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Reaction-diffusion waves in hydro-mechanically coupled porous solids
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  • Qingpei Sun,
  • Manman Hu,
  • Christoph Eckart Schrank,
  • Klaus Regenauer- Lieb
Qingpei Sun
University of Hong Kong
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Manman Hu
University of Hong Kong

Corresponding Author:[email protected]

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Christoph Eckart Schrank
Queensland University of Technology
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Klaus Regenauer- Lieb
UNSW Sydney
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Here, we extend the Fisher-Kolmogorov-Petrovsky-Piskunov equation to capture the interplay of multiscale and multiphysics coupled processes. We use a minimum of two coupled reaction-diffusion equations with additional nonlocal terms that describe the coupling between scales through mutual cross-diffusivities. This system of equations incorporates the physics of interaction of thermo-hydro-chemo-mechanical processes and can be used to understand a variety of localisation phenomena in nature. Applying bifurcation theory to the system of equations suggests that geological patterns can be interpreted as physical representation of three classes of well-known instabilities: Turing instability, Hopf bifurcation, and a chaotic regime of complex soliton-like waves. For specific parameters, the proposed system of equations predicts all three classes of instabilities encountered in nature. The third class appears for small fluid release reactions rates as a slow quasi-soliton wave for which our parametric diagram shows possible transition into the Hopf- or Turing-style instability upon dynamic evolution of coefficients.