Comparative Evolution of Jupiter and Saturn
  We present evolutionary sequences for Jupiter and Saturn, based on new nongray model atmospheres, which take into account the evolution of the solar luminosity and partitioning of dense components to deeper layers. The results are used to set limits on the extent to which possible interior phase separation of hydrogen and helium may have progressed in the two planets. When combined with static models constrained by the gravity field, our evolutionary calculations constrain the helium mass fraction in Jupiter to be between 0.20 and 0.27, relative to total hydrogen and helium. This is in agreement with the Galileo determination. The helium mass fraction in Saturn's atmosphere lies between 0.11 and 0.25, higher than the Voyager determination. Based on the discrepancy between the Galileo and Voyager results for Jupiter, and our models, we predict that Cassini measurements will yield a higher atmospheric helium mass fraction for Saturn relative to the Voyager value. 
W.B. Hubbard, T. Guillot, M.S. Marley, A. Burrows, J.I. Lunine, and   D.S. Saumon