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

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 Gamma = b/a and the dimensionless driving parameter S = delta ga(3)/nu D-C, which involve the gap thickness a, the slab width b, the fractional density difference delta between the unreacted and reacted solutions. the gravitational acceleration g, the kinematic viscosity nu, and the catalyst molecular diffusivity D-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 approximate to 1 mm.