  In this letter we analyze the effects of an externally applied electric field
on thermal fluctuations for a fluid containing charged species. We show in
particular that the fluctuating Poisson-Nernst-Planck equations for charged
multispecies diffusion coupled with the fluctuating fluid momentum equation,
result in enhanced charge transport. Although this transport is advective in
nature, it can macroscopically be represented as electrodiffusion with
renormalized electric conductivity. We calculate the renormalized electric
conductivity by deriving and integrating the structure factor coefficients of
the fluctuating quantities and show that the renormalized electric conductivity
and diffusion coefficients are consistent although they originate from
different noise terms. In addition, the fluctuating hydrodynamics approach
recovers the electrophoretic and relaxation corrections obtained by
Debye-Huckel-Onsager theory, and provides a quantitative theory that predicts a
non-zero cross-diffusion Maxwell-Stefan coefficient that agrees well with
experimental measurements. Finally, we show that strong applied electric fields
result in anisotropically enhanced velocity fluctuations and reduced
fluctuations of salt concentrations.
