Pattern formation and evolution near autocatalytic reaction fronts in a narrow vertical slab
Year: 1996
Type: article
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 \ensuremath{\Gamma}=b/a and the dimensionless driving parameter S=\ensuremath{\delta}${\mathit{ga}}^{3}$/\ensuremath{\nu}${\mathit{D}}_{\mathit{C}}$, which involve the gap thickness a, the slab width b, the fractional density difference \ensuremath{\delta} between the unreacted and reacted solutions, the gravitational acceleration g, the kinematic viscosity \ensuremath{\nu}, and the catalyst molecular diffusivity ${\mathit{D}}_{\mathit{C}}$. 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\ensuremath{\approxeq}1 mm. \textcopyright{} 1996 The American Physical Society.
Authors: Jie Huang, Boyd F. Edwards
Institution: West Virginia University
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2042801294