Pattern formation and evolution near autocatalytic reaction fronts in a narrow vertical slab

Jie Huang and Boyd F. Edwards
Phys. Rev. E 54, 2620 – Published 1 September 1996
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Abstract

Linear analysis and nonlinear numerical simulations of autocatalytic reaction fronts ascending in narrow vertically unbounded slabs describe the growth, development, and annihilation of fingers in the front, the dynamics of edge suppression, and a secondary transition to a two-roll state above the onset of convection. The pattern formation and evolution of the reaction fronts are determined by the horizontal aspect ratio Γ=b/a and the dimensionless driving parameter Sga3DC, which involve the gap thickness a, the slab width b, the fractional density difference δ between the unreacted and reacted solutions, the gravitational acceleration g, the kinematic viscosity ν, and the catalyst molecular diffusivity DC. The reaction fronts satisfy a chemical reaction-diffusion equation and two-dimensional Navier-Stokes equations describing the average Poiseuille velocity in the vertical plane perpendicular to the gap direction. The wavelength of maximum growth rate reaches a minimum value at a≊1 mm. © 1996 The American Physical Society.

  • Received 20 November 1995

DOI:https://doi.org/10.1103/PhysRevE.54.2620

©1996 American Physical Society

Authors & Affiliations

Jie Huang and Boyd F. Edwards

  • Department of Physics, West Virginia University, P.O. Box 6315, Morgantown, West Virginia 26506-6315

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Issue

Vol. 54, Iss. 3 — September 1996

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