Transverse momentum transport in O2 gas under the influence of a magnetic field

Hulsman, H.; Burgmans, A.L.J.; Waasdijk, E.J. Van; Knaap, H.F.P.

doi:10.1016/0031-8914(70)90213-2

Cited by 19 publications

(4 citation statements)

References 9 publications

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“…Expressions similar to (24), (25) with (28), (30) have been obtained previously 12 for the Senftlebeneffect 13 of the paramagnetic gas 02 subject to approximations referred to as the "uncoupled model". Next, the dependence of em on the magnitude H of the magnetic field and on the number density n is considered.…”

Section: Km = *And(«)mentioning

confidence: 73%

Magnetic-field Induced Change of the Viscosity of Diamagnetic Gases with Anisotropic Magnetic Susceptibility

Hess

1975

Zeitschrift Für Naturforschung A

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The influence of a high magnetic field on the viscosity of diamagnetic gases of linear, symmetric and asymmetric top molecules is studied within the frame-work of the kinetic theory based on the Waldmann-Snider equation. The quadratic Zeeman effect associated with the anisotropic magnetic susceptibility is taken into account in addition to the usual linear Zeeman splitting.A viscous flow in a polyatomic gas gives rise to a collision-induced alignment of the molecular rotational angular momentum. The alignment, in turn, affects the value of the viscosity. Hence application of an external field has an influence on the transport coefficient if the alignment is appreciably altered by the field-induced motion of the rotational angular momentum of a molecule between two successive collisions. This phenomenon, known as the Senftleben-Beenakker effect 2 , has been studied extensively both experimentally and theoretically for gases of paramagnetic and diamagnetic linear and symmetric top molecules in the presence of a magnetic field 2 , and for polar gases of symmetric top molecules in the presence of an electric field 2 . If the relevant field Hamiltonian is of dipolar type (1st order Zeeman and Stark effects) the fieldinduced change of the transport coefficients depends on the magnitudes of the magnetic and electric fields H and E and on the pressure of the gas via H/P and E/P. Polar gases of linear ^-molecules in the presence of an electric field (2nd order Stark effect) where an E 2 /P dependence can be expected have been treated theoretically 3 but no measurements have been reported so far.In this note, theoretical expressions derived from the Waldmann-Snider equation 4 are presented for the magnetic-field-induced change of the viscosity of diamagnetic gases in the presence of strong magnetic fields. The quadratic (2nd order) Zeeman effect associated with the anisotropic molecular susceptibility is taken into account in addition to the usual linear (1st order) Zeeman effect. The quadratic term is of particular importance for heavier (organic) molecules 5 . Linear, symmetric and asymmetric top molecules are treated.Reprint requests to Dr. S. Hess, Institut für Theoretische Physik der Universität Erlangen-Nürnberg, D-8520 Erlangen, Glückstraße 6. Waldmann-Snider Equation and Field HamiltonianThe nonequilibrium state of a polyatomic gas is characterized by the distribution function (operator) f (t,X,p,J...) where p and hJ are the linear and rotational angular momenta and the dots stand for additional operators specifying the internal state of a molecule. The average ( W) of an operator W(p,J,.. The 2nd, 3rd and 4th term in Eq. (1) describe the change of due to the free flight, to the internal motion, and to the binary collisions of the molecules. For diamagnetic molecules in the presence of a strong magnetic field H = Hh(hh = l) the Hamiltonian can be written as 5 -C^hJ-hCzHzjihJJh (2) where 777 denotes the symmetric traceless part of a tensor. The coefficients Ct and C2 which, in general, depend on the internal quan...

