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For a Newtonian fluid wall, shear stress (τ w) can be related to shear rate by = ˙ where μ is the dynamic viscosity of the fluid. For non-Newtonian fluids, there are different constitutive laws depending on the fluid, which relates the stress tensor to the shear rate tensor.
The following equation illustrates the relation between shear rate and shear stress for a fluid with laminar flow only in the direction x: =, where: τ x y {\displaystyle \tau _{xy}} is the shear stress in the components x and y, i.e. the force component on the direction x per unit surface that is normal to the direction y (so it is parallel to ...
A single viscosity measurement at a constant speed in a typical viscometer is a measurement of the instrument viscosity of a fluid (not the apparent viscosity). In the case of non-Newtonian fluids, measurement of apparent viscosity without knowledge of the shear rate is of limited value: the measurement cannot be compared to other measurements if the speed and geometry of the two instruments ...
In a Newtonian fluid, the relation between the shear stress and the shear rate is linear, passing through the origin, the constant of proportionality being the coefficient of viscosity. In a non-Newtonian fluid, the relation between the shear stress and the shear rate is different. The fluid can even exhibit time-dependent viscosity. Therefore ...
For some fluids, the viscosity is constant over a wide range of shear rates (Newtonian fluids). The fluids without a constant viscosity (non-Newtonian fluids) cannot be described by a single number. Non-Newtonian fluids exhibit a variety of different correlations between shear stress and shear rate.
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.
Viscosity; Rheopecty: The longer the fluid is subjected to a shear force, the higher the viscosity. Time-dependent shear thickening behavior. Thixotropy: The longer a fluid is subjected to a shear force, the lower its viscosity. It is a time-dependent shear thinning behavior. Shear thickening: Similar to rheopecty, but independent of the ...
In a Newtonian fluid, the relation between the shear stress and the shear rate is linear, passing through the origin, the constant of proportionality being the coefficient of viscosity. In a non-Newtonian fluid, the relation between the shear stress and the shear rate is different, and can even be time-dependent.