A fluid shows an increase in apparent viscosity as the stirrer speed (and shear rate) is increased. Which rheological class best describes this behavior?

Introduction:
Correctly classifying a fluid's rheology is essential for impeller selection, scale-up, and predicting power draw. When apparent viscosity increases with shear rate, the fluid does not conform to Newtonian or pseudoplastic expectations. Instead, the behavior is characteristic of shear thickening, known as dilatancy, and it has important consequences for mixing and pumping operations.

Given Data / Assumptions:

• Observed trend: viscosity rises as stirrer speed increases.
• Shear rate is proportional to rotational speed for a given geometry.
• No mention of time-dependent effects at constant shear.

Concept / Approach:
In dilatant fluids, increasing shear rate forces particles or microstructures into configurations that resist flow more strongly, elevating viscosity. Examples include concentrated starch suspensions and some dense slurries. This is opposite to pseudoplastic (shear-thinning) fluids and distinct from thixotropy, which is time dependent at constant shear.

Step-by-Step Solution:

Verification / Alternative check:
Plotting shear stress versus shear rate on log-log scales yields a slope (flow behavior index n) greater than 1 for dilatant fluids in the Ostwald-de Waele model: tau = K * (gamma_dot)^n.

Why Other Options Are Wrong:

• Newtonian: No change of viscosity with shear rate.
• Pseudoplastic: Viscosity would decrease with shear rate.
• Thixotropic: Concerns time effects at constant shear, not rate dependence alone.

Common Pitfalls:
Confusing shear-thickening with simple high-solids viscosity. Even at constant solids, shear-thickening emerges above a critical shear rate, impacting motor sizing and cavitation risk.

Final Answer:
dilatant