Identify the correct behavior of a dilatant (shear-thickening) fluid when subjected to increasing impeller speed or shear rate in a mixing operation.

Introduction:
Dilatant or shear-thickening fluids display an increase in apparent viscosity with rising shear rate. Recognizing this behavior is crucial to avoid overloading mixers and pumps and to prevent unexpected heat generation or poor mixing performance in formulations containing suspended solids or concentrated starch systems.

Given Data / Assumptions:

• Dilatancy refers to viscosity increase with shear rate.
• Impeller speed is a practical proxy for shear rate in stirred tanks.
• Other non-Newtonian behaviors include shear thinning and time-dependent effects.

Concept / Approach:
As shear rate increases, particle networks or microstructures in dilatant fluids resist flow more strongly, raising viscosity. This is the opposite of pseudoplastic fluids, which show decreased viscosity with shear rate due to alignment or structure breakdown.

Step-by-Step Solution:
Step 1: Recall that dilatant = shear-thickening.Step 2: Translate higher impeller speed to higher shear rate at the fluid scale.Step 3: Conclude that apparent viscosity rises with speed for a dilatant fluid.Step 4: Select the option that states an increase in viscosity with increasing speed.

Verification / Alternative check:
Rheograms of shear-thickening suspensions show upward-curving stress–shear rate plots. In mixing trials, torque demand often increases disproportionately at higher speeds.

Why Other Options Are Wrong:

• constant viscosity: Newtonian behavior, not dilatant.
• changes during mixing but returns: Thixotropy or rheopexy, time-dependent effects.
• decreases with speed: Pseudoplastic (shear-thinning).
• no dependence on shear rate: Contradicts shear-thickening definition.

Common Pitfalls:
Operating at high speeds with shear-thickening slurries can cause motor overloads; engineers should perform torque checks and consider lower speeds or different impellers.

Final Answer:
increases with increasing stirrer speed