Senftleben-Beenakker Effect Research Articles

On the Thermomagnetic Gas Torque for Collinear Static and Alternating Magnetic Fields

Abstract Results obtained within the framework of kinetic theory are presented for the part of the thermo-magnetic gas torque which stems from the thermal pressure and is associated with the influence of the magnetic fields on the viscosity (Senftleben-Beenakker effect). Good qualitative agreement and a quantitative agreement within a factor of roughly 1.5 are found between the theory and the experimental data of Smith and Scott [1969].

Kinetic Theory for Mixtures of Dilute Gases of Linear Rotating Molecules in an External Magnetic Field (Formal Theory)

Abstract A transport theory is developed for mixtures of dilute gases consisting of linear rotating diamagnetic molecules in an external homogeneous magnetic field. This formalism is adequate for a treatment of the Senftleben-Beenakker effects for gas mixtures. Starting point is the system of linearized Waldmann-Snider equations. A complete scheme of orthogonal expansion tensors in velocity and rotational angular momentum is given, up to tensors of third rank and power. The moment method is applied to solve the coupled system of Waldmann-Snider equations and the resulting system of transport relaxation equations (TRE) is stated up to third rank tensor equations. The local conservation laws - linearized in the deviation from thermal equilibrium - are derivated from the TRE.

Thermomagnetic Force in Oxygen

A thin disk surrounded by a polyatomic gas has been found to experience a force in a direction normal to its surface when a thermal gradient and an external magnetic field are applied. This force has been measured as a function of field and pressure for oxygen. The nature of the field and pressure dependence indicates that this force effect has its origin in the same molecular-collision processes as does the field-induced decrease of the viscosity (Senftleben-Beenakker effect).

Linear response theory of transport phenomena in dilute polyatomic gases

Abstract On the basis of linear response theory general nonlocal relations, connecting thermodynamic fluxes and forces, and Kubo-type formulae for the transport coefficients are derived. These formulae allow a simple discussion of symmetry relations between the transport coefficients. For dilute gases and homogeneous forces we show, using van Hove's two-resolvent formalism, that the transport coefficients can be expressed by means of the collision operator of the linearized Waldmann-Snider equation. This method allows a systematic treatment of the magnetic and electric Senftleben-Beenakker effects. The present results agree with those obtained by solving the Waldmann-Snider kinetic equation by means of a Chapman-Enskog expansion in the lowest approximation.

On the Nonspherical Scattering Amplitude for Inelastic Molecular Collisions

The rotational angular momentum dependence of the nonspherical scattering amplitude is investigated for inelastic collisions of linear molecules. As far as the approximation of small nonsphericity can be applied, this dependence is obtained from the angular momentum dependence of the nonspherical interaction potential. The connection between the nonspherical scattering amplitude and observables that can be measured by molecular scattering experiments involving a polarized beam is discussed. Some qualitative remarks are made on collision brackets occurring in the theoretical expressions for the bulk viscosity and for the Senftleben-Beenakker effect for H2 and HD

On the Pressure Dependence of the Transport Properties of Dilute Polyatomic Gases

Abstract It is shown that the transport coefficients of dilute polyatomic gases in the ordinary Navier-Stokes regime contain an extra pressure dependence when the internal state Hamiltonian does not commute with the nonequilibrium distribution function-density matrix for the gas. As a specific example, the pressure dependence of the shear viscosity of a gas of paramagnetic 2Σ molecules is considered. Furthermore, the pressure dependence of the Senftleben and Senftleben-Beenakker effects is discussed and examples are given of the different types of molecules for which pressure dependence in the field-free as well as in the field-dependent transport coefficients may be expected.

Rotational Angular Momentum Dependence of the Scattering Amplitude for Elastic Molecular Collisions

The rotational angular momentum (spin) dependence of the binary scattering amplitude operator is investigated for elastic collisions of homonuclear diatomic molecules with monatomic and diatomic particles. Starting point is a formal expansion of the T-matrix (and consequently of the scattering amplitude) with respect to the nonsphericity parameter ε which essentially measures the ratio of the nonspherical and spherical parts of the interaction potential. A transscription of angle dependent potential functions into a spin operator notation is introduced. Potential functions and values for ε may be inferred from the data available in the literature for the interactions: H2—He (ε ≈ 1/4) and H2—H2 (ε ≈ 1/20). As far as elastic events are concerned, irreducible spin tensors of even rank only occur with the interaction potential and consequently with the scattering amplitude in order ε. The most important terms of the scattering amplitude of diatomic molecules are quadratic in the spins. These terms are discussed in detail. In order ε2 the scattering amplitude also contains irreducible spin tensors of odd rank. A knowledge of the orders of magnitude of the various spin — dependent terms is of interest for the SENFTLEBEN-BEENAKKER effect and for NMR in polyatomic gases.

