Solute transport in porous media is strongly influenced by both hydrodynamic instabilities and physicochemical interactions, such as adsorption. In this study, we investigate the coupled dynamics of a finite solute blob subjected to Langmuir type nonlinear adsorption and viscous fingering (VF) instabilities during miscible displacement. To resolve the complex interplay between adsorption and instability, we solved the governing equations using a high-resolution Fourier pseudospectral method. While linear adsorption leads to symmetric blob spreading, the nonlinear Langmuir regime exhibits highly asymmetric solute profiles characterized by the formation of a rear rarefaction wave and a sharp leading shock layer. Additionally, the net advection of the blob is noticeably reduced in the upstream direction as the Langmuir adsorption parameter $b$ increases. We have found that for the range of adsorption parameters for a given suitable log mobility ratio, the VF instability was suppressed and introduced a new comet shape structure. Furthermore, we examine the impact of adsorption on mixing by tracking the degree of mixing over time. Interestingly, we observe a nonmonotonic dependence of mixing on the Langmuir parameter for a suitable log mobility ratio. The coupled effect of VF at the rear interface and of Langmuir adsorption provides a powerful mechanism to enhance or reduce the mixing and VF depending on the need of the application.

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• Adsorption isotherm
• Fingering instability
• Flows in porous media