The structure of non-equilibrium angular momentum polarizations in polyatomic gases

Abstract:

In the kinetic theory of non-equilibrium phenomena in dilute polyatomic gases there is a characteristic difference between the treatment of non- spherical and spherical particles. This difference stems from the fact that in a polyatomic gas, i.e. a gas of non-spherical particles, in the non-equilibrium state not only the distribution of molecular velocities becomes anisotropic, but that also the distribution of the orientations of the molecules is affected by macroscopic thermodynamic forces. These deviations from an isotropic distribution of angular momenta, or polarizations, are generally complicated in nature and may depend on both velocity and angular momentum. Their presence was first realized by Pidduck in 1922. In their book on non-uniform gases Chapman and Cowling were aware of the anisotropies in both the velocity and the rotational angular momentum, but in subsequent calculations they neglected the effects of the angular momentum dependent terms. Later in 1961, Kagan and Afanasiev showed that for a simplified classical model such terms give rise to sizable contributions to the transport properties. Experimental information on polarizations are obtained in various ways. First of all, field effects on transport phenomena, which as Kagan and Maksimov showed are a direct consequence of the existence of such polarizations, yield a wealth of data. Secondly, information is obtained by measuring the non-equilibrium birefringence caused by the anisotropy in the orientational distribution of the molecules. Additional information on certain aspects, e.g. relaxation times of polarizations, can be obtained from a study of phenomena which are determined by (equilibrium) fluctuations, such as the depolarized Rayleigh line broadening and nuclear magnetic resonance. Polarizations can be thought of as consisting of two parts: a tensorial factor (of rank one of higher) depending on the orientation of the molecule and the direction in which the molecule is moving, and a scalar factor depending on the magnitudes of both the molecular velocity and the rotational angular momentum. From studies of the dependence of field effects on the orientation of the field with respect to the gradient, the tensorial factors of polarizations produced by various macroscopic thermodynamic forces have been determined unambiguously. On the scalar structure, however, no information can be obtained from these experiments separately. An analogous situation exists with respect to the importance of higher order Sonine polynomials in the molecular velocity when one considers transport phenomena of noble gases. Measurement of one transport property by itself does not allow any conclusions to be drawn in this regard. One can, however, resort in this case to the verification of specific relations involving the Eucken factor. In a similar way internal consistency checks and a comparison of field effects with optical measurements might lead to more detailed information about the structure of polarization in polyatomic gases. So far such comparisons have not or only partially been carried out. In this thesis two experiments are described which enable some decisive consistency checks to be performed. In chapter II experiments on the influence of external electric and magnetic fields on the viscosity of some polar gases are described. Next, in chapter III, experiments on the influence of a magnetic field on diffusion in N2-noble gases are presented. These experiments–apart from yielding new numerical results–show very clearly that the structure of polarizations is much more complicated than was usually assumed so far, and that it is not possible to get detailed quantitative information on the scalar factor from experiments on field effects alone. For this reason a detailed analysis and comparison between the results of field effects and the results of optical measurements has been carried out. As we will see in chapter IV this comparison indeed clarifies the structure of polarizations. In order to present the results in a uniform and unambiguous way the kinetic theory of rotation molecules, which for this purpose has been modified and extended, is formulated at the beginning of this thesis in chapter I.