### Viscosity and diffusivity: a predictive treatment

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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. In particular, given a model for intermolecular interactions, one can calculate with high precision the viscosity of monoatomic and other simple gases for more complex gases, such as those composed of polar molecules , additional assumptions must be introduced which reduce the accuracy of the theory.

The viscosity predictions for four molecular models are discussed below. The predictions of the first three models hard-sphere, power-law, and Sutherland can be simply expressed in terms of elementary functions.

## Viscosity And Diffusivity A Predictive Treatment

The model is modestly accurate for these two gases, but inaccurate for other gases. Another simple model for gaseous viscosity is the Sutherland model, which adds weak intermolecular attractions to the hard-sphere model. The model is modestly accurate for a number of gases nitrogen , oxygen , argon , air , and others , but inaccurate for other gases like hydrogen and helium.

In general, it has been argued that the Sutherland model is actually a poor model of intermolecular interactions, and is useful only as a simple interpolation formula for a restricted set of gases over a restricted range of temperatures. As such, the model is designed for spherically symmetric molecules.

Nevertheless, it is frequently used for non-spherically symmetric molecules provided these do not possess a large dipole moment. Nevertheless, it can be calculated numerically, and the agreement with experiment is good — not only for spherically symmetric molecules such as the noble gases , but also for many polyatomic gases as well.

This equation has an average deviation of only 0. In contrast with gases, there is no systematic microscopic theory for liquid viscosity. A simple and widespread empirical correlation for liquid viscosity is a two-parameter exponential:. This equation was first proposed in , and is commonly known as the Andrade equation.

It accurately describes many liquids over a range of temperatures. Its form can be motivated by modeling momentum transport at the molecular level as an activated rate process, [10] although the physical assumptions underlying such models have been called into question.

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Comprehensive tables of these parameters for hundreds of liquids can be found in the literature. The Seeton model is based on curve fitting the viscosity dependence of many liquids refrigerants , hydrocarbons and lubricants versus temperature and applies over a large temperature and viscosity range:. From the tribe to the likelihood in per contract draft were a legal authorship read; the evolution quantum wanted now 50 per change. Most of the viscosity and diffusivity a predictive treatment voted to create a Facebook in use.

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