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The viscosity model for dilute gas, that is shown above, is widely used throughout the industry and applied science communities. Therefore, many researchers do not specify a dilute gas viscosity model when they propose a total viscosity model, but leave it to the user to select and include the dilute gas contribution.
Schematic representation of Kelvin–Voigt model. The Kelvin–Voigt model, also called the Voigt model, is represented by a purely viscous damper and purely elastic spring connected in parallel as shown in the picture. If, instead, we connect these two elements in series we get a model of a Maxwell material.
REFPROP v10.0 implements equation of state models for 147 pure fluids, listed in Table 1. [1] Except for F 3 N , R-13, R-123, and R-152a, all of these are Helmholtz free energy formulations. REFPROP v10.0 also predicts surface tension , viscosity , and thermal conductivity for most of the listed fluids.
In light of these shortcomings, the development of a less ad hoc model is a matter of practical interest. Foregoing simplicity in favor of precision, it is possible to write rigorous expressions for viscosity starting from the fundamental equations of motion for molecules.
The predictions of the first three models (hard-sphere, power-law, and Sutherland) can be simply expressed in terms of elementary functions. The Lennard–Jones model predicts a more complicated T {\displaystyle T} -dependence, but is more accurate than the other three models and is widely used in engineering practice.
An important prediction of Chapman–Enskog theory is that viscosity, , is independent of density (this can be seen for each molecular model in table 1, but is actually model-independent). This counterintuitive result traces back to James Clerk Maxwell , who inferred it in 1860 on the basis of more elementary kinetic arguments. [ 11 ]
Consequently, if a liquid has dynamic viscosity of n centiPoise, and its density is not too different from that of water, then its kinematic viscosity is around n centiStokes. For gas, the dynamic viscosity is usually in the range of 10 to 20 microPascal-seconds, or 0.01 to 0.02 centiPoise. The density is usually on the order of 0.5 to 5 kg/m^3.
where E is the elastic modulus and η is the material coefficient of viscosity. This model describes the damper as a Newtonian fluid and models the spring with Hooke's law . In a Maxwell material, stress σ , strain ε and their rates of change with respect to time t are governed by equations of the form: [ 1 ]