Williams-Boltzmann equation

In spite of have been proposed many approximated solutions to Boltzmann equation (including the Grad s method of 13 moments, expansions of generalized polynomial, bimodal distributions functions), however the Chapman-Enskog is the most popular outline for generalize hydrodynamic equations starting from kinetics equations kind Boltzmann (James William, 1979 Cercignani, 1988). 

There are two superposition principles that are important in the theory of Viscoelasticity. The first of these is the Boltzmann superposition principle, which describes the response of a material to different loading histories (22). The second is the time-temperature superposition principle or WLF (Williams, Landel, and Ferry) equation, which describes the effect of temperature on the time scale of the response. 

In the literature the GPBE is known by many different names, depending on the research field. For example, in statistical physics, when written for the velocity NDF, it is called the Boltzmann kinetic equation and in the combustion literature, when written for droplets, it is known as the spray or Williams equation. 

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