Experimental evidence and theoretical analysis of anomalous diffusion during water infiltration in porous building materials

Abstract

The infiltration of liquid and the propagation of the moisture front in non-saturated porous media are generally described by a diffusion equation that predicts a scaling law of the type x/(t)1/2 in one dimension. This model, generally referred to as the theory of unsaturated flow, was systematically applied to account for water movements in porous building materials. In this paper, two sets of nuclear magnetic resonance (NMR) one-dimensional water absorption profiles, respectively measured in a fired-clay brick and a limestone specimen, are re-examined according to this model. The reinterpretation of the NMR absorption data provides evidence that the infiltration front does not propagate as t1/2 neither in brick nor in limestone, i.e. the absorption process does not conform to the predictions of the unsaturated flow theory in these materials. A new theoretical model for infiltration, based on the assumption of a non-Fickian diffusion mechanism, is thus introduced. The water transfer in partially saturated materials is assumed to follow the general nonlinear diffusion equation (∂θ/∂t)-(∂/∂x)[D(θ)(∂θ/∂x)n] = 0, with n real. For one-dimensional infiltration, the water content θ can be expressed in terms of the single variable ϕ* = xt-α, with α = 1/(n + 1) and the cumulative water infiltration I is given at any time by I = ∫θ0θ1x dθ = tα∫θ0θ1ϕ* dθ = S*tα. The NMR absorption data are shown to be compatible with a non-Fickian diffusion process scaling as t0.58 in brick and as t0.61 in the limestone specimen. The application of the new anomalous diffusion model to brick indicates that the previous t1/2 relation may underestimate the volume of absorbed water by about 30% after only 100 hours. This result has particular relevance for evaluating the durability of building structures.

A model for reactive porous transport during re-wetting of hardened concrete

“…We emphasize here that similar stalling behavior has been reported by several other authors performing experiments on porous building materials [43,32,35] although these authors attributed this behaviour to an anomalous diffusion mechanism. Our primary aim here has been to show that a similar phenomenon can arise from pore clogging caused by hydration of residual silicates in concrete.…”

Simulation of diffusion in a crowded environment

“…1 The illustration of the vector field representing attempts of molecular displacements towards neighboring lattice sites as assumed in the DLL model. The marked areas represent various local situations: (1) elements (yellow) try to move in the opposite direction (an unsuccessful attempt), (2) an attempt of motion starts from an element (violet) that when moved would not be replaced by any of its neighbors (an unsuccessful attempt), and (3) each green element replaces one of its neighbors (successful attempts).…”

Scaling relations in the diffusive infiltration in fractals

“…These features are observed in a large variety of systems, such as hydration of rocks, water or dye absorption in soils or rocks, injection of liquids in fractures or nanoporous solids, etc. In some cases, models of convective/advective motion and diffusion are studied in deterministic or randomized fractals [20][21][22][23][24][25][26][27]. However, in several other cases, diffusion is the dominant mechanism in the infiltration problem, which motivates the study of anomalous diffusion models and the study of the geometry of porous or fractured media [23,[28][29][30][31][32][33][34][35].…”