  The algebraic properties of drift-flux two-phase fluids models without
gravitational and wall friction forces are studied. More precisely, for the two
fluids we consider equation of states of polytropic gases. We perform a
classification scheme of the unknown parameters of the model such that to
determine all the possible admitted Lie symmetries. We find that in the most
general case the dynamical system of hyperbolic equations is invariant under
the action of a four dimensional Lie algebra, while the larger number of
admitted Lie symmetries is six. For each admitted Lie algebra the
one-dimensional optimal system is derived which is applied for the
determination of all the unique similarity transformations which lead to
similarity solutions. Our results are compared with that of previous studies
from where we see that most of the solutions presented in this study have not
found before in the literature.
