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First-encounter time of two diffusing particles in two- and three-dimensional confinement
F Le Vot1, S B Yuste1, E Abad2
1Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06071 Badajoz, Spain.
Physical Review. E
|May 20, 2022
Summary
Confinement drastically alters diffusing particle encounter times. Monte Carlo simulations reveal survival probability and first-encounter time dynamics in confined 2D/3D spaces, offering insights into particle interactions.
Area of Science:
- Statistical Physics
- Computational Physics
- Physical Chemistry
Background:
- Particle diffusion behavior is significantly altered by confinement effects.
- Understanding first-encounter time statistics is crucial for various physical and chemical processes.
Purpose of the Study:
- To investigate the impact of reflecting boundaries on the first-encounter time statistics of a two-particle system.
- To analyze survival probability S(t) and first-encounter time probability density H(t) in confined domains.
Main Methods:
- Utilized Monte Carlo simulations to model a two-particle system in 2D and 3D domains with reflecting boundaries.
- Analyzed survival probability S(t), first-encounter time density H(t), mean first-encounter time
, and decay time T.
Main Results:
- Derived empirical formulas for
and T, and an empirical lower bound tB for boundary deviation. - Found that for small particles,
is dominated by total diffusivity (D=D1+D2), unlike in 1D. - Identified weak dependence of subleading contributions to T on diffusivity ratio (D1/D2) in 2D.
Conclusions:
- Confinement significantly modifies first-encounter time statistics, with boundary effects becoming prominent over time.
- The dominant contribution to decay time T is linked to total diffusivity, offering a simplified model for confined systems.
- Provided insights into approximating mean first-encounter time
with decay time T under specific conditions.
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