  We study the long-wavelength effective description of two general classes of
charged dilatonic (asymptotically flat) black p-branes including D/NS/M-branes
in ten and eleven dimensional supergravity. In particular, we consider
gravitational brane solutions in a hydrodynamic derivative expansion (to first
order) for arbitrary dilaton coupling and for general brane and co-dimension
and determine their effective electro-fluid-dynamic descriptions by exacting
the characterizing transport coefficients. We also investigate the stability
properties of the corresponding hydrodynamic systems by analyzing their
response to small long-wavelength perturbations. For branes carrying unsmeared
charge, we find that in a certain regime of parameter space there exists a
branch of stable charged configurations. This is in accordance with the
expectation that D/NS/M-branes have stable configurations, except for the D5,
D6, and NS5. In contrast, we find that Maxwell charged brane configurations are
Gregory-Laflamme unstable independently of the charge and, in particular,
verify that smeared configurations of D0-branes are unstable. Finally, we
provide a modification to the mapping presented in arxiv:1211.2815 and utilize
it to provide a non-trivial cross-check on a certain subset of our transport
coefficients with the results of arXiv:1110.2320.
