All Physics Faculty Publications

Document Type

Article

Journal/Book Title/Conference

Physical Review E

Volume

54

Issue

3

Publisher

American Physical Society

Publication Date

9-1-1996

First Page

2620

Last Page

2627

DOI

10.1103/PhysRevE.54.2620

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 S=δga3/νDC, 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.

Comments

http://link.aps.org/doi/10.1103/PhysRevE.54.2620

Published by American Physical Society in Physical Review E. Publisher PDF is available for download through the link above.