INHOMOGENEOUS 2-SPECIES ANNIHILATION IN THE STEADY-STATE

We investigate steady-state geometrical properties of the reaction interface in the two-species annihilation process, A + B --> 0, when a flux j of A and B particles is injected at opposite extremities of a finite domain. By balancing the input flux with the number of reactions, we determine that the width w of the reaction zone scales as j-1/3 in the large flux limit, and that the concentration in this zone is proportional to j2/3. This same behaviour is deduced from the solution to the reaction-diffusion equation. In the low flux limit, the concentration is almost independent of position and is proportional to square-root j. In the latter case, the local reaction rate reaches maximum at the edges of the system rather than at the midpoint. When the two species approach at a finite velocity, there exists a critical velocity, above which the reactants essentially pass through each other. Results similar to those in one dimension are found in two- and three-dimensional radial geometries. Finally, we apply the quasistatic approximation to our steady-state solution to recover the known time dependence for the reaction zone width for the case of initially separated components with no external input.