Experimental evidence and theoretical analysis of anomalous diffusion during water infiltration in porous building materials
Bibliographic record
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 t 1/2 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 = ∫ θ 0 θ 1 x dθ = t α ∫ θ 0 θ 1 ϕ* dθ = S * t α . The NMR absorption data are shown to be compatible with a non-Fickian diffusion process scaling as t 0.58 in brick and as t 0.61 in the limestone specimen. The application of the new anomalous diffusion model to brick indicates that the previous t 1/2 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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".