Rate equations, spatial moments, and concentration profiles for mobile-immobile models with power-law and mixed waiting time distributions
- We present a framework for systems in which diffusion-advection transport of a tracer substance in a mobile zone is interrupted by trapping in an immobile zone. Our model unifies different model approaches based on distributed-order diffusion equations, exciton diffusion rate models, and random-walk models for multirate mobile-immobile mass transport. We study various forms for the trapping time dynamics and their effects on the tracer mass in the mobile zone. Moreover, we find the associated breakthrough curves, the tracer density at a fixed point in space as a function of time, and the mobile and immobile concentration profiles and the respective moments of the transport. Specifically, we derive explicit forms for the anomalous transport dynamics and an asymptotic power-law decay of the mobile mass for a Mittag-Leffler trapping time distribution. In our analysis we point out that even for exponential trapping time densities, transient anomalous transport is observed. Our results have direct applications in geophysicalWe present a framework for systems in which diffusion-advection transport of a tracer substance in a mobile zone is interrupted by trapping in an immobile zone. Our model unifies different model approaches based on distributed-order diffusion equations, exciton diffusion rate models, and random-walk models for multirate mobile-immobile mass transport. We study various forms for the trapping time dynamics and their effects on the tracer mass in the mobile zone. Moreover, we find the associated breakthrough curves, the tracer density at a fixed point in space as a function of time, and the mobile and immobile concentration profiles and the respective moments of the transport. Specifically, we derive explicit forms for the anomalous transport dynamics and an asymptotic power-law decay of the mobile mass for a Mittag-Leffler trapping time distribution. In our analysis we point out that even for exponential trapping time densities, transient anomalous transport is observed. Our results have direct applications in geophysical contexts, but also in biological, soft matter, and solid state systems.…
Author details: | Timo J. DoerriesORCiD, Aleksei ChechkinORCiDGND, Rina Schumer, Ralf MetzlerORCiDGND |
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DOI: | https://doi.org/10.1103/PhysRevE.105.014105 |
ISSN: | 2470-0045 |
ISSN: | 2470-0053 |
Pubmed ID: | https://pubmed.ncbi.nlm.nih.gov/35193292 |
Title of parent work (English): | Physical review : E, Statistical, nonlinear and soft matter physics |
Publisher: | The American Institute of Physics |
Place of publishing: | Woodbury, NY |
Publication type: | Article |
Language: | English |
Date of first publication: | 2022/01/04 |
Publication year: | 2022 |
Release date: | 2024/05/02 |
Volume: | 105 |
Issue: | 1 |
Article number: | 014105 |
Number of pages: | 24 |
Funding institution: | German Science Foundation [DFG ME 1535/12-1]; Foundation for Polish; Science (Fundacja na rzecz Nauki Polskiej); Polish National Agency for; Academic Exchange (NAWA) |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
Peer review: | Referiert |
External remark: | Erratum: https://www.doi.org/10.1103/PhysRevE.105.029901 |