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14.1 Classification of Non-Newtonian Fluids

2 min readLast Updated on July 19, 2024

Fluids come in two main types: Newtonian and non-Newtonian. Newtonian fluids have a simple, linear relationship between shear stress and shear rate. Non-Newtonian fluids are more complex, with varying viscosity based on shear rate or time.

Non-Newtonian fluids can be time-independent, time-dependent, or viscoelastic. They include shear-thinning fluids like blood, shear-thickening fluids like cornstarch in water, and viscoplastic fluids with yield stress like toothpaste. Understanding these differences is key to predicting fluid behavior.

Classification of Fluids

Newtonian vs non-Newtonian fluids

Top images from around the web for Newtonian vs non-Newtonian fluids
Top images from around the web for Newtonian vs non-Newtonian fluids
  • Newtonian fluids exhibit a linear relationship between shear stress and shear rate, where the constant of proportionality is the dynamic viscosity (water, air, and honey)
    • Constitutive equation: τ=μdudy\tau = \mu \frac{du}{dy} relates shear stress τ\tau, dynamic viscosity μ\mu, and shear rate dudy\frac{du}{dy} (velocity gradient)
  • Non-Newtonian fluids have a nonlinear relationship between shear stress and shear rate, with viscosity varying depending on shear rate or time (blood, ketchup, and toothpaste)
    • Constitutive equations for non-Newtonian fluids are more complex and vary based on the specific fluid type

Categories of non-Newtonian fluids

  • Time-independent fluids have shear stress depending only on shear rate, not time, and include shear-thinning (pseudoplastic) and shear-thickening (dilatant) fluids (paint and cornstarch suspension)
  • Time-dependent fluids have shear stress depending on both shear rate and time, such as thixotropic and rheopectic fluids (yogurt and printer ink)
  • Viscoelastic fluids exhibit both viscous and elastic properties, demonstrating time-dependent strain and stress relaxation (polymer solutions and melts, and silly putty)

Non-Newtonian Fluid Characteristics

Characteristics of shear-dependent fluids

  • Shear-thinning (pseudoplastic) fluids experience a decrease in apparent viscosity with increasing shear rate (blood, paint, and ketchup)
    • Constitutive equation: Power-law model τ=K(dudy)n\tau = K(\frac{du}{dy})^n, where n<1n < 1, KK is the consistency index, and nn is the flow behavior index
  • Shear-thickening (dilatant) fluids experience an increase in apparent viscosity with increasing shear rate (cornstarch suspension and certain colloids)
    • Constitutive equation: Power-law model τ=K(dudy)n\tau = K(\frac{du}{dy})^n, where n>1n > 1

Yield stress in viscoplastic fluids

  • Yield stress τy\tau_y is the minimum shear stress required to initiate flow; below τy\tau_y, the fluid behaves like a solid, and above τy\tau_y, the fluid starts to flow (toothpaste, mayonnaise, and drilling mud)
  • Viscoplastic fluids exhibit yield stress behavior and can be described by constitutive equations such as:
    1. Bingham plastic model: τ=τy+μpdudy\tau = \tau_y + \mu_p \frac{du}{dy}, where μp\mu_p is the plastic viscosity
    2. Herschel-Bulkley model: τ=τy+K(dudy)n\tau = \tau_y + K(\frac{du}{dy})^n, combining yield stress and power-law behavior
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© 2025 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.

© 2025 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.
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