Glossary

14.3 Flow Behavior of Non-Newtonian Fluids

4 min read•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 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 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
    • have flatter velocity profiles due to reduced viscosity near the pipe wall
    • 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
    • : 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(1−43λ+13λ4)+8μpVR2(1−λ2)\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+1n−rn+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(1−r2R2)−τ0R2μp(1−rR)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 rR≥2μpVτ0R\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

Key Terms to Review (18)

Bingham Plastic Model: The Bingham Plastic Model describes a type of non-Newtonian fluid that behaves as a solid until a certain yield stress is exceeded, after which it flows like a viscous fluid. This model helps in understanding how materials like toothpaste or certain slurries require an initial force to start flowing, connecting the concept of yield stress to fluid behavior.
Capillary Flow Experiments: Capillary flow experiments are studies designed to investigate the movement of fluids through small diameter tubes or porous materials due to capillary action. This phenomenon is crucial for understanding how non-Newtonian fluids behave in confined spaces, where the effects of surface tension and viscosity interplay significantly.
Cauchy Stress Tensor: The Cauchy stress tensor is a mathematical representation of stress within a material, defined at a point in the body under consideration. It captures how internal forces are distributed across different orientations and is crucial for understanding how materials deform and flow, particularly when dealing with non-Newtonian fluids where the relationship between stress and strain rate is complex.
Continuity equation: The continuity equation is a fundamental principle in fluid mechanics that expresses the conservation of mass within a fluid flow. It states that the mass flow rate of a fluid must remain constant from one cross-section of a pipe or channel to another, provided there are no mass additions or losses. This concept connects with various aspects of fluid behavior and dynamics, playing a crucial role in understanding how fluids move and behave under different conditions.
Critical shear rate: Critical shear rate refers to the specific rate of shear stress at which a non-Newtonian fluid transitions from one flow behavior to another, particularly from a more viscous state to a less viscous state. This concept is essential for understanding how non-Newtonian fluids behave under different flow conditions, as their viscosity can change significantly depending on the shear rate applied. It plays a crucial role in predicting how these fluids will perform in various applications, such as mixing, pumping, and processing.
Flow regimes: Flow regimes refer to the distinct patterns and behaviors of fluid motion, which can vary based on factors like viscosity, flow rate, and external forces. These regimes can be classified into different categories, such as laminar and turbulent flow, which have significant implications for how fluids behave under various conditions, especially in the context of non-Newtonian fluids where viscosity can change with shear rate.
Navier-Stokes Equations: The Navier-Stokes equations are a set of nonlinear partial differential equations that describe the motion of fluid substances. These equations are fundamental in fluid mechanics, capturing how velocity, pressure, temperature, and density of a fluid are related over time and space, making them essential for understanding various fluid behaviors and phenomena.
Navier-Stokes Equations for Non-Newtonian Fluids: The Navier-Stokes equations for non-Newtonian fluids describe the motion of fluids whose viscosity changes with the rate of shear strain or stress. These equations extend the classical Navier-Stokes equations, which apply to Newtonian fluids, by incorporating additional parameters to account for the complex flow behavior exhibited by non-Newtonian materials. Understanding these equations is crucial for predicting the flow patterns and behaviors of various substances encountered in real-world applications, including polymers, slurries, and biological fluids.
Power-law model: The power-law model is a mathematical relationship used to describe the flow behavior of non-Newtonian fluids, where the shear stress is proportional to a power of the shear rate. This model helps in characterizing how different fluids respond to applied forces, especially when they do not follow Newton's linear relationship. It is particularly relevant for understanding complex fluids that exhibit non-linear flow behavior under varying conditions.
Rheometry: Rheometry is the experimental technique used to measure the flow and deformation behavior of materials, particularly non-Newtonian fluids, under applied stress or strain. This technique helps in understanding how these fluids respond to different forces, which is crucial for their applications in various industries such as food, pharmaceuticals, and polymers. By analyzing the viscosity and elasticity of these materials, rheometry provides valuable insights into their performance during processing and end-use.
Rheopexy: Rheopexy refers to the phenomenon where certain non-Newtonian fluids exhibit an increase in viscosity over time when subjected to a constant shear stress or strain. This behavior is significant in understanding how materials respond to applied forces, particularly in situations where prolonged shear is involved, like mixing or pumping. Rheopexy contrasts with other flow behaviors and plays a crucial role in applications ranging from industrial processes to biological fluids.
Shear-thickening fluids: Shear-thickening fluids are a type of non-Newtonian fluid that exhibit an increase in viscosity with an increase in shear rate. This unique behavior means that these fluids become thicker and resist flow more when subjected to higher forces or stress, which is contrary to the behavior of Newtonian fluids that maintain constant viscosity. This property allows shear-thickening fluids to behave differently under various flow conditions, making them interesting for applications in industries such as personal protective equipment and food processing.
Shear-thinning fluids: Shear-thinning fluids, also known as pseudoplastic fluids, are non-Newtonian fluids that exhibit a decrease in viscosity with an increase in shear rate. This behavior means that when these fluids are stirred or agitated, they become less viscous and flow more easily, which is a crucial property in many applications like paints, food products, and biological fluids. Understanding this characteristic helps in classifying non-Newtonian fluids and analyzing their flow behavior under various conditions.
Thixotropy: Thixotropy is a property of certain non-Newtonian fluids that become less viscous when subjected to shear stress, allowing them to flow more easily. This unique behavior makes thixotropic fluids return to a more viscous state when left undisturbed, highlighting their ability to change viscosity over time based on the application of stress. Such fluids are commonly found in various industries, impacting how materials are processed and applied.
Transition point: The transition point refers to the critical threshold in the flow behavior of non-Newtonian fluids where the fluid shifts from one flow regime to another, typically from laminar to turbulent or vice versa. This concept is crucial in understanding how non-Newtonian fluids behave under varying shear rates and influences factors such as viscosity and flow resistance.
Viscometry: Viscometry is the measurement of a fluid's viscosity, which indicates its resistance to flow. This term is particularly significant in understanding the flow behavior of non-Newtonian fluids, as these fluids exhibit varying viscosity depending on the applied shear rate or stress. Viscometry helps in characterizing these fluids and allows engineers and scientists to predict how they will behave under different flow conditions.
Viscosity: Viscosity is a measure of a fluid's resistance to deformation and flow, essentially describing how thick or sticky a fluid is. This property plays a crucial role in understanding fluid behavior under different conditions and directly affects various phenomena, such as flow rates, pressure distribution, and energy loss in fluid systems.
Yield stress: Yield stress is the minimum stress required to initiate flow in a material, specifically in non-Newtonian fluids. It represents a threshold that must be exceeded for the fluid to start deforming or flowing under applied stress. This concept is critical in understanding how different fluids respond to forces and is key to classifying non-Newtonian fluids, modeling their behavior, and analyzing their flow characteristics.
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