  We discuss the effect of chemical separation as matter freezes at the base of
the ocean of an accreting neutron star, and the subsequent enrichment of the
ocean in light elements and inward transport of heat through convective mixing.
We extend the steady-state results of Medin & Cumming 2011 to transiently
accreting neutron stars, by considering the time-dependent cases of heating
during accretion outbursts and cooling during quiescence. Convective mixing is
extremely efficient, flattening the composition profile in about one convective
turnover time (weeks to months at the base of the ocean). During accretion
outbursts, inward heat transport has only a small effect on the temperature
profile in the outer layers until the ocean is strongly enriched in light
elements, a process that takes hundreds of years to complete. During
quiescence, however, inward heat transport rapidly cools the outer layers of
the ocean while keeping the inner layers hot. We find that this leads to a
sharp drop in surface emission at around a week followed by a gradual recovery
as cooling becomes dominated by the crust. Such a dip should be observable in
the light curves of these neutron star transients, if enough data is taken at a
few days to a month after the end of accretion. If such a dip is definitively
observed, it will provide strong constraints on the chemical composition of the
ocean and outer crust.
