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Updated: May 22, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

Reaction-diffusion process driven by a localized source: first-passage properties.

P L Krapivsky1

  • 1Department of Physics, Boston University, Boston, Massachusetts 02215, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 17, 2012
PubMed
Summary
This summary is machine-generated.

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This study models atom reactions, finding survival probability depends on dimension. Diffusing atoms survive indefinitely in 1D, decay algebraically in 2D, and exponentially in 3D.

Area of Science:

  • Chemical Physics
  • Statistical Mechanics
  • Mathematical Biology

Background:

  • Reaction-diffusion systems are fundamental to many physical and biological processes.
  • Understanding molecular formation kinetics is crucial for predicting system behavior.
  • The spatial dimensionality significantly impacts emergent phenomena in diffusion-controlled reactions.

Purpose of the Study:

  • To analyze the survival probability of diffusing atoms in a reaction-diffusion process.
  • To investigate the influence of spatial dimensionality on molecular formation and atom survival.
  • To characterize the asymptotic behavior of the molecular cloud radius and atom survival probability.

Main Methods:

  • Mathematical modeling of a two-species reaction-diffusion system.

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  • Analytical solutions and asymptotic analysis in different spatial dimensions (d=1, 2, 3).
  • Investigation of the survival probability function and its dependence on time and system parameters.

    • Main Results:

    • The molecular cloud radius grows as t^(1/d) in d≥2 dimensions.
    • Survival probability saturates in 1D.
    • Algebraic decay in 2D (exponent depends on flux) and stretched exponential decay in 3D.

    Conclusions:

    • Spatial dimensionality critically determines the long-term fate of diffusing species in reaction-diffusion systems.
    • The model provides insights into processes like aggregation and pattern formation.
    • The distinct survival behaviors highlight the importance of dimensionality in reaction-diffusion dynamics.