  We present a detailed, two dimensional numerical study of the microphysical
conditions and dynamical evolution of accretion disks around black holes when
neutrino emission is the main source of cooling. Such structures are likely to
form after the gravitational collapse of massive rotating stellar cores, or the
coalescence of two compact objects in a binary (e.g., the Hulse--Taylor
system). The physical composition is determined self consistently by
considering two regimes: neutrino--opaque and neutrino--transparent, with a
detailed equation of state which takes into account neutronization, nuclear
statistical equilibrium of a gas of free nucleons and alpha particles,
blackbody radiation and a relativistic Fermi gas of arbitrary degeneracy.
Various neutrino emission processes are considered, with electron/positron
capture onto free nucleons providing the dominant contribution to the cooling
rate. We find that important temporal and spatial scales, related to the
optically thin/optically thick transition are present in the disk, and manifest
themselves clearly in the energy output in neutrinos. This transition produces
an inversion of the lepton gradient in the innermost regions of the flow which
drives convective motions, and affects the density and disk scale height radial
profiles. The electron fraction remains low in the region close to the black
hole, and if preserved in an outflow, could give rise to heavy element
nucleosynthesis. Our specific initial conditions arise from the binary merger
context, and so we explore the implications of our results for the production
of gamma ray bursts.
