Abstract
Differential flows of species, which may arise in reactive systems due to external fields such as electric fields or pressure gradients, may significantly affect the characteristics and stability of propagating fronts. A generalized Kuramoto-Sivashinsky equation describing the dynamics of perturbations of a planar front in systems with differential flows is derived and analyzed. The analysis shows that a differential flow parallel to the front may have either a destabilizing or a stabilizing effect. The effect of a lateral flow does not depend on its direction, while normal flows have a stabilizing effect when running in one direction and a destabilizing effect in the other. These analytical conclusions are verified in numerical experiments with a model of a cubic autocatalytic reaction. As a result of the instability, a periodic pattern of modulation appears on the front. In the case of lateral flow, the pattern drifts along the front. With normal flow, the pattern is stationary. The simulations show that both lateral and normal differential flows have a significant effect on the front velocity.