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The shear rate at the inner wall of a Newtonian fluid flowing within a pipe [2] is ˙ =, where: ˙ is the shear rate, measured in reciprocal seconds; v is the linear fluid velocity; d is the inside diameter of the pipe.
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 ...
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 passage of time. Shear thinning: Similar to thixotropy, but independent of the passage of time.
Plot of shear rate as a function of the shear stress. Dilatants in green. A dilatant (/ d aɪ ˈ l eɪ t ə n t /, / d ɪ-/) (also termed shear thickening [1]) material is one in which viscosity increases with the rate of shear strain. Such a shear thickening fluid, also known by the initialism STF, is an example of a non-Newtonian fluid.
The viscosity of a non-Newtonian fluid is defined by a power law: [5] = ˙ where η is the viscosity after shear is applied, η 0 is the initial viscosity, γ is the shear rate, and if <, the fluid is shear thinning, >, the fluid is shear thickening,
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 non-Newtonian fluid is a fluid whose flow properties differ in any way from those of Newtonian fluids. Most commonly the viscosity of non-Newtonian fluids is a function of shear rate or shear rate history. However, there are some non-Newtonian fluids with shear-independent viscosity, that nonetheless exhibit normal stress-differences or other ...
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.