  Jupiter's atmosphere has been observed to be depleted in helium (Yatm~0.24),
suggesting active helium sedimentation in the interior. This is accounted for
in standard Jupiter structure and evolution models through the assumption of an
outer, He-depleted envelope that is separated from the He-enriched deep
interior by a sharp boundary. Here we aim to develop a model for Jupiter's
inhomogeneous thermal evolution that relies on a more self-consistent
description of the internal profiles of He abundance, temperature, and heat
flux. We make use of recent numerical simulations on H/He demixing, and on
layered (LDD) and oscillatory (ODD) double diffusive convection, and assume an
idealized planet model composed of a H/He envelope and a massive core. A
general framework for the construction of interior models with He rain is
described. Despite, or perhaps because of, our simplifications made we find
that self-consistent models are rare. For instance, no model for ODD convection
is found. We modify the H/He phase diagram of Lorenzen et al. to reproduce
Jupiter's atmospheric helium abundance and examine evolution models as a
function of the LDD layer height, from those that prolong Jupiter's cooling
time to those that actually shorten it. Resulting models that meet the
luminosity constraint have layer heights of about 0.1-1 km, corresponding to
~10,-20,000 layers in the rain zone between ~1 and 3-4.5 Mbars. Present
limitations and directions for future work are discussed, such as the formation
and sinking of He droplets.
