  A popular hypothesis that explains the anomalies of supercooled water is the
existence of a metastable liquid-liquid transition hidden below the line of
homogeneous nucleation. If this transition exists and if it is terminated by a
critical point, the addition of a solute should generate a line of
liquid-liquid critical points emanating from the critical point of pure
metastable water. We have analyzed thermodynamic consequences of this scenario.
In particular, we consider the behavior of two systems, H2O-NaCl and
H2O-glycerol. We find the behavior of the heat capacity in supercooled aqueous
solutions of NaCl, as reported by Archer and Carter, to be consistent with the
presence of the metastable liquid-liquid transition. We suggest an
interpretation of the liquid-liquid transition in aqueous solutions of
glycerol, recently observed by Murata and Tanaka, elucidating the non-conserved
nature of the order parameter, its coupling with density and concentration, and
the peculiarity of "spinodal decomposition without phase separation". We also
show how the shape of the critical line in a solution controls the difference
in concentration of the coexisting liquid phases.
