Time-Dependent Equation

The time-dependent behavior of the electro-diffusive system can be derived from conservation of mass. For a porous system with constant porosity φ, the rate change in concentration is proportional to the negative divergence of the bulk flux ${\bf j}^b_i$:

$$\phi\frac{\partial c_i}{\partial t} -\nabla\ \cdot {\bf j}^b_i \frac{D^s_i}{F} \nabla\cdot \left(1+\frac{\partial \ln\gamma_i}{\... ...abla c_i + \frac{{\cal F}}{RT} z_i \frac{D^s_i}{F} \nabla\cdot c_i \nabla\psi_D$$ = = (9)

This time-dependent equation and Eqn. 6 form a system of equations containing two variables (c and ψ_D) and two parameters (φ and F). Since the variables γ_i and ψ_D can be calculated from the physico-chemical properties of the electrolyte, the two parameters φ and F completely characterize the time-dependent behavior of systems with arbitrary speciation.

Characterizing the electro-diffusion transport by Eqn. 9 and Eqn. 6, which have the porosity and the formation factor as the only adjustable parameters, has great experimental advantages. The porosity of a cementitious material can be determined by a number of methods such as standardized test methods or mercury intrusion porosimetry. The formation factor can be determined from conductivity measurements [36] and pore extraction [37]. Therefore, it is conceivable that one could use appropriate transport equations to accurately predict the diffusive transport in a cementitious system without performing any diffusion measurements.