Constitutive Behavior — In which class of fluids is the shear stress–shear rate relation non-linear over practical ranges?

Introduction:
Designing mixers, pumps, and pipelines requires knowing how shear stress tau depends on shear rate gamma_dot. Newtonian fluids have tau = mu * gamma_dot (a straight line through the origin), whereas non-Newtonian fluids deviate from linearity, often dramatically, affecting power draw and pressure drop.

Given Data / Assumptions:

• Continuum regime with isothermal conditions.
• Definition: Newtonian if viscosity is constant and tau proportional to gamma_dot.
• Non-Newtonian if viscosity depends on rate and/or time.

Concept / Approach:

Non-Newtonian classes include shear-thinning, shear-thickening, Bingham plastic, Herschel–Bulkley, thixotropic, and rheopectic behaviors. Each yields a non-linear tau–gamma_dot curve or incorporates a yield stress, invalidating a single constant viscosity description across operating ranges.

Step-by-Step Solution:

Verification / Alternative check:

Rheometer measurements for paints, ketchup, polymer melts, and cell broths show curved tau–gamma_dot plots, unlike water or mineral oils at moderate rates.

Why Other Options Are Wrong:

A: Newtonian is linear by definition. C and D: Incorrect generalizations. E: Gas behavior is not directly a constitutive fluid class and under most laminar conditions ideal gases behave Newtonian.

Common Pitfalls:

Using a single viscosity number for complex fluids; always report the shear rate (and time history if relevant).

Final Answer:

Non-Newtonian fluids