Monatomic gases viscosity

S. Chapman. The Kinetic Theory of Simple and Composite Monatomic Gases Viscosity, Thermal Conductivity, and Diffusion. Proc. R. Soc. A, 98 1-20,1916. 

The viscosity, themial conductivity and diffusion coefficient of a monatomic gas at low pressure depend only on the pair potential but through a more involved sequence of integrations than the second virial coefficient. The transport properties can be expressed in temis of collision integrals defined [111] by... 

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... 

For gases in the low-density limit, a kinetic-theory expression similar to that for viscosity can be used to evaluate single-component thermal conductivity. For a monatomic gas, meaning a gas with no rotational of vibrational degrees of freedom, the thermal conductivity is expressed as... 

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... 

It turns out to be a surprisingly difficult task to determine accurately the thermal conductivity of polyatomic gases from the viscosity. Many of the approaches are motivated by the ideas of Eucken. The so-called Eucken factor is a nondimensional group determined by dividing the kinetic-theory expression for a monatomic gas by that for viscosity, yielding... 

The viscosity of a pure monatomic gas of molecular weight M may be expressed in terms of the Lennard-Jones parameters by... 

Chapman, S. 1916 On the law of distribution of molecular velocities, and on the theory of viscosity and thermal conduction, in a non-uniform simple monatomic gas. Philosophical... 

The generalization in Eqn (2.11) involves the viscosity fi and the dilatational viscosity k to characterize a fluid. Usually, it is not necessary to know the value of k in fluid mechanics problems. For gases, we often assume it to be close to the values of an ideal monatomic gas, for which k is practically zero. We also assume that liquids are incompressible fluids, (V-v) = 0, and k is negligible. 

The first term of equation (4.127) is an approximation to the translational contribution to the thermal conductivity of the mixture. It is obtained by making use of equations (4.122)-(4.125) for the thermal conductivity of a monatomic gas mixture. For this purpose approximate translational contributions to the thermal conductivity of each pure component X, tr and an interaction thermal conductivity for each unlike interaction Xqq are evaluated by the heuristic application of equation (4.125) for monatomic species to polyatomic gases. Thus, the technique requires the availability of experimental viscosity data for pure gases and the interaction viscosity for each binary system or estimates of them. As the discussion of Section 4.2 makes clear, the use of... 

If correlations of a spherical monatomic gas are considered, the dilute-gas effective collision cross sections or collision integrals, evaluated for a specific intermolecular potential, can be substimted directly for calculation of the dilute-gas term. From this point of view, it may not be appropriate to fit dilute-gas thermal conductivity and viscosity... 

The choice of ambient gas will also have a major impact on sonochemical reactivity. Monatomic gases give much more heating than diatomic, which aie much bcttei than polyatomic gases (including solvent vapor). The choice of the solvent also has a profound influence on the observed sonochemistry. In addition to vapor pressure, other liquid properlies, such as surface tension and viscosity, will alter the threshold of cavitation. The chemical reactivity of the solvent is often much more important. No solvent is inert under the high temperature conditions of cavitation. 

Subsequently, and of greater significance in the context of this volume, it was shown that it was possible to determine the pair potential of monatomic species directly from measurements of the viscosity of the dilute gas, by a process of iterative inversion (Maitland et al. 1987). As an illustration of the success that can be achieved. Figure 2.1 compares the pair potential that is obtained by application of the inversion process to the viscosity data for argon with that currently thought to be the best available pair potential for argon which is consistent with a wide variety of experimental and theoretical information. 

To apply the above scheme, accurate experimental measurements for the transport properties of the monatomic fluids were collected. In Table 10.1 the experimental measurements of diffusion, viscosity and thermal conductivity used for the correlation scheme are shown. This table also includes a note of the experimental method used, the quoted accuracy, the temperature range, the maximum pressure and the number of data sets. The data cover the range of compressed gas and the liquid range but not the critical region, where there is an enhancement (Chapter 6) which cannot be accounted for in terms of this simple molecular model. 

Formally, the relationship between the coefficient of viscosity of a dilute polyatomic gas and the related effective cross section is identical to that for monatomic gases (Chapter 4). In a practical, engineering form it is given by... 

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