Kinetic Theory for a Dilute Gas of Particles with Spin. II. Relaxation Coefficients

The relaxation coefficients to be discussed are given by collision brackets pertaining to the linearized collision operator of the generalized Boltzmann equation for particles with spin. The order of magnitude of various nondiagonal relaxation coefficients which are of interest for the SENFTLEBEN-BEENAKKER effect is investigated. Those nondiagonal relaxation coefficients which are linear in the nonsphericity parameter ε (ε essentially measures the ratio of the nonspherical and the spherical parts of the interaction potential), as well as some diagonal relaxation coefficients are expressed in terms of generalized Omega-integrals.

Senftleben-Beenakker effect on the heat conductivity of a gas of regular octahedral molecules (SF 6, UF 6)

For a gas of regular octahedral molecules, terms in the distribution function involving 4th rank spin tensors should give an important contribution to the Senftleben-Beenakker effect. The resulting magnetic field dependence of the heat conductivity is stated.

External Field Dependence of Transport Properties. I. Thermal Conduction in a Fluid of Rough Spheres

A theory of thermal conduction is developed for a gas composed of rotating molecules which is subject to an external electric or magnetic field. This theory of the Senftleben–Beenakker effect is based upon a kinetic equation of the Boltzmann variety and is sufficiently general to include virtually all cases of interest. Application has been made to the rough-sphere model of collisional events and numerical values of the three independent elements of the thermal conductivity tensor obtained. Although the model is rather unrealistic, comparisons with experiment have been made whenever possible. Agreement as to order of magnitude and functional dependence upon field strength is satisfactory but by no means perfect. In these calculations it has been assumed that the molecules either were diamagnetic, e.g., N2, or paramagnetic doublets, e.g., NO. The calculations were extended to high density by invoking a modification of the Enksog theory for a dense gas of smooth spheres. The flux of internal angular momentum caused by a gradient of temperature has been computed.

Electric field Senftleben-Beenakker effects

The transport properties of a dilute gas of polar molecules in the presence of a static homogenous electric field are obtained using as a starting point a form of the Waldmann-Snider transport equation. This transport equation differs from the simpler form found for the magnetic field analogue because of the non-diagonality of the electric dipole moment operator, and hence of the density matrix, in the internal energy. A closed equation for the diagonal part alone is derived. There is a marked difference between the behaviour of symmetric top molecules and linear Σ-molecules: the changes in the transport coefficients due to the application of the electric field occur at much higher field values for the latter, which also have a functional dependence on E 2/ p rather than on E/ p as for symmetric top molecules. It is found that these Senftleben-Beenakker effects have, for linear molecules, saturation values very different from their magnetic field analogues while, for symmetric top molecules, the electric and magnetic saturation values coicide to a good approximation. Furthermore, a cross effect between the heat-flux vector and the pressure tensor occurs only in the case of symmetric top molecules.

On the Senftleben-Beenakker effect in mixtures: I. The magnetic field dependence of the shear viscosity tensor in mixtures of diamagnetic gases

The theory has been developed for the magnetic field dependence of the shear viscosity tensor of a dilute gas mixture consisting of linear diamagnetic molecules (Senftleben-Beenakker effect). For binary mixtures of diamagnetic and noble gases explicit expressions have been derived, which show that these mixtures offer interesting possibilities for the measurement of angular momentum reorientation cross sections for molecule-noble gas collisions.

The influence of angular momentum anisotropy on the heat conductivity of dilute diatomic gases

The influence of angular momentum anisotropy on the heat conductivity of a dilute gas consisting of diamagnetic linear molecules is investigated. By the use of a new technique to solve the expansion coefficients of the molecular distribution function it was possible to obtain a solution for this function which does not contain any further approximations than those implied by the choice of trial functions for this distribution function. Secondly it is clearly exhibited how angular momentum reorientation cross sections enter into the formalism when an external magnetic field is applied (Senftleben-Beenakker effect). In this way it was possible to obtain the value of one of these cross sections for CO and N 2 from the experimental results on this effect. Moreover it is pointed out how all cross sections entering into the formulae for the heat conductivity and viscosity of H 2 and D 2 can be obtained separately from the combined experimental results on both transport coefficients.