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Updated: Jun 22, 2026
08:01
The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
Front propagation in a one-dimensional autocatalytic reaction-subdiffusion system.
H H Schmidt-Martens1, D Froemberg, I M Sokolov
1Institut für Physik, Humboldt-Universität zu Berlin, Newtonstrasse 15, 12489 Berlin, Germany.
Summary
This study numerically investigates an autocatalytic reaction on a lattice. We found that reaction front propagation failure is due to a stable form front moving at a time-decaying velocity.
Area of Science:
- Chemical kinetics
- Statistical physics
- Complex systems
Background:
- Autocatalytic reactions are fundamental in chemical and biological systems.
- Subdiffusion, characterized by power-law waiting times, affects reaction dynamics.
- Previous work indicated propagation failure in similar systems.
Purpose of the Study:
- To numerically investigate the autocatalytic irreversible reaction A+B-->2A.
- To analyze subdiffusive reactant behavior on a one-dimensional lattice.
- To elucidate the mechanism behind previously observed propagation failure.
Main Methods:
- Numerical simulations on a one-dimensional lattice.
- Modeling reactants with symmetric continuous-time random walks.
- Utilizing a power-law waiting time density function psi(t) ~ t^(-1-alpha), with 0
Main Results:
- The study confirms propagation failure under specific conditions.
- Identified that failure corresponds to the propagation of a stable form front.
- Observed that the front velocity decays over time.
Conclusions:
- The observed propagation failure is a consequence of a stable front's subdiffusive motion.
- The time-dependent velocity of this stable front dictates the overall reaction propagation.
- This finding provides insight into reaction dynamics in complex, subdiffusive environments.
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