The single-valued diffusion coefficient for ionic diffusion through porous media

Abstract

The current literature on ionic diffusion through porous media teaches that the diffusion coefficient is a complicated function depending on concentration, concentration gradient, and electrical potential gradient. This paper documents how natural diffusion tests and migration tests (electrically enhanced transport) lead to the measurement of a unique diffusion coefficient for a given ionic species and a given material. Natural diffusion tests for chloride and a ceramic of TiO2 were implemented at two different concentration levels. The experiments were designed to emphasize the impact of the membrane potential in the pore solution on the chloride flux. By accounting for the membrane potential it is shown that the chloride diffusion coefficient is unique for a given material. An iterative method based on a numerical model solving the continuity equations and the current law is proposed to determine the diffusion coefficient. The approach is applied with success to published results on a cement-based material. Migration tests were also performed with chloride in a cementitious material, where the chloride transport is enhanced by an external electrical field. The experimental results reveal the competition between diffusion and electrical effects in the case of noncontaminated porous materials. By varying the electrical potential difference it is shown that the flux of chloride varies linearly with the electrical field, meaning that the chloride diffusion coefficient does not depend on the electrical field. The main conclusion is that there is only one chloride diffusion coefficient for a given porous material.

Determination of the transport properties of a blended concrete from its electrical properties measured during a migration test

“…Owing to the membrane potential a few seconds after the test has started the electrical field is no longer constant. This non-linearity of the electric field is due to the membrane potential gradient and it is equivalent to the liquid junction potential (Lorente et al, 2007) in a concrete migration test. Equation 3 shows the ionic and the membrane potentials for the electrical field.…”

“…In the references (Claisse and Beresford, 1997;Khitab et al, 2005;Krabbenhoft and Krabbenhoft, 2008;Lorente et al, 2007;Narsilio et al, 2007;Sugiyama et al, 2003;Truc et al, 2000) the Nernst-Planck equation has been used as the way to find the flux of ions and the transport properties of chlorides in concrete. Some researchers have used it coupled either to the conservation equation or accounting for the distribution and evolution of the electrical field.…”

Effect of the non-linear membrane potential on the migration of ionic species in concrete

“…The results of the experimental program were compared with these numerical simulations. The nonlinear behaviour of the electrical field during normal diffusion and migration has been reported previously by some researchers [4]- [5], [6], however, the authors are not aware of any experimental evidence for it.…”

“…The migration flux of species i is defined in equation 3 [12]. Equation 3where u i is the mobility of species i in the pore fluid [m 2 s −1 volt −1 ], z i is the electrical charge of specie i, F is the Faraday constant [9.65 x10 4 Coulomb/mol], and E is the electrical potential [V]. In the same way, the diffusion coefficient is proportional to the mobility of each ion [1].…”

Electrokinetic phenomena in microstructures

“…The velocity profile will change to a concave shape in the fully developed region when the Reynolds number is large. Lorente et al (2007) used two different kinds of experiments to calculate the diffusion coefficient through the porous media. In the first, the porous medium sample was subjected to a concentration gradient, while in the second an electric field was applied.…”