Coupled Water and Salt Transport in Porous Materials: Rapid Determination of a Varying Diffusion Coefficient from Experimental Data

Abstract

A direct method for an accurate and rapid evaluation of a varying salt diffusion coefficient, \(D\), from experimental data is proposed for a coupled water and salt transport in porous materials. The evaluation uses data on the moisture and salt concentration profiles and is based on a formula obtained from the Boltzmann-Matano method. The coupled transport is described by the diffusion-advection model of Bear and Bachmat. A simple expression for \(D\) in the center of the concentration interval is deduced from the formula to provide a rapid estimate on \(D\). Possible extensions of this analytical approach are pointed out, suggesting that it can serve as a convenient general tool in engineering calculations. The theoretical results are applied to a laboratory experiment in which a coupled moisture and chloride transport had been investigated in a lime plaster, and the chloride diffusion coefficient had been obtained numerically in dependence on the chloride concentration. The agreement with the numerical results is shown to be rather good, except at low concentrations where our analytical results should be more reliable. It is also shown that the unusually high value of the calculated chloride diffusion coefficient—about three orders of magnitude higher than for free chloride ions in water—cannot be explained by possible inaccuracies in the measurements and/or numerical calculations. The reason is that changes in the measured profiles’ data could cause a change in \(D\) of just the same order of magnitude. This shows that, besides diffusion and advection, additional mechanisms take part in the considered chloride transport.