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

• 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: $\tau = \mu \frac{du}{dy}$ relates shear stress $\tau$, dynamic viscosity $\mu$, and shear rate $\frac{du}{dy}$ (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 $\tau = K(\frac{du}{dy})^n$, where $n < 1$, $K$ is the consistency index, and $n$ 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 $\tau = K(\frac{du}{dy})^n$, where $n > 1$

Yield stress in viscoplastic fluids

• Yield stress $\tau_y$ is the minimum shear stress required to initiate flow; below $\tau_y$, the fluid behaves like a solid, and above $\tau_y$, 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: $\tau = \tau_y + \mu_p \frac{du}{dy}$, where $\mu_p$ is the plastic viscosity
  2. Herschel-Bulkley model: $\tau = \tau_y + K(\frac{du}{dy})^n$, combining yield stress and power-law behavior