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14.3 Flow Behavior of Non-Newtonian Fluids

4 min readLast Updated on July 19, 2024

Non-Newtonian fluids don't follow the rules of regular fluids. They can get thicker or thinner when you push on them, or need a certain force to start moving. This makes them act weird in pipes and channels.

To understand these fluids, we use special equations that describe how they flow. These help us figure out things like how much pressure we need to move them through pipes. Dealing with non-Newtonian fluids can be tricky, but they're used in lots of cool stuff like making plastic toys and food products.

Flow Behavior of Non-Newtonian Fluids

Flow of non-Newtonian fluids

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  • Non-Newtonian fluids exhibit complex flow behavior that deviates from Newtonian fluids
    • Shear-thinning (pseudoplastic) fluids experience decreasing viscosity with increasing shear rate (ketchup, paint)
    • Shear-thickening (dilatant) fluids experience increasing viscosity with increasing shear rate (cornstarch suspension, some colloids)
    • Bingham plastic fluids require a yield stress to initiate flow and then behave as a Newtonian fluid (toothpaste, mayonnaise)
  • Flow in pipes differs from Newtonian fluids
    • Velocity profile deviates from the parabolic profile observed in Newtonian fluids
    • Shear-thinning fluids have flatter velocity profiles due to reduced viscosity near the pipe wall
    • Shear-thickening fluids have more pronounced velocity gradients near the pipe wall due to increased viscosity
  • Flow in channels exhibits similar behavior to pipe flow but with a rectangular cross-section
    • Velocity profile and flow characteristics depend on the specific rheology of the non-Newtonian fluid

Calculations for non-Newtonian fluids

  • Rheological models describe the relationship between shear stress and shear rate for non-Newtonian fluids
    • Power-law (Ostwald-de Waele) model: τ=Kγ˙n\tau = K \dot{\gamma}^n
      1. τ\tau represents shear stress
      2. KK represents consistency index
      3. γ˙\dot{\gamma} represents shear rate
      4. nn represents flow behavior index, where n<1n < 1 for shear-thinning, n>1n > 1 for shear-thickening, and n=1n = 1 for Newtonian fluids
    • Bingham plastic model: τ=τ0+μpγ˙\tau = \tau_0 + \mu_p \dot{\gamma}
      1. τ0\tau_0 represents yield stress
      2. μp\mu_p represents plastic viscosity
  • Pressure drop calculations for non-Newtonian fluids
    • Modified Hagen-Poiseuille equation for power-law fluids: ΔP=2KLR1+1n(3n+14n)n(8VD)n\Delta P = \frac{2KL}{R^{1+\frac{1}{n}}}\left(\frac{3n+1}{4n}\right)^n\left(\frac{8V}{D}\right)^n
      • ΔP\Delta P represents pressure drop
      • LL represents pipe length
      • RR represents pipe radius
      • VV represents average velocity
      • DD represents pipe diameter
    • Buckingham-Reiner equation for Bingham plastic fluids: ΔPL=4τ03R(143λ+13λ4)+8μpVR2(1λ2)\frac{\Delta P}{L} = \frac{4\tau_0}{3R}\left(1-\frac{4}{3}\lambda+\frac{1}{3}\lambda^4\right) + \frac{8\mu_pV}{R^2}\left(1-\frac{\lambda}{2}\right)
      • λ=Rτ02μpV\lambda = \frac{R\tau_0}{2\mu_pV} represents the dimensionless yield stress parameter
  • Velocity profile calculations for non-Newtonian fluids
    • Power-law fluids: v(r)=(nn+1)(ΔPR2KL)1n[Rn+1nrn+1n]v(r) = \left(\frac{n}{n+1}\right)\left(\frac{\Delta PR}{2KL}\right)^{\frac{1}{n}}\left[R^{\frac{n+1}{n}}-r^{\frac{n+1}{n}}\right]
      • v(r)v(r) represents velocity at radial position rr
    • Bingham plastic fluids: v(r)=ΔPR24μpL(1r2R2)τ0R2μp(1rR)v(r) = \frac{\Delta PR^2}{4\mu_pL}\left(1-\frac{r^2}{R^2}\right) - \frac{\tau_0R}{2\mu_p}\left(1-\frac{r}{R}\right) for rR2μpVτ0R\frac{r}{R} \geq \frac{2\mu_pV}{\tau_0R}

Challenges with non-Newtonian fluids

  • Pumping and transport of non-Newtonian fluids
    • Higher pressure drop compared to Newtonian fluids due to complex rheological behavior
    • Potential for flow instabilities and non-uniform flow, leading to processing issues
    • Selection of appropriate pump types and materials to handle the specific fluid properties
  • Heat transfer in non-Newtonian fluids
    • Modified heat transfer correlations are needed to account for the fluid's rheological behavior
    • Potential for reduced heat transfer efficiency due to viscosity effects and non-uniform flow
  • Mixing and agitation of non-Newtonian fluids
    • Increased power requirements for mixing due to higher viscosities and yield stresses
    • Potential for dead zones and poor mixing efficiency, leading to product quality issues
    • Selection of appropriate impeller types and configurations to ensure adequate mixing
  • Rheological characterization of non-Newtonian fluids
    • Accurate measurement of fluid properties is critical for proper design and operation of systems
    • Consideration of shear rate range, temperature, and time-dependent effects is necessary
    • Selection of appropriate rheological models and parameters to describe the fluid behavior

Applications of non-Newtonian fluids

  • Polymer processing involves non-Newtonian fluid behavior
    • Extrusion processes, where molten polymers exhibit shear-thinning behavior (plastic sheets, pipes)
    • Injection molding, where flow behavior affects mold filling and product quality (plastic parts, toys)
    • Fiber spinning, where elongational viscosity is critical for process stability and fiber properties (synthetic fibers, textiles)
  • Food engineering relies on understanding non-Newtonian fluid behavior
    • Pumping and transport of food products, such as ketchup and mayonnaise
    • Extrusion of food products, like pasta and snack foods
    • Mixing and blending of food ingredients, such as dough and sauces
  • Other industrial applications involving non-Newtonian fluids
    • Drilling fluids in the oil and gas industry, which exhibit shear-thinning and yield stress behavior
    • Blood flow in biomedical engineering, as blood exhibits shear-thinning behavior
    • Slurry transport in mining and construction, where suspensions can display non-Newtonian characteristics
    • Printing and coating processes, where ink and coating formulations may exhibit non-Newtonian 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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