Normal diffusion in a medium connected to a subdiffusive medium with absorption.

Area of Science:

• Physics
• Physical Chemistry
• Chemical Engineering

Background:

• Normal diffusion describes particle movement in a uniform medium.
• Subdiffusion involves slower particle movement, often influenced by complex environments.
• Absorption is a process where particles are removed from the system.

Purpose of the Study:

• To develop a mathematical model for diffusion between a normal medium (A) and a subdiffusive medium (B) with absorption.
• To analyze the behavior of diffusing particles at the interface of these two media.
• To explore methods for detecting absorption in medium B using measurements solely from medium A.

Main Methods:

• A mathematical model was formulated combining normal diffusion in medium A with subdiffusion and absorption in medium B.
• The subdiffusion-absorption equation, featuring a fractional time derivative, was used to describe medium B.
• Specific boundary conditions were applied at the interface between medium A and medium B.
• Analytical solutions were derived for the diffusion equations.

Main Results:

• The model provides solutions describing particle concentration over time in both media.
• The presence and rate of absorption in medium B influence the concentration profiles in medium A.
• Distinct concentration patterns emerge depending on whether absorption is active in medium B.

Conclusions:

• The developed model accurately describes diffusion with absorption across different media types.
• Experimental determination of absorption in medium B is feasible by monitoring particle concentration in medium A.
• This work offers a framework for studying complex diffusion phenomena in heterogeneous systems.