InterPore2026

Quantifying the occurrences of anomalous diffusion through disordered porous structures of subsurface geomaterials

20 May 2026, 10:05

1h 30m

Poster Presentation (MS03) Flow, transport and mechanics in fractured porous media Poster

Speaker

Ashish Rajyaguru (TU Darmstadt)

Description

Chemical diffusion in disordered porous media plays a crucial role in various geochemical processes, including secondary mineral formation, dissolution kinetics, redox reactions, nutrient transport at root-soil interfaces, and interactions between solutes and charged surfaces. Therefore, a robust quantitative understanding of these processes is essential across multiple disciplines in geoscience and engineering. In this study, we present a unique experimental diffusion cell setup to investigate the Fickian diffusion limit in fully saturated disordered porous structures.
We present breakthrough curves (BTCs) for bromide diffusion across five distinct chalk and dolomite samples [1]. Our results reveal that during the initial phase of the experiments, the bromide tracer exhibits Fickian diffusion. However, as diffusion continues over time, the tails of the BTCs exhibit a transition from Fickian to anomalous diffusion. This research effectively clarifies the characteristics of anomalous (non-Fickian) diffusion, challenging the classical assumption that diffusion is solely Fickian in complex porous media.
Using the Continuous Time Random Walk (CTRW) framework, we provide spatial concentration profiles and temporal breakthrough curves that correlate with experimental data in cases where solute diffusion exhibits anomalous behavior [2, 3]. The robust mechanistic foundations of the CTRW framework enabled us to derive solutions to an associated fractional diffusion equation across a wide range of power law values, from nearly Fickian to highly anomalous diffusion behaviors. Notably, these solutions clearly distinguish between early-time Fickian and anomalous diffusion, with the differences becoming more pronounced over time. The observation that diffusion in natural rocks can exhibit distinct, potentially widespread anomalous behavior suggests that diffusion-driven processes in subsurface regions should be analyzed using methods that accommodate non-Fickian diffusion.