Paradoxes of subdiffusive infiltration in disordered systems.

Area of Science:

• Physics
• Materials Science
• Physical Chemistry

Background:

• Particle diffusion between materials is common, occurring via normal or anomalous mechanisms.
• Anomalous diffusion exhibits unique behaviors not seen in normal diffusion.
• Understanding diffusion in disordered systems is crucial for many scientific fields.

Purpose of the Study:

• To investigate the non-local effects and drift against flow in anomalous diffusion.
• To model and explain the observed anomalous diffusion phenomena.
• To determine if this behavior is a general feature of diffusion in disordered systems.

Main Methods:

• Utilizing a continuous time random walk (CTRW) model.
• Solving diffusion equations derived from the CTRW model.
• Analyzing the quenched trap model for similar drift behaviors.

Main Results:

• Anomalous diffusion can lead to an averaged net drift in one direction, even if the net flow is opposite.
• This drift is independent of the medium's properties, indicating non-locality.
• Similar drift against flow was observed in the quenched trap model.

Conclusions:

• The observed drift against flow is a general characteristic of diffusion in disordered systems.
• Anomalous diffusion processes exhibit non-local properties.
• The CTRW model effectively describes these complex diffusion behaviors.