Formulation of molecular diffusion in planetary atmospheres

Abstract

We report on a formulation of molecular diffusion for ionized multi-component atmospheres that is valid in the diffusion and small electron mass limits. The formulation is based on the construction of successive approximations of the diffusion matrix by means of the projective iterative algorithm of Ern and Giovangigli [Projected iterative algorithms with application to multicomponent transport. Lin. Alg. and its Appl. 250, 289–315], and allows naturally for different temperatures for the neutral, ion and electron constituents of the gas. The reported expressions incorporate the effect of electric forces preventing charge separation, are explicit in the driving forces and mass conservative. Yet approximate, their accuracy can be easily tested and improved upon by going to a higher approximation of the diffusion matrix. We have illustrated the formulation with a model that solves the composition of Mars’ atmosphere. The continuity equations of the model are linearized and marched in time with an implicit numerical scheme, allowing thus for large time steps. It is found that the first and second approximations of the diffusion matrix are probably optimal trade-offs between computational cost and accuracy. Finally, the formulation is tested against more conventional approximations of the molecular diffusion velocities of neutral and ion species, showing the importance of the various assumptions that may restrict their applicability.