Journal
NEW JOURNAL OF PHYSICS
Volume 24, Issue 12, Pages -Publisher
IOP Publishing Ltd
DOI: 10.1088/1367-2630/aca70c
Keywords
diffusion; anomalous diffusion; breakthrough curves; constant boundary concentration
Categories
Funding
- German Research Foundation (DFG) [ME 1535/12-1]
- European Union [701647]
- Swiss Society of Friends of the Weizmann Institute of Science
- Crystal Family Foundation
- Estate of Claire Weiss
- P. & A. Guggenheim-Ascarelli Foundation
Ask authors/readers for more resources
In this study, we investigate the dynamics of the concentration profile in a one-dimensional, semi-infinite disordered system connected to a reservoir of tracer particles kept at constant concentration. By using the Montroll-Weiss equation and the fractional diffusion equation, we obtain analytical expressions for the concentration profile and derive the tracer flux and breakthrough curve. We demonstrate a long-time power-law behavior for the residual breakthrough curves and compare it with experimental measurements.
For an effectively one-dimensional, semi-infinite disordered system connected to a reservoir of tracer particles kept at constant concentration, we provide the dynamics of the concentration profile. Technically, we start with the Montroll-Weiss equation of a continuous time random walk with a scale-free waiting time density. From this we pass to a formulation in terms of the fractional diffusion equation for the concentration profile C(x, t) in a semi-infinite space for the boundary condition C(0, t) = C-0, using a subordination approach. From this we deduce the tracer flux and the so-called breakthrough curve (BTC) at a given distance from the tracer source. In particular, BTCs are routinely measured in geophysical contexts but are also of interest in single-particle tracking experiments. For the residual' BTCs, given by 1- P(x, t), we demonstrate a long-time power-law behaviour that can be compared conveniently to experimental measurements. For completeness we also derive expressions for the moments in this constant-concentration boundary condition.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available