  Recent Monte Carlo plasma simulations to study in crystallizing carbon-oxygen
(CO) white dwarfs (WDs) the phase separation of Ne22 (the most abundant metal
after carbon and oxygen) have shown that, under the right conditions, a
distillation process that transports Ne22 toward the WD centre is efficient and
releases a considerable amount of gravitational energy that can lead to cooling
delays of up to several Gyr. Here we present the first CO WD stellar evolution
models that self-consistently include the effect of neon distillation, and
cover the full range of CO WD masses, for a progenitor metallicity twice-solar
appropriate for the old open cluster NGC 6791. The old age (about 8.5 Gyr) and
high metallicity of this cluster -- hence the high neon content (about 3% by
mass) in the cores of its WDs -- maximize the effect of neon distillation in
the models to be compared with the observed cooling sequence. We discuss the
effect of distillation on the internal chemical stratification and cooling time
of the models, confirming that distillation causes cooling delays up to several
Gyr, that depend in a non-monotonic way on the mass. We also show how our
models produce luminosity functions (LFs) that can match the faint end of the
observed WD LF in NGC 6791, for ages consistent with the range determined from
a sample of cluster's eclipsing binary stars, and the main sequence turn-off.
Without the inclusion of distillation the theoretical WD cooling sequences
reach too faint magnitudes compared to the observations. We also propose James
Webb Space Telescope observations that can independently demonstrate the
efficiency of neon distillation in the interiors of NGC 6791 WDs, and help
resolve the current uncertainty on the treatment of the electron conduction
opacities for the hydrogen-helium envelope of the WD models.
