests after rest can reveal slow structural buildup consistent with rheopexy.

Why Other Options Are Wrong:

• (a) Newtonian: viscosity independent of rate and time.
• (b) Pseudoplastic + thixotropic: both thinning trends, opposite to observation.
• (d) Contradictory pair (dilatant + pseudoplastic) mixes opposing rate behaviors.
• (e) Yield-stress models address onset of flow, not the described rate/time thickening.

Common Pitfalls:
Confusing thixotropy with pseudoplasticity; attributing thermal rise to rheopexy; overlooking particle–particle structure buildup that can cause time-thickening in concentrated suspensions.

Final Answer:
Dilatant, rheopectic fluid