  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 zeta/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 zeta/s near T_c. For constructions that exhibit a
smooth cross-over, like QCD does, the rise in zeta/s is more modest. We
conjecture that divergences in zeta/s for black hole horizons are related to
extrema of the entropy density as a function of temperature.
