Hydrodynamic escape

We saw earlier that only light atoms can escape in significant amounts by Jeans' escape mechanism from the atmospheres of Titan and Triton. However, if the flux of light atoms is large then heavier atoms may also be driven off by "blowoff" (Chamberlain and Hunten, 1987). Substituting the empirical expression for the diffusion coefficient (Equation 3.14) into the diffusion equation (Equation 3.17) we have b( 1 dnt 11 dT\

where b is the empirical binary collision parameter. This equation may be rearranged to give dz = ^ b + h + Tdz) (33)

This equation assumes that the individual gases may be treated separately. However if two gases are considered, moving with different fluxes of, respectively, and then their combined diffusion equations, ignoring the dT/dz terms which are found to be negligible (Chamberlain and Hunten, 1987), are dn1 n1 1 , , , .

dn2 n2 1 "dz" ="H2 + b (n2" n1&2)-

With a bit of manipulation the flux of the heavier gas of mass M2, blown by a flux of lighter gas molecules of mass M1 may be shown to be f" , (Mc - MA

where fn is the mole fraction of component n and kT


is called the crossover mass and represents the heaviest species that can be removed in this way. This effect is clearly negligible in the giant planet atmospheres since the Jeans' flux of even the lightest atom hydrogen is so low.

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