We present a calculation of eta/s for the meson gas (zero baryon number), with the viscosity computed within unitarized NLO chiral perturbation theory, and confirm the observation that eta/s decreases towards the possible phase transition to a quark-gluon plasma/liquid. The value is somewhat higher than previously estimated in LO chi PT. We also examine the case of atomic Argon gas to check the discontinuity of eta/s across a first order phase transition. Our results suggest employing this dimensionless number, sometimes called KSS number (in analogy with other ratios in fluid mechanics such as Reynolds number or Prandtl number) to pin down the phase transition and critical end point to a cross-over in strongly interacting nuclear matter between the hadron gas and quark and gluon plasma/liquid.

Comment: Revised for PRD. Shorter (by one section) than first version. 6 pp, 4 figures