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Effect of the irreversible A+B→C reaction on the onset and the growth of the buoyancy-driven instability in a porous medium: Asymptotic, linear, and nonlinear stability analyses

Min Chan Kim*

  • Department of Chemical Engineering, Jeju National University, Jeju 63243, Republic of Korea

  • *mckim@cheju.ac.kr
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Phys. Rev. Fluids 4, 073901 – Published 2 July, 2019

DOI: https://doi.org/10.1103/PhysRevFluids.4.073901

Abstract

Taking different diffusivities into account, the effect of irreversible A+B →C reaction on the growth of a buoyancy-driven instability in a Hele-Shaw cell is analyzed theoretically. For the limiting cases of infinitely fast reaction, an asymptotic stability analysis is conducted based on base density profile. To confirm the asymptotic stability analysis, under the linear stability theory, new linear stability equations are derived and solved numerically. In addition, fully nonlinear numerical simulations are conducted using the Fourier spectral method. The present asymptotic and linear stability analyses and nonlinear numerical simulations are in good agreement, and they modify the previous general classification of stability. For some cases where a stable barrier is sandwiched by two unstable regions, we also conducted linear and nonlinear analyses. It is interesting that for a certain case, instabilities with different wavelengths are possible below and above a central stable barrier.

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Phys. Rev. Fluids 4, 073901– Published 2 July, 2019
  • Received 10 March 2019
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