Coefficients of viscosity for a fluid in a magnetic field or in a rotating system

Abstract

The linear equations between the elements of the viscous pressure tensor and the rates of deformation are investigated for the case of an isotropic fluid in an external magnetic field or for the equivalent case of a rotating fluid. Since these equations can be incorporated within the thermodynamics of irreversible processes, the Onsager reciprocity relations hold for the scheme of phenomenological coefficients.

For the present case the viscous behaviour is seen to be described by 8 coefficients between which one Onsager relation exists. The remaining 7 independent coefficients can be combined in a linear way so as to yield 5 coefficients of ordinary viscosity, the other 2 coefficients then describing the volume viscosity and a cross-effect between the ordinary and the volume viscosity, respectively. For the special case of vanishing volume viscosity the equations are compared with those derived from kinetic theory by Chapman and Cowling for an ionized gas in a magnetic field.