  In this paper, using the Gauge/gravity duality techniques, we explore the
hydrodynamic regime of a very special class of strongly coupled QFTs that come
up with an emerging UV length scale in the presence of a negative hyperscaling
violating exponent. The dual gravitational counterpart for these QFTs consists
of scalar dressed black brane solutions of exactly integrable Einstein-scalar
gravity model with Domain Wall (DW) asymptotics. In the first part of our
analysis we compute the $ R $-charge diffusion for the boundary theory and find
that (unlike the case for the pure $ AdS_{4} $ black branes) it scales quite
non trivially with the temperature. In the second part of our analysis, we
compute the $ \eta/s $ ratio both in the non extremal as well as in the
extremal limit of these special class of gauge theories and it turns out to be
eqaul to $ 1/4\pi $ in both the cases. These results therefore suggest that the
quantum critical systems in the presence of (negative) hyperscaling violation
at UV, might fall under a separate universality class as compared to those
conventional quantum critical systems with the usual $ AdS_4 $ duals.
