Anomalous Diffusion in Driven Electrolytes due to Hydrodynamic Fluctuations

The stochastic dynamics of tracers arising from hydrodynamic fluctuations in a driven electrolyte is studied using a self-consistent field-theory framework in all dimensions. A plethora of scaling behaviour that includes two distinct regimes of anomalous diffusion is found, and the crossovers between them are characterized in terms of the different tuning parameters. A short-time ballistic regime is found to be accessible beyond two dimensions, whereas a long-time diffusive regime is found to be present only at four dimensions and above. The results showcase how long-ranged hydrodynamic interactions can dominate the dynamics of non-equilibrium steady states in ionic suspensions and produce strong fluctuations despite the presence of Debye screening.