A time-variant diffusion model combining Fick’s law and time-fractional dynamics and its validation and linear evolution during drying of porous media

Moisture transport during drying in porous media often exhibits anomalous diffusion that deviates from Fick’s laws. While time-fractional models effectively capture these anomalies, their fractional diffusion coefficient, Dα, possesses a nonstandard dimension (m2/sα) that obscures its physical meaning and precludes the direct comparison of intrinsic diffusivity across materials. In this study, an anomalous diffusion factor K (t) varying with time is introduced, which integrates the memory effect of time-fractional calculus into a Fickian framework, restoring the standard diffusion dimension (m2/s). This hybrid model is validated against drying experiments from five porous biomaterials. A key discovery is the universal linear evolution of K(t) (K(t) ≈ kt + b) across all materials tested. The slope k emerges as a novel physical descriptor: its sign classifies sub-diffusion (k < 0) or super-diffusion (k > 0), while its magnitude quantitatively gauges the deviation from Fickian behavior (|k|→0). For radiata pine at 90 °C, K(t) in the longitudinal direction ranges from 2.37 × 10⁻⁹ to 1.92 × 10⁻⁸ m²/s, consistent with thermally enhanced transport. This study establishes a new paradigm for the mechanistic quantification of moisture transport in complex porous media and enhances the understanding of coupled heat and mass transfer in such media, particularly in the context of non-Fickian transport under thermal gradients.