Temperature in ideal gas mixtures in Couette flow: A maximum-entropy approach

A binary mixture of ideal gases in Couette flow is studied in the framework of information theory. It is shown that if the total shear viscous pressure is imposed as a constraint, there is equipartition of energy between the different chemical species but not amongst the different spatial directions. In contrast, if a same shear rate is imposed on both species, there is no equipartition between species neither amongst spatial directions. In both situations, the thermodynamic temperature, defined from the Lagrange multiplier conjugated to the internal energy, is the same for both species, independently of the equality or not of their local-equilibrium temperature.