Fluids- Non-Newtonian Fluids Flashcards
What is the relationship between shear stress and dynamic viscosity for Newtonian fluids?
τ=μdu/dy
Where du/dy is the velocity gradient between two plates
Formula for non-Newtonian fluid’s apparent viscosity
μa=τ/(du/dy)
Where a is subscript
Rheology
The study of the deformation of flowing fluids
Non-Newtonian fluids
Fluids for which the shear stress is not linearly related to the shear strain rate.
Newtonian fluids
Fluids for which the shear stress is linearly proportional to the shear strain rate
Shear thinning fluids
Aka pseudoplastic fluids. The more the fluid is sheared, the less viscous it becomes.
Plastic fluids
Those in which the shear thinning effect is extreme.
Bingham plastic fluids
Fluids where a finite stress called the yield stress is required before the fluid begins to flow at all.
Shear thickening fluids
Aka dilatant. The more the fluid is sheared, the more viscous it becomes.
Examples of shear thinning, thickening and Bingham plastic fluids
Thinning- ketchup
Thickening- custard
Bingham plastic- mayonnaise
Power law model for shear thinning and thickening fluids
τ=Kγ•^n
Where γ• has dot above and is the velocity gradient
K is consistency factor
n is power law index and is 1 for Newtonian, <1 for thin and >1 for thick
How to get power law model to change sign of shear stress correctly with strain rate
τ=K[γ•]^(n-1)xγ•
Where the one in brackets is magnitude
Formula for apparent viscosity using power law model
μa=τ/γ•=K[γ•]^(n-1)
Square brackets mean magnitude
See page 4
How can real fluids behave over different ranges of shear rate?
At small enough shear rate become Newtonian. At intermediate shear rate become power law. At large enough shear rate become Newtonian.
Often only one of these ranges of shear rate is significant and apparent viscosity in that range used in calculations.
Where to find Carreau model for non-Newtonian fluids
Page 6 of notes which gives definition of parameters
