Poiseuille advection of chemical reaction fronts: Eikonal approximation

An eikonal equation including fluid advection is derived from the cubic reaction-diffusion-advection equation, and is used to investigate the speeds and shapes of chemical reaction fronts subject to Poiseuille flow between parallel plates. Although the eikonal equation is usually regarded as valid when the front thickness is small compared to the radius of curvature of the front and to the size of the system, it is also found to be valid when the reaction front is thick with respect to the gap width. This new regime of applicability of the eikonal equation is consistent with its derivation, which requires only that the reaction front curvature and the fluid velocity vary negligibly across the front. The front distortion and the front speed increase with increasing η, defined as the ratio of the gap half-width to the reaction front thickness. Analytical limits of the front distortion and front velocity for small and large η are compared with general numerical results.