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Section: Km = *And(«)mentioning

confidence: 73%

Magnetic-field Induced Change of the Viscosity of Diamagnetic Gases with Anisotropic Magnetic Susceptibility

Hess

1975

Zeitschrift Für Naturforschung A

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“…Also quite sensitive to the anisotropy are the transport property field-effect phenomena [32]. The analysis of measurements of this type is complicated by the 3E nature of the 02 molecule: a two-part structure has been observed [46] both for the shear viscosity and the thermal conductivity field-effects in pure 02. No measurements of the shear viscosity field-effects have been carried out for O2-Rg mixtures, and it is unlikely that they will be in the near future.…”

Section: Discussionmentioning

confidence: 99%

Classical trajectory calculation of transport and relaxation properties of O₂-He, Ne mixtures

1993

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Accurate classical trajectory calculations have been carried out to assess the quality of two O2-He and two O2-Ne potential energy surfaces. The four potential energy surfaces have been obtained originally from the inversion of molecular beam scattering data and a limited selection of transport property data. In all four cases the transport property data were analysed using the infinite-order sudden approximation for the scattering dynamics, combined with first Chapman-Cowling approximation expressions for the transport coefficients. The present analyses employ considerably more accurate classical trajectory calculations for the scattering dynamics, together with Chapman-Cowling second approximation expressions for the transport coefficients. The higher level of approximation is clearly seen to be necessary at the present level of comparison. Moreover, the present analyses also examine a number of relaxation and field-effect phenomena (which are very much more sensitive to the anisotropic nature of the potential energy surfaces than are the ordinary transport phenomena), including pressure-broadening of the magnetic dipole-allowed and rotational Raman spectral lines of 02. For each interaction only one of the two potential surfaces examined is found to agree well with all the non-equilibrium phenomena presently examined. For the O2-He interaction the potential of Faubel et al. and for the O2-Ne interaction, the potential of Beneventi et al. provide the best overall agreement with available experimental data. It is clear that the measurement of additional relaxation and field-effect phenomena for O2-He, Ne mixtures would be most useful for further delineation between proposed potential energy surfaces for these interactions.

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“…What would seem to be closest in spirit to the energy sudden approximation would be to calculate all velocity averages of the energy-dependent cross sections CT as if the j states are degenerate (so y ' = y) and to obtain the energy inelasticity from the differences in the j-state Boltzmann factors in the gain and loss terms. The result of this procedure can be written in the general form (40) [(2L + 1)(2Z + l ) ] " ' P ( Z , L )~X j ' j ( Z i + 1)(2j' + 1) x I with X y j given in this approximation as XgG = 2[[pi'/(2j'+ 1)]1/2 -kj/(2j + I ) ]~/~] = This method is labeled DG as being the closest to treating the j states as being degenerate (DG).…”

Section: (35)mentioning

confidence: 99%

Kinetic cross sections in the infinite order sudden approximation

Snider¹,

Coombe²

1982

J. Phys. Chem.

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The translational-internal coupling scheme allows a factorization of energy-dependent and kinetic cross sections into internal and translational parts. WKB-IOS phase shifts for the N2-Ar potential of Kistemaker and deVries are used to calculate the translational factors. A T-matrix version of the theory based on calculating only downward collisions is used as an attempt to lessen the effect of ignoring energy inelastic effects in the phase shift computation. All kinetic cross sections associated with the viscosity Senftleben-Beenakker effect are estimated in this manner. IntroductionThe computational efficiency of the infinite order sud-

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Transverse momentum transport in O2 gas under the influence of a magnetic field

Cited by 19 publications

References 9 publications

Magnetic-field Induced Change of the Viscosity of Diamagnetic Gases with Anisotropic Magnetic Susceptibility

Magnetic-field Induced Change of the Viscosity of Diamagnetic Gases with Anisotropic Magnetic Susceptibility

Classical trajectory calculation of transport and relaxation properties of O₂-He, Ne mixtures

Kinetic cross sections in the infinite order sudden approximation

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Transverse momentum transport in O2 gas under the influence of a magnetic field

Cited by 19 publications

References 9 publications

Magnetic-field Induced Change of the Viscosity of Diamagnetic Gases with Anisotropic Magnetic Susceptibility

Magnetic-field Induced Change of the Viscosity of Diamagnetic Gases with Anisotropic Magnetic Susceptibility

Classical trajectory calculation of transport and relaxation properties of O2-He, Ne mixtures

Kinetic cross sections in the infinite order sudden approximation

Contact Info

Product

Resources

About

Classical trajectory calculation of transport and relaxation properties of O₂-He, Ne mixtures