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The WLF equation is a consequence of time–temperature superposition (TTSP), which mathematically is an application of Boltzmann's superposition principle. It is TTSP, not WLF, that allows the assembly of a compliance master curve that spans more time, or frequency, than afforded by the time available for experimentation or the frequency range ...
Robert F. Landel (October 10, 1925 – September 10, 2024) was an American physical chemist at the Jet Propulsion Laboratory noted for his contribution to development of the Williams–Landel–Ferry equation, [1] [2] and for a particular form of hyperelastic energy function, the Valanis-Landel form.
Washington Legal Foundation, an American conservative non-profit legal organisation in Washington, D.C.; World Law Foundation, an international organisation dedicated to the rule of law, based in Madrid, Spain
The WLF-model can be developed from Doolittle's concept of free volume and the thermal expansion coefficient . α T E {\displaystyle \alpha _{\rm {TE}}} has a discontinuity when going below T g {\displaystyle T_{g}} for these types of materials, which can be seen as a phase shift going to more of a solid state (the glassy region).
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 .
A difference equation is an equation where the unknown is a function f that occurs in the equation through f(x), f(x−1), ..., f(x−k), for some whole integer k called the order of the equation. If x is restricted to be an integer, a difference equation is the same as a recurrence relation
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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].