Dissolution kinetics with feedback

  • Avner Friedman
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 57)


Consider a solid particle composed of chemical A. the particle is in a solution of chemical B. As the particle dissolves, the A that enters the solution reacts with B to form chemical C. Then C diffuses back to the particle and adsorbs to the particle’s surface. The presence of C on the particle’s surface inhibits the dissolution, and ultimately shuts it down entirely. This process was recently modeled by Kam-Chuen Ng and David S. Ross from Eastman Kodak. The mathematical model is expressed as a Stefan problem for reaction-diffusion system. On May 7, 1993 David Ross presented the model, described some asymptotic analysis, both for large reaction rates and for small time. He concluded with several open problems regarding this system.


Solid Particle Free Boundary Total Surface Area Final Size Dissolution Kinetic 
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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  1. [1]
    W. Xie, The Stefan problem with a kinetic condition at the free boundary, SIAM J. Math. Anal, 21 (1990), 362–373.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 1994

Authors and Affiliations

  • Avner Friedman
    • 1
  1. 1.Institute for Mathematics and its ApplicationsUniversity of MinnesotaMinneapolisUSA

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