We consider the large deviations for two-time scale stochastic electrokinetic flow in a smooth bounded domain \(\mathcal {D}\) , modelled by a slow component which is a stochastic Nernst-Planck-Navier-Stokes system perturbed by multiplicative noise and equipped with a blocking boundary conditions for ionic species concentrations and a fast component. The existence and uniqueness of global pathwise solution to the stochastic controlled system are proved, then the large deviations is built using the weak convergence method and time discretization technique. As an application, we investigate the exit problem.
