Viscosity Chapman-Enskog expression

Since the forms of the Chapman-Enskog expressions for dilute-gas viscosity and conductivity are so similar, it might be expected that there is a simple relationship between thermal conductivity and viscosity. Indeed, for monatomic gases, combining Eqs. 3.41 and 3.136 yields... 

Using the viscosity versus temperature table evaluated from the Chapman-Enskog expression in the previous problem, determine a best fit for the S parameter in the form of a Sutherland viscosity expression. Assume reference values of 7o = 273 K and i o = 1.716 x 10-5 N-s/m2. 

Similarly show that the Chapman-Enskog expression for viscosity, Eq. 12.89, reduces to Eq. 12.50 for the special case of a hard-sphere interaction potential. 

The Chapman-Enskog solution of the Boltzmaim equation [112] leads to the following expressions for the transport coefficients. The viscosity of a pure, monatomic gas can be written as... 

Riazi-Whitson They presented a generahzed correlation in terms of viscosity and molar density that was apphcable to both gases and liqmds. The average absolute deviation for gases was only about 8 percent, while for liquids it was 15 percent. Their expression relies on the Chapman-Enskog correlation [Eq. (5-194)] for the low-pressure diffusivity and the Stiel-Thodos correlation for low-pressure viscosity ... 

As illustrated in the low-density limit of Fig. 3.3, the viscosity of gases increases with increasing temperature. Moreover, for pressures well below the critical pressure, there is very little pressure dependence. The kinetic theory of dilute gases provides the theoretical basis for the temperature dependence. The Chapman-Enskog theory provides an expression for dilute pure-species viscosities as... 

Using the theory developed by Chapman-Enskog (see Ref. 14), a hierarchy of continuum fluid mechanics formulations may be derived from the Boltzmann equation as perturbations to the Maxwellian velocity distribution function. The first three equation sets are well known (1) the Euler equations, in which the velocity distribution is exactly the Maxwellian form (2) the Navier-Stokes equations, which represent a small deviation from Maxwellian and rely on linear expressions for viscosity and thermal conductivity and (3) the Burnett equations, which include second order derivatives for viscosity and thermal conductivity. 

If gaseous systems have high densities, both the kinetic theory of gases and the Chapman-Enskog theory fail to properly describe the transport coefficients behavior. Furthermore, the previously derived expression for viscosity and... 

The first-order Chapman-Enskog solution of the Boltzmann equation for the viscosity and thermal conductivity of monatomic species are given by the expressions in terms of effective collision cross sections outlined in Chapter 4. However, in order to be consistent with the original papers, here the equivalent expressions in terms of collision integrals are adopted. 

A temperature-dependent expression for gas viscosity of a pure mono-atomic gas is given by Chapman-Enskog s kinetic theory as... 

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