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

The infiltration of liquid and the propagation of the moisture front in non -saturated porous media are generally described by a diffusion equation tha t predicts a scaling law of the type x/(t)(1/2) in one dimension. This mode l, generally referred to as the theory of unsaturated flow, was systematica lly applied to account for water movements in porous building materials. In this paper, two sets of nuclear magnetic resonance (NMR) one-dimensional w ater absorption profiles, respectively measured in a fired-clay brick and a limestone specimen, are re-examined according to this model. The reinterpr etation of the NMR absorption data provides evidence that the infiltration front does not propagate as t(1/2) neither in brick nor in limestone, i.e. the absorption process does not conform to the predictions of the unsaturat ed flow theory in these materials. A new theoretical model for infiltration , based on the assumption of a non-Fickian diffusion mechanism, is thus int roduced. The water transfer in partially saturated materials is assumed to follow the general nonlinear diffusion equation (partial derivative theta/p artial derivativet) - (partial derivative/partial derivativex)[D(theta)(par tial derivative theta/partial derivativex)(n)] = 0, with n real. For one-di mensional infiltration, the water content 0 can be expressed in terms of th e single variable phi* = xt(-alpha), with alpha = 1/(n + 1) and the cumulat ive water infiltration I is given at any time by I integral (theta1)(theta0 ) x d theta = t(alpha) integral (theta1)(theta0) phi* d theta = S*t(alpha). The NMR absorption data are shown to be compatible with a non-Fickian diff usion process scaling as t(0.58) in brick and as t(0.61) in the limestone s pecimen. The application of the new anomalous diffusion model to brick indi cates that the previous t(1/2) relation may underestimate the volume of abs orbed water by about 30% after only 100 hours. This result has particular r elevance for evaluating the durability of building structures.