# Interfacial Reaction Kinetics

Source: [Interfacial Reaction Kinetics](<https://www.sota2.com/research/paper/68fa1eae7a2b558e29323ec5>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-23T15:34:10.627Z

Authors: Ben O'Shaughnessy, Dimitrios Vavylonis (2) \_\_INSTITUTION\_2\_\_ Dept Chemical Engineering, Columbia Univ (2) Dept Physics, Columbia Univ)

Published: 1998-07-08T06:14:03.000Z

## Abstract

We study irreversible A-B reaction kinetics at a fixed interface separating two immiscible bulk phases, A and B. We consider general dynamical exponent $z$, where $x\_t\\sim t^{1/z}$ is the rms diffusion distance after time $t$. At short times the number of reactions per unit area, $R\_t$, is {\\em 2nd order} in the far-field reactant densities $n\_A^{\\infty},n\_B^{\\infty}$. For spatial dimensions $d$ above a critical value $d\_c=z-1$, simple mean field (MF) kinetics pertain, $R\_t\\sim Q\_b t n\_A^{\\infty} n\_B^{\\infty}$ where $Q\_b$ is the local reactivity. For low dimensions $d\<d\_c$, this MF regime is followed by 2nd order diffusion controlled (DC) kinetics, $R\_t \\approx x\_t^{d+1} n\_A^{\\infty} n\_B^{\\infty}$, provided $Q\_b \> Q\_b^\* \\sim (n\_B^{\\infty})^{\[z-(d+1)\]/d}$. Logarithmic corrections arise in marginal cases. At long times, a cross-over to {\\em 1st order} DC kinetics occurs: $R\_t \\approx x\_t n\_A^{\\infty}$. A density depletion hole grows on the more dilute A side. In the symmetric case ($n\_A^{\\infty}=n\_B^{\\infty}$), when $d\<d\_c$ the long time decay of the interfacial reactant density, $n\_A^s$, is determined by fluctuations in the initial reactant distribution, giving $n\_A^s \\sim t^{-d/(2z)}$. Correspondingly, A-rich and B-rich regions develop at the interface analogously to the segregation effects established by other authors for the bulk reaction $A+B\\to\\emptyset$. For $d\>d\_c$ fluctuations are unimportant: local mean field theory applies at the interface (joint density distribution approximating the product of A and B densities) and $n\_A^s \\sim t^{(1-z)/(2z)}$. We apply our results to simple molecules (Fickian diffusion, $z=2$) and to several models of short-time polymer diffusion ($z\>2$).

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/9807110>)

[PDF](<https://arxiv.org/pdf/cond-mat/9807110.pdf>)