Coupled Diffusive Transport

Historically, ionic transport in cementitious systems has been characterized by Fick's law of diffusive transport [9]. The flux j_i of the i-th ionic species is proportional to the gradient in the amount-of-substance concentration c_i of that species, with the proportionality being the apparent diffusion coefficient D ^a_i of that species[15]:

$${\bf j}_i = -D^a_i \nabla c_i$$ (1)

(Vector quantities are denoted in bold type face.) For concentrated electrolytes, this equation quickly becomes inadequate due to ion-ion interactions. One method to address this is to use a tensor diffusion coefficient [16] so that ion-ion effects are incorporated in a empirical manner. Unfortunately, this requires extensive experimental data before one can apply this approach.

An alternative approach is to incorporate the ion-ion interactions at a fundamental level so that one directly calculates the effects of having other species present. Fortunately, this can be achieved in a relatively straightforward manner. The electro-diffusion equation as a model for the transport of ionic species has been used in solid-state systems [8], biological systems [17,18], and cementitious systems [4,5,19,20,21,22]. While it has been used to successfully characterize observed transport in cement and concrete systems, it is also useful for systematic studies of transport in nonreactive porous systems. As such, it is a powerful investigative tool for answering "what if" questions. Here, a systematic test of its applicability to porous systems is undertaken.

The electro-diffusion equation is formulated first for a bulk electrolyte. From this equation, the equation for a porous material is formulated using the principles of volume averaging over a representative elemental volume (REV) [23].