Decay Entropy Scaling of Radionuclide Intervention Efficacy in Unsaturated Soil Profiles: A Theoretical Model
Year: 2026
Type: article
Abstract: The relationship between radionuclide contamination depth and subsurface intervention efficacy remains theoretically unconstrained. Conventional intuition assumes monotonic efficacy decline with depth due to increased transport pathlength and attenuation. To derive a mathematically rigorous, falsifiable relationship between depth‑dependent decay entropy and intervention efficacy in unsaturated soils, explicitly challenging the depth‑inverse efficacy paradigm. A coupled advection‑dispersion‑decay model (1‑D semi‑infinite domain, constant water flux, homogeneous porous medium) is formulated with a novel decay entropy metric – defined as the Shannon entropy of the radionuclide age distribution at depth . The intervention (step reduction of surface source by fraction at yields a time‑integrated efficacy , where is the instantaneous relative concentration reduction. Using the Green’s function solution for a flux boundary and the age probability density (with ), we prove that . For fixed mean age, the integral decreases monotonically with increasing entropy . Consequently: where depends on . This predicts higher efficacy at greater depth because broader age distributions (higher ) increase the fraction of radionuclides with ages – i.e., those already affected by the source reduction. Deeper contamination () is more responsive to surface‑applied interventions (e.g., capping, phytoremediation, chemical injection) than shallower contamination – exactly opposing conventional wisdom. A complete experimental design is provided (Section 2.6): 20 soil cores to 1 m, sectioned every 10 cm; compute from ¹³⁷Cs activity profile (λ = 2.3×10⁻² yr⁻¹); apply surface source‑reduction treatment; monitor dissolved ¹³⁷Cs at 10, 30, 60, 90 cm depth for two years; test positive correlation between and . Negative or null correlation falsifies the model. Two Testable Policy‑Relevant Predictions: (1) Depth‑integrated radionuclide activity is a superior predictor of remediation success than surface activity (2) Decay entropy gradients can zone sites for intervention priority (highest → highest efficacy). A complete, mathematically explicit, falsifiable theoretical framework linking decay entropy to intervention efficacy in unsaturated soils.
Author: Monday Sunday Adiaha
Language: English
Subfield: Pollution
Field: Environmental Science
Domain: Physical Sciences
SDG: Life on land
Open Access status: hybrid
OpenAlex ID: W7214673872