Multiscale Mathematical Modelling of Anomalous Transport and Structural Heterogeneity in Complex Porous Materials

Predicting solute migration through complex porous materials requires a representation of how microscopic geometry, connected pathways, and slow exchange domains influence measurable transport over several scales. Conventional continuum models can be effective when sufficient averaging occurs, yet persistent velocity correlations, storage in weakly swept volumes, and structural transitions may produce early breakthrough, asymmetrical spreading, or prolonged late release. This conceptual and comparative study examines the relationship between pore connectivity, mesoscopic heterogeneity, and mathematical descriptions of non-Fickian motion. It contrasts local advection–dispersion models, heterogeneous continua, multirate mass transfer, continuous-time random walks, spatially fractional formulations, and correlated-velocity descriptions, emphasizing the physical interpretation and identifiability of their assumptions. A scale-aware framework is developed for selecting structural measurements, constructing model hierarchies, and designing validation experiments that distinguish competing mechanisms. Particular attention is paid to observation support, boundary effects, mass preservation, uncertainty propagation, and the difference between plume spreading and molecular mixing. Rather than reporting unperformed numerical experiments, the article synthesizes established theoretical and experimental literature to identify circumstances in which reduced mathematical models can support defensible predictions beyond their calibration conditions. The analysis indicates that predictive value depends less on formal mathematical complexity than on preserving the transport mechanisms relevant to the intended spatial scale, temporal horizon, and observable.