Rheology – Shape of shear stress vs rate-of-shear curve For a non-Newtonian fluid, the graph of shear stress (tau) versus rate of shear (du/dy) is generally:

Introduction:Rheology studies how materials flow and deform. Newtonian fluids obey a linear relation tau = mu * (du/dy), yielding a straight-line plot through the origin. Non-Newtonian fluids deviate from this linearity, producing a curve on a tau versus shear-rate diagram, reflecting shear-thinning, shear-thickening, or yield-stress behavior.

Given Data / Assumptions:

• Isothermal, steady simple shear.
• Non-Newtonian fluid (e.g., polymer solutions, slurries, paints, blood).
• Plot of shear stress against shear rate.

Concept / Approach:

Non-Newtonian classes include: pseudoplastic (shear-thinning), dilatant (shear-thickening), Bingham plastic (yield stress then linear), and Herschel–Bulkley (yield plus power-law). Their constitutive laws lead to nonlinear tau–(du/dy) relationships, hence a curve rather than a straight line. The exact curvature depends on microstructure alignment, particle interactions, and polymer chain dynamics under shear.

Step-by-Step Solution:

Verification / Alternative check:

Rheometer data for paints and polymer melts show decreasing apparent viscosity with shear rate (concave-down curves), while cornstarch–water mixtures show increasing stress with shear rate more than linearly (concave-up), confirming curvature in both cases.

Why Other Options Are Wrong:

Straight or horizontal/vertical lines represent special limiting cases (Newtonian, perfectly plastic), not generic non-Newtonian behavior.

Common Pitfalls:

Assuming a single viscosity can describe all shear rates; for non-Newtonian fluids, report viscosity together with the shear rate or provide a flow curve.

Final Answer:

Correct