  We have derived and solved numerically the Boltzmann-Vlasov transport
equations that includes both two-body collisions and the chiral phase
transition by mean of NJL-field dynamics. The scope is to understand if the
field dynamics supply new genuine effects on the build-up of the elliptic flow
$v_2$, a measure of the asymmetry in the momentum space, and in particular if
it can affect the relation between $v_2$ and the shear viscosity to entropy
ratio $\eta/s$. Solving the transport equation with a constant cross section
for the condition of $Au+Au$ collisions at $\sqrt{s_{NN}}=200$ AGeV it is shown
a sizable suppression of $v_2$ due to the attractive nature of the field
dynamics that generates the constituent mass. However the key result is that if
$\eta/s$ of the system is kept fixed by an appropriate local renormalization of
the cross section the $v_2$ does not depend on the details of the collisional
and/or field dynamics and in particular it is not affected significantly by the
chiral phase transition.
