Which statement best defines a Newtonian fluid in terms of viscosity behavior during mixing or under varying shear rates?

Introduction:
Classifying fluids by how their viscosity responds to shear is essential for designing agitation and transfer operations. Newtonian fluids exhibit the simplest behavior, which greatly simplifies engineering correlations and scale-up.

Given Data / Assumptions:

• Viscosity is defined as the ratio of shear stress to shear rate.
• Mechanical agitation varies shear rate but should not alter viscosity for Newtonian fluids.
• Time dependence is characteristic of thixotropy or rheopexy, not Newtonian behavior.

Concept / Approach:
Newtonian fluids have constant viscosity μ such that τ = μ * γ_dot. Thus, regardless of impeller speed (which changes γ_dot), μ remains constant, barring temperature changes. Non-Newtonian behaviors involve shear-thinning, shear-thickening, or time-dependent structural changes in the fluid.

Step-by-Step Solution:
Step 1: Identify that Newtonian definition requires constant μ with respect to γ_dot.Step 2: Compare options; only the option stating constant viscosity independent of mixing conditions matches the definition.Step 3: Recognize that options implying changes with speed or time correspond to non-Newtonian categories.Step 4: Select the correct constant-viscosity statement.

Verification / Alternative check:
Standard references list water, dilute salt solutions, and light oils as Newtonian; their viscosity is a function of temperature and pressure, not shear rate or mixing time within typical ranges.

Why Other Options Are Wrong:

• changes during mixing but returns after: Thixotropic behavior.
• increases with speed: Dilatant (shear-thickening).
• decreases with speed: Pseudoplastic (shear-thinning).
• depends only on time: Time dependence is non-Newtonian.

Common Pitfalls:
Confusing thermal effects with shear dependence; a rise in temperature can lower viscosity, but that is not a shear-rate effect.

Final Answer:
is constant regardless of the stirrer speed or mixing time