Questions: Non-Newtonian Fluids

Question 1

Paint flows easily under the high shear of a brush stroke but then stays on the wall without dripping once applied. Which type of non-Newtonian behavior does this describe?

• A. Shear-thickening (dilatant) — the paint hardens when the brush applies force
• B. Bingham plastic — the paint has a yield stress that keeps it in place once extruded from the brush
• C. Shear-thinning (pseudoplastic) — viscosity is low under the high shear of brushing and recovers at rest
• D. Viscoelastic — the paint stores elastic energy during brushing and releases it afterward

Answer: (C)

Shear-thinning fluids have an apparent viscosity that decreases as shear rate increases. During brushing, the high shear rate reduces viscosity dramatically, making the paint flow easily. Once on the wall, shear rate drops to near zero, and viscosity recovers — the paint becomes thick enough not to drip. This is the deliberate design goal of architectural paints. Note that the recovery happens instantaneously with the reduction in shear rate; if the recovery were time-dependent (the paint slowly thickened after the shear stopped), that would be thixotropy — a related but distinct phenomenon.

Question 2

A dense cornstarch suspension flows easily when stirred gently but solidifies momentarily when struck or stepped on. Which model best describes this behavior?

• A. Bingham plastic — it has a yield stress that must be overcome before flow begins
• B. Shear-thinning — the gentle stirring exceeds the yield stress while the strike does not
• C. Shear-thickening (dilatant) — apparent viscosity increases with increasing shear rate
• D. Viscoelastic — stored elastic energy causes the solid-like response to impact

Answer: (C)

A cornstarch suspension is the classic shear-thickening (dilatant) fluid: apparent viscosity increases as shear rate increases (power-law exponent n > 1). Gentle stirring applies low shear, giving low viscosity and easy flow. A sudden strike applies very high shear rate, dramatically increasing apparent viscosity and producing solid-like resistance. This is opposite to shear-thinning behavior. Note the contrast with Bingham plastics: cornstarch flows at low shear rates but resists at high shear rates, while a Bingham plastic is solid below a yield stress and flows above it.

Question 3

Shear-thinning and thixotropy are two names for the same phenomenon: both describe fluids whose viscosity decreases as they are sheared.

• T. True
• F. False

Answer: False

These are distinct phenomena. Shear-thinning (pseudoplastic behavior) is an instantaneous response: the apparent viscosity depends only on the current shear rate, with no memory of past shear history. Apply a shear rate, the viscosity is determined immediately. Thixotropy is time-dependent: the viscosity decreases gradually at a constant shear rate as the fluid's internal structure breaks down, and then gradually recovers when shear is removed. Many real fluids (like ketchup) are both shear-thinning and thixotropic, but the two effects operate on different timescales and arise from different mechanisms.

Question 4

A Bingham plastic flows at most shear rates — below the yield stress it has very high viscosity, and above it the viscosity drops.

• T. True
• F. False

Answer: False

This description incorrectly treats the yield stress as a viscosity threshold rather than a flow threshold. A true Bingham plastic does not flow at all when shear stress is below the yield stress τ_y — the material deforms elastically (like a solid) but the strain rate is zero. Only when τ > τ_y does the material flow, with a linear stress-strain rate relationship τ = τ_y + μ_p·γ̇. Toothpaste sitting on a brush is a good example: it does not slowly drip or creep — it sits immobile because the gravitational stress is below τ_y. The Bingham model is a solid-then-fluid transition, not a high-viscosity-to-low-viscosity transition.

Question 5

Explain why assuming Newtonian behavior for blood would lead to incorrect predictions in cardiovascular engineering applications.

Model answer: Blood is a shear-thinning fluid: its apparent viscosity decreases as shear rate increases. In large arteries with high flow rates and high shear, blood behaves nearly Newtonian. But in small capillaries with low shear rates, blood viscosity is significantly higher than the Newtonian value — red blood cells aggregate into rouleaux (stacks) at low shear, increasing resistance. Assuming constant Newtonian viscosity would underestimate resistance in small vessels and overestimate it in large ones, giving incorrect pressure drop predictions, wrong flow distributions, and misleading predictions about conditions like atherosclerosis where local shear rates are altered. Medical device design (artificial hearts, stents) requires rheologically accurate blood models.

Blood's shear-thinning behavior arises from the deformability and aggregation of red blood cells. At high shear, cells deform and align, reducing viscosity. At low shear, they aggregate into rouleaux, increasing viscosity. This variation is physiologically significant: the cardiovascular system operates across a wide range of shear rates from the aorta to capillaries. The power-law or Carreau model captures this behavior far better than the Newtonian model. Beyond blood, many biological fluids (synovial fluid in joints, mucus in airways) are non-Newtonian, making rheology essential to biomedical engineering.