Thermodynamics and bulk viscosity of approximate black hole duals to finite temperature quantum chromodynamics

We consider classes of translationally invariant black hole solutions whose equations of state closely resemble that of QCD at zero chemical potential. We use these backgrounds to compute the ratio ζ/s of bulk viscosity to entropy density. For a class of black holes that exhibits a first-order transition, we observe a sharp rise in ζ/s near Tc. For constructions that exhibit a smooth crossover, like QCD does, the rise in ζ/s is more modest. We conjecture that divergences in ζ/s for black hole horizons are related to extrema of the entropy density as a function of temperature.