  We propose a self-similar (SS) solution to hydrodynamic non-relativistic flow
behind a spherical strong blast wave (BW) passing through a homogeneous plasma
with efficient relativistic particle acceleration at the shock front. The flow
is described by an ideal two-fluid model with a relativistic component so that
the post-shock gas has an effective SS adiabatic index $ \gamma $ varying from
$ 5/3 $ to $ 4/3 $. This solution is calculated numerically and compared with
the standard Sedov solution. We find that the BW center in our solution is
dominated by the relativistic component with $ \gamma =4/3 $ for the divergence
of expansion there, and the relativistic component dominates the interior for a
moderate acceleration efficiency at the shock front. The overall efficiency of
relativistic particle acceleration can be enhanced by a factor of $ 2 $ due to
the slower adiabatic energy loss rate of the relativistic component during
expansion. Tendency of the dominance by the relativistic component may be
common in expanding astrophysical two-fluid systems such as supernova remnants,
lobes of radio galaxies.
