Onset of convection for autocatalytic reaction fronts: Laterally unbounded system

Convective Instability of Autocatalytic Reaction Fronts in Vertical Cylinders

Existence and Stability of Propagating Fronts for an Autocatalytic Reaction-Diffusion System

We study a one-dimensional reaction-diffusion system which describes an isothermal autocatalytic chemical reaction involving both a quadratic (A + B → 2B) and a cubic (A+ 2B → 3B) autocatalysis. The parameters of this system are the ratio D = DB/DA of the diffusion constants of the reactant A and the autocatalyst B, and the relative activity k of the cubic reaction. First, for all values of D >...

Dispersion curves in the diffusional instability of autocatalytic reaction fronts.

A (linear) stability analysis of planar reaction fronts to transverse perturbations is considered for systems based on cubic autocatalysis and a model for the chlorite-tetrathionate reaction. Dispersion curves (plots of the growth rate sigma against a transverse wave-number k) are obtained. In both cases it is seen that there is a nonzero value D0 of D (the ratio of the diffusion coefficients o...

Propagation of fronts of a reaction-convection-diffusion equation

We study the speed of propagating fronts of the convection reaction diffusion equation ut + μuux = uxx + f(u) for reaction terms f(u) such that in the non convective case fronts joining two equilibrium states exist. A variational principle for the wave speed is constructed from which upper and lower bounds are obtained. We find that, in general, there is a transition value μc below which advect...

Minimal speed of fronts of reaction-convection-diffusion equations.

We study the minimal speed of propagating fronts of convection-reaction-diffusion equations of the form u(t)+microphi(u)u(x)=u(xx)+f(u) for positive reaction terms with f(')(0)>0. The function phi(u) is continuous and vanishes at u=0. A variational principle for the minimal speed of the waves is constructed from which upper and lower bounds are obtained. This permits the a priori assessment of ...