  We consider charged dilatonic black branes in AdS_5 and examine the effects
of perturbative higher derivative corrections on the ratio of shear viscosity
to entropy density eta/s of the dual plasma. The structure of eta/s is
controlled by the relative hierarchy between the two scales in the plasma, the
temperature and the chemical potential. In this model the background
near-horizon geometry interpolates between a Lifshitz-like brane at low
temperature, and an AdS brane at high temperatures -- with AdS asymptotics in
both cases. As a result, in this construction the viscosity to entropy ratio
flows as a function of temperature, from a value in the IR which is sensitive
to the dynamical exponent z, to the simple result expected for an AdS brane in
the UV. Coupling the scalar directly to the higher derivative terms generates
additional temperature dependence, and leads to a particularly interesting
structure for eta/s in the IR.
