TY  - JOUR
A1  - Doerries, Timo J.
A1  - Chechkin, Aleksei
A1  - Schumer, Rina
A1  - Metzler, Ralf
T1  - Rate equations, spatial moments, and concentration profiles for mobile-immobile models with power-law and mixed waiting time distributions
T2  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - 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 geophysical contexts, but also in biological, soft matter, and solid state systems.
Y1  - 2022
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/63489
SN  - 2470-0045
SN  - 2470-0053
SN  - 2470-0061
VL  - 105
IS  - 1
PB  - The American Institute of Physics
CY  - Woodbury, NY
ER  -