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For the simple shear case, it is just a gradient of velocity in a flowing material. The SI unit of measurement for shear rate is s −1, expressed as "reciprocal seconds" or "inverse seconds". [1] However, when modelling fluids in 3D, it is common to consider a scalar value for the shear rate by calculating the second invariant of the strain ...
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 ...
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 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 viscosity is not a material constant, but a material property that depends on temperature, pressure, fluid mixture composition, local velocity variations. This functional relationship is described by a mathematical viscosity model called a constitutive equation which is usually far more complex than the defining equation of shear viscosity ...
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 ...
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 one dimension, the constitutive equation of the Herschel-Bulkley model after the yield stress has been reached can be written in the form: [3] [4] ˙ =, < = + ˙, where is the shear stress [Pa], the yield stress [Pa], the consistency index [Pa s], ˙ the shear rate [s], and the flow index [dimensionless].