ABSTRACT
Despite these advances, only recently the rigorous bridging between phenomena at the three dierent scales (nano-, micro-, and macroscales) has been accomplished by the authors (Murad and Moyne 2008). Historically, models to describe the electrical double layer (EDL) in nanopores have emerged from the Poisson-Boltzmann (PB) framework, which provides a systematic way for computing the local ionic concentration and electric potential proles (Achari et al. 1999, Hunter 1994, Van Olphen 1977). On the other hand, the development of macroscopic models has pursued a totally dierent approach, seated on the modied form of the eective stress principle coupled with hydrodynamics based on the generalized form of Darcy’s law and Nernst-Planck-based theories (Moyne and Murad 2006a,b). e correlation between the magnitude of the eective coecients and the local electric potential and ion distribution proles in the nanopores was only established recently by the authors (Moyne and Murad 2006a,b). Considering only monovalent ions (NaCl, KCl), the authors adopted the local PB description of the electric potential and ion distribution and upscaled their local picture considering swelling clay soil composed of two levels of porosity (nano-and micropores) (Murad and Moyne 2008). Substantial improvement was achieved within the multiscale description as the constitutive laws for the eective parameters, such as chemo-osmotic and electroosmotic permeabilities, eective diusivity, and swelling pressure, can be accurately reconstructed numerically exploring the local ionic proles provided by Poisson-Boltzmann framework.
