Chapman-Enskog theory, flow

The Chapman-Enskog theory of flow In a one-component fluid yields the following approximation to the momentum balance equation (Jil). 

Expressions for the transport coefficients suitable for use in computational simulations of chemically reacting flows are usually based on the Chapman-Enskog theory. The theory has been extended to address in detail transport properties in multicomponent systems [103,178]. 

The uncertainties Ay/yhave been calculated taking into account the errors on Io/Iat and L (thickness of the recombination boundary layer) but also on the flow parameters the diffusion coefficient Do,air determined using the Chapman-Enskog theory, the mean square atomic velocity V determined using the gas kinetic theory (rarefied gas). The accuracy on these two last values is due essentially to that of the gas temperature, measured by emission spectroscopy (N2 rotational temperature), this leads to a total accuracy of 35%. 

The forces of attraction and repulsion between molecules must be considered for a more accurate and rigorous representation of the gas flow. Chapman and Enskog proposed a well-known theory in which they use a distribution function, the Boltzmann equation, instead of the mean free path. Using this approach, for a pair of non-polar molecules, an intermolecular potential, V (r), is given in the potential function proposed by the Lennard-Jones potential ... 

When heat flows through a mixture initially of uniform composition, small diffusion currents are set up, with one component transported in the direction of heat flow, and the other in the opposite direction. This is known as the thermal diffusion effect. The existence of thermal diffusion was predicted theoretically in 1911 by Enskog [El, E2] from the kinetic theory of gases and confirmed experimentally by Chapman [Cl, C2] in 1916. It is not surprising that the effect was not discovered sooner, because it is very small. For example, when a mixture of 50 percent hydrogen and 50 percent nitrogen is held in a temperature gradient between 260 and 10°C, the difference in composition at steady state is only 5 percent. In isotopic mixtures the effect is even smaller. 

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