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Crystal Growth — Ostwald Ripening

  • Avner Friedman
  • David S. Ross
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 3)

Abstract

The silver halide crystals of photographic emulsions are precipitated from solutions of halides and silver salts. For example, if we mix solutions of silver nitrate (AgNO3) and potassium bromide (KBr), the following reaction takes place:

AgNO3 (solution)+KBr (solution) → AgBr (solid)+KNO3 (solution).

Keywords

Surface Tension Mass Balance Equation Silver Salt Silver Halide Silver Bromide 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    A. W. Adamson, Physical Chemistry of Surfaces, 4th edition, Interscience-Wiley, New York (1982).Google Scholar
  2. 2.
    A. Friedman, Mathematics in Industrial Problems, Part 7, IMA Volumes in Mathematics and its Applications, #67, Springer-Verlag, New York (1994).Google Scholar
  3. 3.
    A. Friedman and W. Littman, Industrial Mathematics, SIAM, Philadelphia (1994).CrossRefGoogle Scholar
  4. 4.
    A. Friedman and B. Ou, A model of crystal precipitation, J. Diff. Eqs., 137 (1989), 550–575.MathSciNetzbMATHGoogle Scholar
  5. 5.
    A. Friedman, B. Ou and D. S. Ross, Crystal precipitation with discrete initial data, J. Diff. Eqs., 137 (1989), 576–590.MathSciNetzbMATHGoogle Scholar
  6. 6.
    B. Meerson, Fluctuations provide strong selection in Ostwald ripening, Physical Review E, 60 (1999), 3072–3075.CrossRefGoogle Scholar
  7. 7.
    B. Niethammer and R. L. Pego, On the initial-value problem in the Lifshitz-Slyozov-Wagner theory of Ostwald ripening, SIAM J. Math. Analysis, 31 (2000), 457–485.MathSciNetCrossRefGoogle Scholar
  8. 8.
    B. Niethammer and R. L. Pego, Non-self-similar behavior in the LSW theory of Ostwald ripening, J. Statistical Physics, 95 (1999), 867–902.MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    I. Rubinstein and B. Zaltzman, Diffusional mechanism of “strong selection” in Ostwald ripening, Physical review E, 60 (1999), no. 6.Google Scholar
  10. 10.
    N. S. Tavare, Simulation of Ostwald’s ripening in a reactive batch crystallizer, Amer. Inst. Chem. Eng. J., 33 (1985), 152–156.CrossRefGoogle Scholar
  11. 11.
    J. J. L. Velazquez, The Becker-Döring equations and the Lifshitz-Slyozov theory of warsening, J. Statistical Physics, 92 (1998), 195–238.MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    J. J. L. Velazquez, On the effect of stochastic fluctuations in the dynamics of the Lifshitz-Slyozov-Wagner model, J. Statistical Physics, 99 (2000), 57–113.MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    P. W. Voorhees, The theory of Ostwald ripening, J. Statistical Physics, 38 (1985), 231–252.CrossRefGoogle Scholar
  14. 14.
    P. W. Voorhees, Ostwald ripening of two-phase mixtures, Annu. Rev. Mater. Sci., 22 (1992), 192–215.CrossRefGoogle Scholar
  15. 15.
    J. Zhang, A nonlinear multi-dimensional conservation law, J. Math. Anal. Appl., 204 (1996), 353–388.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Avner Friedman
    • 1
  • David S. Ross
    • 2
  1. 1.Department of MathematicsOhio State UniversityColumbusUSA
  2. 2.Department of Mathematics and StatisticsRochester Institute of TechnologyRochesterUSA

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