  In this paper we study bulk viscosity in a thermal QCD model with large
number of colors at two extreme limits: the very weak and the very strong 't
Hooft couplings. The weak coupling scenario is based on kinetic theory, and one
may go to the very strong coupling dynamics via an intermediate coupling
regime. Although the former has a clear description in terms of kinetic theory,
the intermediate coupling regime, which uses lattice results, suffers from
usual technical challenges that render an explicit determination of bulk
viscosity somewhat difficult. On the other hand, the very strong 't Hooft
coupling dynamics may be studied using string theories at both weak and strong
string couplings using gravity duals in type IIB as well as M-theory
respectively. In type IIB we provide the precise fluctuation modes of the
metric in the gravity dual responsible for bulk viscosity, compute the speed of
sound in the medium and analyze the ratio of the bulk to shear viscosities. In
M-theory, where we uplift the type IIA mirror dual of the UV complete type IIB
model, we study and compare both the bulk viscosity and the sound speed by
analyzing the quasi-normal modes in the system at strong IIA string coupling.
By deriving the spectral function, we show the consistency of our results both
for the actual values of the parameters involved as well for the bound on the
ratio of bulk to shear viscosities.
