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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 ...
Shear thinning in a polymeric system: dependence of apparent viscosity on shear rate. η 0 is the zero shear rate viscosity and η ∞ is the infinite shear viscosity plateau. At both sufficiently high and very low shear rates, viscosity of a polymer system is independent of the shear rate.
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 .
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 ...
Similarly, the sliding rate, also called the deviatoric strain rate or shear strain rate is the derivative with respect to time of the shear strain. Engineering sliding strain can be defined as the angular displacement created by an applied shear stress, τ {\displaystyle \tau } .
Note that all thixotropic fluids are extremely shear thinning, but they are significantly time dependent, whereas the colloidal "shear thinning" fluids respond instantaneously to changes in shear rate. Thus, to avoid confusion, the latter classification is more clearly termed pseudoplastic. Another example of a shear thinning fluid is blood.
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.
For low shear rates, dilute suspensions or suspensions involving small particles, the viscosity of the fluid is a much stronger effect than the inertia of the particles. The particles do not interact strongly with each other.