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Contributions to Advanced Dynamics and Continuum Mechanics pp 53–72Cite as

Stress and Diffusion Assisted Chemical Reaction Front Kinetics in Cylindrical Structures

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Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 114))

Abstract

Following up on a previous paper in which planar and spherical geometries were discussed we now present a similar analysis of the influence of stress on the diffusion induced velocity of chemical reaction fronts in cylindrical objects. The essential equations of mechanochemistry and stationary diffusion are briefly revisited. Various models for the dependence of the diffusion coefficient on stress are presented, a phenomenological pressure-based one as well as a more advanced tensorial approach. The resulting field equations are solved analytically and the speeds of the reaction fronts predicted by the various diffusion models are compared and discussed.

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Notes

  1. 1.

    For an easier understanding the argument is presented in Cartesian coordinates.

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Acknowledgements

Support of this work by a joint grant from the Russian Foundation for Basic Research (18-19-00160) and the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG, MU 1752/47-1) is gratefully acknowledged.

Author information

Authors and Affiliations

  1. Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, Bol’shoy pr. 61, V.O., 199178, Saint Petersburg, Russia

    Polina Grigoreva & Elena N. Vilchevskaya

  2. Peter the Great St. Petersburg Polytechnical University (SPbPU), Politekhnicheskaja 29, 195251, Saint Petersburg, Russia

    Polina Grigoreva & Elena N. Vilchevskaya

  3. Institute of Mechanics, Chair of Continuum Mechanics and Materials Theory, Technical University of Berlin, Einsteinufer 5, 10587, Berlin, Germany

    Wolfgang H. Müller

Authors
  1. Polina Grigoreva
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  2. Elena N. Vilchevskaya
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  3. Wolfgang H. Müller
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Corresponding author

Correspondence to Polina Grigoreva .

Editor information

Editors and Affiliations

  1. Institut für Mechanik, Otto-von-Guericke-Universität Magdeburg, Magdeburg, Germany

    Holm Altenbach

  2. Institut für Technische Mechanik, Johannes Kepler Universität Linz, Linz, Austria

    Hans Irschik

  3. Institute of Continuous Media Mechanics, Russian Academy of Sciences, Perm, Russia

    Valery P. Matveenko

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Grigoreva, P., Vilchevskaya, E.N., Müller, W.H. (2019). Stress and Diffusion Assisted Chemical Reaction Front Kinetics in Cylindrical Structures. In: Altenbach, H., Irschik, H., Matveenko, V. (eds) Contributions to Advanced Dynamics and Continuum Mechanics. Advanced Structured Materials, vol 114. Springer, Cham. https://doi.org/10.1007/978-3-030-21251-3_4

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