Book contents
- Frontmatter
- Contents
- Contributors
- Preface
- Part I Reaction-Diffusion Systems and Models of Catalysis
- 1 Scaling theories of diffusion-controlled and ballistically controlled bimolecular reactions
- 2 The coalescence process, A + A → A, and the method of interparticle distribution functions
- 3 Critical phenomena at absorbing states
- Part II Kinetic Ising Models
- Part III Ordering, Coagulation, Phase Separation
- Part IV Random Adsorption and Relaxation Processes
- Part V Fluctuations in Particle and Surface Systems
- Part VI Diffusion and Transport in One Dimension
- Part VII Experimental Results
- Index
- Abbreviations
1 - Scaling theories of diffusion-controlled and ballistically controlled bimolecular reactions
Published online by Cambridge University Press: 18 December 2009
- Frontmatter
- Contents
- Contributors
- Preface
- Part I Reaction-Diffusion Systems and Models of Catalysis
- 1 Scaling theories of diffusion-controlled and ballistically controlled bimolecular reactions
- 2 The coalescence process, A + A → A, and the method of interparticle distribution functions
- 3 Critical phenomena at absorbing states
- Part II Kinetic Ising Models
- Part III Ordering, Coagulation, Phase Separation
- Part IV Random Adsorption and Relaxation Processes
- Part V Fluctuations in Particle and Surface Systems
- Part VI Diffusion and Transport in One Dimension
- Part VII Experimental Results
- Index
- Abbreviations
Summary
Basic features of the kinetics of diffusion-controlled two-species annihilation, A + B → 0, as well as that of single-species annihilation, A + A→ 0, and coalescence, A + A → A, under diffusion-controlled and ballistically controlled conditions, are reviewed in this chapter. For two-species annihilation, the basic mechanism that leads to the formation of a coarsening mosaic of A- and B-domains is described. Implications for the distribution of reactants are also discussed. For single-species annihilation, intriguing phenomena arise for ‘heterogeneous’ systems, where the mobilities (in the diffusion-controlled case) or the velocities (in the ballistically controlled case) of each ‘species’ are drawn from a distribution. For such systems, the concentrations of the different ‘species’ decay with time at different power-law rates. Scaling approaches account for many aspects of the kinetics. New phenomena associated with discrete initial velocity distributions and with mixed ballistic and diffusive reactant motion are discussed. A scaling approach is outlined to describe the kinetics of a ballistic coalescence process which models traffic on a single-lane road with no passing allowed.
Introduction
There are a number of interesting kinetic and geometric features associated with diffusion-controlled two-species annihilation, A + B → 0, and with single-species reactions, A + A → 0 and A + A → A, under diffusion-controlled and ballistically controlled conditions.
In two-species annihilation, there is a spontaneous symmetry breaking in which large-scale single-species heterogeneities form when the initial concentrations of the two species are equal and spatially uniform.
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- Publisher: Cambridge University PressPrint publication year: 1997
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