Nernst–Planck analysis of propagating reaction-diffusion fronts in the aqueous iodate–arsenous acid system

Abstract

Propagating fronts can be generated in solution by combining diffusion and chemical reactions with an autocatalytic feedback mechanism. Front propagation is usually analyzed in terms of the rate equations for the chemical reactions and Fick’s laws of molecular diffusion. In practice, however, reaction-diffusion fronts are known mainly for aqueous electrolyte solutions. A more accurate description of front propagation in these systems is developed by using Nernst–Planck (NP) transport equations. This treatment includes diffusion fluxes driven by the concentration gradients and, for the ionic species, the migration fluxes driven by the electric field which is generated internally by the diffusion of ions of different mobility. NP equations are used to describe propagating fronts for the iodate oxidation of aqueous arsenous acid. The analysis provides a detailed picture of front structure and propagation, including concentration profiles, reaction rate profiles and velocity profiles for the solution species. After a short induction period, fully-developed fronts reach steady velocities and the profiles across the fronts transformed from laboratory coordinates to the frame of reference moving with the front become time-independent. The velocities of the autocatalytic I⁻ ions ahead of the fronts are nearly identical to the steady front velocities. Electric fields generated by ionic diffusion across the fronts reach maximum strengths of about 0.4 V cm⁻¹, producing ion migration velocities as large as 50% of the front velocities.