DOI: 10.1063/1.454474. Diffusion-controlled reactions: Mathematical formulation, variational principles, and rigorous bounds

Diffusion-controlled reactions: Mathematical formulation, variational principles, and rigorous bounds

10.1063/1.454474

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

This paper is concerned with the problem of predicting the effective rate constant k associated with diffusion-controlled reactions in media composed of static and reactive traps (sinks) which are generally distributed randomly throughout a region containing reactive particles. The effective equation for diffusion-controlled reactions is derived using the method of homogenization. This leads to a rigorous definition of k. General variational principles are then formulated to obtain rigorous upper and lower bounds on k. These variational principles are applied by evaluating them for three different types of admissible fields. The upper and lower bounds which result are computed for both random and periodic arrays of equisized spherical sinks.

Bibliography

Rubinstein, J., & Torquato, S. (1988). Diffusion-controlled reactions: Mathematical formulation, variational principles, and rigorous bounds. The Journal of Chemical Physics, 88(10), 6372â6380.

Authors 2

Jacob Rubinstein (first)
S. Torquato (additional)

References 32 Referenced 90

10.1146/annurev.pc.34.100183.002425 / Annu. Rev. Phys. Chem. (1983)
{'key': '2024021006030918000_r2', 'first-page': '557', 'volume': '17', 'year': '1916', 'journal-title': 'Phys. Z.'} / Phys. Z. (1916)
10.1063/1.432087 / J. Chem. Phys. (1976)
10.1016/0378-4371(87)90053-7 / Physica A (1987)
10.1016/0378-4371(85)90097-4 / Physica A (1985)
10.1063/1.443249 / J. Chem. Phys. (1982)
10.1063/1.445012 / J. Chem. Phys. (1983)
10.1063/1.448116 / J. Chem. Phys. (1984)
10.1016/0378-4371(87)90054-9 / Physica A (1987)
10.1063/1.450975 / J. Chem. Phys. (1986)
10.1103/PhysRevB.35.248 / Phys. Rev. B (1987)
10.1063/1.1696373 / J. Chem. Phys. (1965)
10.1143/JPSJ.40.567 / J. Phys. Soc. Jpn. (1976)
10.1063/1.335593 / J. Appl. Phys. (1985)
10.1103/PhysRevB.33.6428 / Phys. Rev. B (1986)
10.1007/BF01020577 / J. Stat. Phys. (1986)
10.1063/1.1706246 / Phys. Fluids (1961)
10.1063/1.1706534 / Phys. Fluids (1962)
{'key': '2024021006030918000_r15b', 'volume': '29', 'year': '1963', 'journal-title': 'Physica'} / Physica (1963)
10.1063/1.1692887 / Phys. Fluids (1970)
{'key': '2024021006030918000_r16'}
{'key': '2024021006030918000_r17'}
10.1063/1.438088 / J. Chem. Phys. (1979)
10.1063/1.444011 / J. Chem. Phys. (1982)
10.1063/1.447497 / J. Chem. Phys. (1984)
10.1063/1.451351 / J. Chem. Phys. (1986)
10.1063/1.452872 / J. Chem. Phys. (1987)
10.1063/1.450727 / J. Chem. Phys. (1986)
10.1063/1.866367 / Phys. Fluids (1987)
{'key': '2024021006030918000_r23a'}
10.1017/S0022112067001326 / J. Fluid Mech. (1967)
10.1063/1.866068 / Phys. Fluids (1987)

Dates

Type	When
Created	23 years, 1 month ago (July 26, 2002, 9:10 a.m.)
Deposited	1 year, 6 months ago (Feb. 10, 2024, 2:40 a.m.)
Indexed	4 weeks ago (Aug. 2, 2025, 1:23 a.m.)
Issued	37 years, 3 months ago (May 15, 1988)
Published	37 years, 3 months ago (May 15, 1988)
Published Print	37 years, 3 months ago (May 15, 1988)

Funders 0

None

BibTeX

@article{Rubinstein_1988, title={Diffusion-controlled reactions: Mathematical formulation, variational principles, and rigorous bounds}, volume={88}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.454474}, DOI={10.1063/1.454474}, number={10}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Rubinstein, Jacob and Torquato, S.}, year={1988}, month=may, pages={6372–6380} }

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