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A Newtonian fluid is a power-law fluid with a behaviour index of 1, where the shear stress is directly proportional to the shear rate: = These fluids have a constant viscosity, μ, across all shear rates and include many of the most common fluids, such as water, most aqueous solutions, oils, corn syrup, glycerine, air and other gases.
The use of the word "law" in referring to the Glen-Nye model of ice rheology may obscure the complexity of factors which determine the range of viscous ice flow parameter values even within a single glacier, as well as the significant assumptions and simplifications made by the model itself. [13] [14] [7]
The power law model is used to display the behavior of Newtonian and non-Newtonian fluids and measures shear stress as a function of strain rate. The relationship between shear stress, strain rate and the velocity gradient for the power law model are: τ x y = − m | γ ˙ | n − 1 d v x d y , {\displaystyle \tau _{xy}=-m\left|{\dot {\gamma ...
This book contains several examples of different non-dimensionalizations and scalings of the Navier–Stokes equations, see p. 430. Krantz, William B. (2007). Scaling Analysis in Modeling Transport and Reaction Processes: A Systematic Approach to Model Building and the Art of Approximation. John Wiley & Sons. ISBN 9780471772613.
Where: , , and are material coefficients: is the viscosity at zero shear rate (Pa.s), is the viscosity at infinite shear rate (Pa.s), is the characteristic time (s) and power index. The dynamics of fluid motions is an important area of physics, with many important and commercially significant applications.
In rheology, shear thinning is the non-Newtonian behavior of fluids whose viscosity decreases under shear strain. It is sometimes considered synonymous for pseudo- plastic behaviour, [ 1 ] [ 2 ] and is usually defined as excluding time-dependent effects, such as thixotropy .
A generalized Newtonian fluid is an idealized fluid for which the shear stress is a function of shear rate at the particular time, but not dependent upon the history of deformation.
Under certain circumstances, flows of granular materials can be modelled as a continuum, for example using the μ rheology. Such continuum models tend to be non-Newtonian, since the apparent viscosity of granular flows increases with pressure and decreases with shear rate. The main difference is the shearing stress and rate of shear.