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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 ...
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 .
The kinetic theory of gases allows accurate calculation of the temperature-variation of gaseous viscosity. The theoretical basis of the kinetic theory is given by the Boltzmann equation and Chapman–Enskog theory, which allow accurate statistical modeling of molecular trajectories.
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.
John Douglass Ferry (May 4, 1912 – October 18, 2002) was a Canadian-born American chemist and biochemist noted for development of surgical products from blood plasma and for studies of the chemistry of large molecules.
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].
In continuum mechanics, a power-law fluid, or the Ostwald–de Waele relationship, is a type of generalized Newtonian fluid.This mathematical relationship is useful because of its simplicity, but only approximately describes the behaviour of a real non-Newtonian fluid.