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Advances in Mathematical Physics
Volume 2015 (2015), Article ID 307312, 6 pages
Research Article

Role of Time Relaxation in a One-Dimensional Diffusion-Advection Model of Water and Salt Transport

1Department of Materials Engineering and Chemistry, Faculty of Civil Engineering, Czech Technical University in Prague, Thakurova 7, 16629 Prague, Czech Republic
2Department of Physics, Constantine the Philosopher University, 94974 Nitra, Slovakia

Received 6 September 2015; Revised 2 November 2015; Accepted 8 November 2015

Academic Editor: Yao-Zhong Zhang

Copyright © 2015 Igor Medved’ and Robert Černý. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The transport of salt, necessarily coupled with the transport of water, through porous building materials may heavily limit their durability due to possible deterioration and structural damage. Usually, the binding of salt to the pore walls is assumed to occur instantly, as soon as the salt is transported by water to a given position. We consider the advection-diffusion model of the transport and generalize it to include possible delays in the binding. Applying the Boltzmann-Matano method, we calculate the diffusion coefficient of the salt in dependence on the salt concentration and show that it increases with the rate of binding. We apply our results to an example of the chloride transport in a lime plaster.