A reduced model for fingering instability in miscible displacement

The classical problem of fingering instability in miscible displacement is revisited. The finger-forming dynamics is considered as a multiple-scale process involving a thin inter-diffusion layer and large-scale background flow affected by the viscosity and/or density stratification. Upon an appropriate separation of ‘fast’ and ‘slow’ variables one ends up with a reduced model dealing directly with the evolving displacement front. As an illustration, the new model is applied for description of fingering in a source-supported flow and in a flow within a vertical channel.