3 evolut ion of the collision is based on the use of the ther- modyn amical relation sT = ϵ + nT that shift the problem to the evaluation of ϵ, n, T . These are easily calculated analyt ically (as for Fig.1) but also numerically summing up the number of the test particles and their energy in each α − cell. To evaluate the temperature we exploit the general formula for a massive gas: e M = 3 z + K 1 ( z ) K 2 ( z ) (7) 0.5 1 1.5 2 T/T$_{C}$ 0 0.5 1 1.5 2 2.5 3 3.5 ( -3P)/T 4 Buballa Ratti Abada 0.8 1 1.2 1.4 1.6 T/T$_{C}$ 0.01 0.1 1 /s ,$^{ζ}$ /s 4 s=1 s ,  =10 mb - NJL s ,  =10 mb s ,  =10 mb - NJL s , 4 s=1 - NJL FIG. 1: Left: Interaction measure shown as a function of temperature T for three different NJL parameter sets. Right: The η/s and ζ/s for the Buballa parametrization as a function of T for various cases as indicated in the legend. NJL parameterizations. Quantitatively the QCD behav- ior is correctly reproduced. In the following we will use the Buballa parametrization that gives the largest values closer to lQCD where however the peak is found to be about a factor two larger at T$_{c}$ . This means that the numerical results on the impact of the mean field in the dynamics of RHIC collisions is reduced respect to a more realistic case. Our final goal is to study a fluid at fixed shear viscosity to entropy ratio η/s extending the study started at cas- cade level [10, 11]. There the strategy was to normalize locally the cross section in order to fix the η/s according to the simple relation σ · η/s = < p > / 15 n valid for a massless gas. Here because of the NJL field the particles acquire a mass hence both the viscosity and the entropy density are modified respect to the simple massless case. We briefly discuss the η and s for a system of massive particles deriving the pertinent formula to renormalize the cross section σ in order to keep fixed locally the η/s . Both η and s have been derived for a thermodynamical system and has been studied also for the case of the NJL model [31]. Here we derive expressions in terms of quanti- ties that can be used easily also in the numerical solution of the transport equations. A widely used formula for η is deduced from the relaxation time approximation, like in Ref.[31]. After integration by parts it is possible to write the shear viscosity for the general case of massive relativistic particles in terms of average quantities that can be easily evaluated numerically: where τ = [ n 〈 σ$_{tr}$v$_{rel}$ 〉] − 1 is the relaxation time, i.e. the time interval between two collisions, and n is the total local density. One can easily see that in the ultra- relativistic limit ( M → 0) the well known formula for the shear viscosity, η = 4 15 〈 p 〉 /σ$_{tr}$ , is recovered. The entropy density cannot be related simply to the local density, s ∼ 4 n , as for the massless case. A suit- able method to evaluate locally s during the dynamical η = τ n 15 [ 4 〈 p 2 E 〉 + M 2 〈 p 2 E 3 〉 ] (6) σ$_{tr,α}$ = 1 15 T$_{α}$ 〈 v$_{rel}$ 〉 4 〈 p $^{2}$/E 〉 α + M 2 α 〈 p $^{2}$/E$^{3}$〉 α ( ϵ$_{α}$ + n$_{α}$T$_{α}$ ) η/s (8) with e the energy per particle, ϵ/n , and K$_{n}$ ( z ) the modified Bessel functions of the second kind, z = M T . We know e and M directly from the code hence we can use Eq.(7) to extract z = M T and therefore the temper- ature. We have checked that the procedure works well performing calculation in a box with particles distributed according to a Boltzmann equilibrium distribution. The behavior of η/s for a thermodynamical system is shown in Fig.1 (right) for a massless free gas (dashed line) and for the NJL (solid line). In both cases the cross sec- tion is fixed to σ = 10 mb . The dot-dashed line indicates the lower bound for η/s . We see that with a constant cross section σ = 10 mb the η/s is even lower than the 1 / 4 π at high T . The lower light lines show the behavior of bulk viscosity to entropy ratio ζ/s in the NJL model for two cases one with σ = 10 mb (green solid line) as above and the other for an η/s fixed at the 1 / 4 π value (dot- dashed line). Of course for the massless case the bulk viscosity is zero, while for non-vanishing masses there is a link between the η and ζ through the relaxation time τ . The last results in a smaller growth of ζ/s when η/s is fixed respect to the case when σ$_{tr}$ is fixed. However in both cases we can see that only at T < 1 . 1 T$_{c}$ we have a non-vanishing ζ/s . This is due to the fact that the ζ is expected to be proportional to the deviation of the sound velocity from 1 / 3, ( c 2 s − 1 / 3) 2 that in the NJL model is known to occur only very close to T$_{c}$ . More importantly for our purposes is that in the NJL the ζ/s remains order of magnitudes lower that first extrapolation from lQCD [32] and also much lower than the smaller values used for first studies with viscous hydrodynamics [19]. Consider- ing that even for much larger values of ζ/s hydrodynam- ics show a small effect, we can judge safe to discard any role of ζ/s in the following results for the elliptic flow. We notice that Eqs.(6) and (7) supply the formula for the normalization of the cross section in each α − cell in order to keep fixed η/s of the system: for a massless gas M → 0 ( p = E, ϵ ∼ 3 nT ) and Eq.(8) reduce to the simple relation σ$_{tr,α}$ = 4 π 15 < p >$_{α}$ /n$_{α}$ used in Ref.s[10, 11, 14, 33] for η/s = 1 / 4 π . Eq.(8) will allow to extend such studies of a fluid at finite viscosity to the case of partons with finite mass. Elliptic Flow - We have run the simulations for Au + Au at √ s$_{NN}$ = 200 AGeV and b = 7 fm . The density dis- tribution in coordinate space is given by the standard