  We present a detailed study of isospin dynamics in peripheral collisions at
Fermi energies. We consider symmetric and mixed collisions of (124,112)Sn
isotopes at 35 and 50 AMeV to study the isospin transport between the different
reaction components (residues, gas and possibly intermediate mass fragments)
and, in particular, the charge equilibration in the mixed system. We evaluate
the effects of drift terms due to asymmetry and density gradients, which are
directly related to the poorly known value and slope of the symmetry energy
below saturation density. We verify the importance of an isoscalar momentum
dependence of the mean field, which is found to influence the isospin transport
since it changes the reaction times. We finally suggest two observables
particularly sensitive to the isovector part of the nuclear equation-of-state:
the correlation between isospin equilibration and kinetic energy loss for
binary events, and the isospin content of the produced mid-rapidity fragments
for neck fragmentation events.
