Predictive models for the flow behavior of porous media that consider the pressure gradient as a single driving force have been experimentally proven to be inadequate for fine-grained clays, specifically to over-predict their permeability. In order to extend to clays, the “water film scenario” is conventionally employed, where an immobile water layer with strong adhesion to the clay particle is considered, thus reducing the available flow passage and achieving an improved prediction of the permeability of clays. Instead, in this paper, it is used an electro-hydrodynamic approach to studying the flow behavior of clays, i.e., the pressure gradient and the induced electric potential gradient (IEPG) are combined to become multiple driving forces for various flows including the solution, the ion and the electric current fluxes. The Nernst-Planck (NP), the Navier-Stokes (NS), and the Poisson-Boltzmann (PB) are coupled to account for the ion migration, the fluid motion, and the electric potential distribution, respectively. The coupled NP-NS-PB equations are not simply modeled, but rather translated into a constitutive law that links these mentioned forces and flows, to be used for giving fundamental knowledge on the IEPG. The numerical investigation is conducted on the clay-KCl diluted system, and the main conclusions are (1) The Debye-Hückel approximation in the PB equation is not suitable for some types of clays with relatively high surface charge density; (2) The IEPG is caused by the electroneutrality requirement of the system, and is positively correlated to the separation of K+ / Cl− due to their differential in hydro-migratability; (3) The way the IEPG acts in the ion migration is decelerating the K+ and accelerating the Cl−, and that acts in the fluid motion is driving an opposite solution flux against the pressure gradient does; and (4) The IEPG is relevant and should be taken into account especially when lab-measurement of hydraulic conductivity on systems with dilute solution, low void fraction (nano-scale) and high surface charge density, otherwise the hydraulic conductivity will be significantly under-measured.