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
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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)
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(dydu)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 τ=K(dydu)n, where n>1
Yield stress in viscoplastic fluids
Yield stress τy is the minimum shear stress required to initiate flow; below τy, the fluid behaves like a solid, and above τy, 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:
Bingham plastic model: τ=τy+μpdydu, where μp is the plastic viscosity
Herschel-Bulkley model: τ=τy+K(dydu)n, combining yield stress and power-law behavior