I will discuss a Banach spaces-based framework and new mixed finite element methods for the numerical solution of the coupled Stokes and Poisson-Nerns-Planck equations (a nonlinear model describing the dynamics of electrically charged incompressible fluids). The pseudostress tensor, the electric field (rescaled gradient of the potential) and total ionic fluxes are used as new mixed unknowns. The resulting fully mixed variational formulation consists of two saddle-point problems, each one with nonlinear source terms depending on the remaining unknowns, and a perturbed saddle-point problem with linear source terms, which is in turn additionally perturbed by a bilinear form. The well-posedness of the continuous formulation is a consequence of a fixed-point strategy in combination with the Banach theorem, the Babuska-Brezzi theory, the solvability of abstract perturbed saddle-point problems, and the Banach-Necas-Babuska theorem. An analogous approach (but using now both the Brouwer and Banach theorems and stability conditions on arbitrary FE subspaces) is employed at the discrete level. A priori error estimates are derived, and examples of discrete spaces that fit the theory, include, e.g., Raviart--Thomas elements along with piecewise polynomials. Finally, several numerical experiments confirm the theoretical error bounds and illustrate the balance-preserving properties and applicability of the proposed family of methods. This talk is based on joint work with Claudio I. Correa and Gabriel N. Gatica (from CI2MA, Concepcion).