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The same goes for shear viscosity. For a Newtonian fluid the shear viscosity is a pure fluid property, but for a non-Newtonian fluid it is not a pure fluid property due to its dependence on the velocity gradient. Neither shear nor volume viscosity are equilibrium parameters or properties, but transport properties.
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.
Trouton's ratio is the ratio of extensional viscosity to shear viscosity. For a Newtonian fluid, the Trouton ratio is 3. [21] [22] Shear-thinning liquids are very commonly, but misleadingly, described as thixotropic. [23] Viscosity may also depend on the fluid's physical state (temperature and pressure) and other, external, factors.
Dynamic viscosity is a material property which describes the resistance of a fluid to shearing flows. It corresponds roughly to the intuitive notion of a fluid's 'thickness'. For instance, honey has a much higher viscosity than water. Viscosity is measured using a viscometer. Measured values span several orders of magnitude.
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,
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.
In these instances, it can be useful to express internal shear stress as shear flow, which is found as the shear stress multiplied by the thickness of the section. An equivalent definition for shear flow is the shear force V per unit length of the perimeter around a thin-walled section. Shear flow has the dimensions of force per unit of length. [1]
At low shear rate (˙ /) a Carreau fluid behaves as a Newtonian fluid with viscosity .At intermediate shear rates (˙ /), a Carreau fluid behaves as a Power-law fluid.At high shear rate, which depends on the power index and the infinite shear-rate viscosity , a Carreau fluid behaves as a Newtonian fluid again with viscosity .