Interaction between shock layer and viscous fingering in a langmuir adsorbed solute

Abstract

The nonlinear evolution of the interface between miscible fluids in porous media exhibits different spatiotemporal patterns. The understanding of the physical mechanism behind these patterns is relevant in a wide variety of physicochemical processes. The displacement of a high viscous fluid by a less viscous one in uniform porous medium results in classical viscous fingering (VF) instability. We find that the nonlinear Langmuir-type adsorption of the solute, dissolved in the displacing fluid, leading to the formation of a shock layer can alter the fingering dynamics. The influence of the shock layer on the evolving instability is examined by numerical simulations. Of particular interest are the formation of the shock layer and its impact on the onset of viscous fingering. In this paper, we reveal a critical mechanism of Langmuir-type adsorption that plays a vital role in the speed up of instability. We further infer that by controlling the non-linear adsorption parameter and viscosity contrast of the fluids, the shock layer either ceases to exist or it can be suppressed with VF instability. Hence, the Langmuir adsorption is identified as a strategy to manipulate the instability in a system involving porous media flows.