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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.
The Vogel–Fulcher–Tammann equation, also known as Vogel–Fulcher–Tammann–Hesse equation or Vogel–Fulcher equation (abbreviated: VFT equation), is used to describe the viscosity of liquids as a function of temperature, and especially its strongly temperature dependent variation in the supercooled regime, upon approaching the glass transition.
Under standard atmospheric conditions (25 °C and pressure of 1 bar), the dynamic viscosity of air is 18.5 μPa·s, roughly 50 times smaller than the viscosity of water at the same temperature. Except at very high pressure, the viscosity of air depends mostly on the temperature.
The empirical relationship of Williams-Landel-Ferry, [10] combined with the principle of time-temperature superposition, can account for variations in the intrinsic viscosity η 0 of amorphous polymers as a function of temperature, for temperatures near the glass transition temperature T g. The WLF model also expresses the change with the ...
The viscosity is not a material constant, but a material property that depends on temperature, pressure, fluid mixture composition, local velocity variations. This functional relationship is described by a mathematical viscosity model called a constitutive equation which is usually far more complex than the defining equation of shear viscosity.
A first-order fluid is another name for a power-law fluid with exponential dependence of viscosity on temperature. (˙,) = ˙ where γ̇ is the shear rate, T is temperature and μ 0, n and b are coefficients.
Chapman–Enskog theory also predicts a simple relation between thermal conductivity, , and viscosity, , in the form =, where is the specific heat at constant volume and is a purely numerical factor. For spherically symmetric molecules, its value is predicted to be very close to 2.5 {\displaystyle 2.5} in a slightly model-dependent way.
η is the viscosity of the solution (at a fixed temperature and pressure), η 0 is the viscosity of the solvent at the same temperature and pressure, A is a coefficient that describes the impact of charge–charge interactions on the viscosity of a solution (it is usually positive) and can be calculated from Debye–Hückel theory,