Propagation speed of a chemical wave front: effect of confinement

In this paper we perform molecular dynamics simulations of a propagating chemical wave front in both confining and unconfining geometries. It is found that the wave front propagation speed is reduced in the case where the fluid is confined and the channel width is sufficiently small, namely, in the order of 40 molecular diameters. For channel widths larger than 40 molecular diameters the effect from the wall on the front speed is negligible. In the wall-fluid boundary region the self-diffusion is a tensorial property; however, in the channel interior the diffusion is a simple scalar coefficient and equals that of the bulk phase. This fact is used to derive an anisotropic reaction diffusion equation. Via numerical analysis of the reaction diffusion equation it is found that a sufficient condition for the observed speed reduction is that the diffusion element parallel to the wall decreases as the distance to the wall decreases, i.e. in the wall-fluid boundary region. Furthermore, it is found that the front speed is independent of the fluid layering in this region and the normal diffusion element as long as it is non-zero and positive