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The effect of a linear adsorption isotherm on the onset of fingeringinstability in a miscible displacement in the application of liquidchromatography, pollutant contamination in aquifers etc. is investigated. Suchfingering instability on the solute dynamics arise due to the miscible viscusfingering (VF) between the displacing fluid and sample solvent. We use aFourier pseudo-spectral method to solve the initial value problem appeared inthe linear stability analysis. The present linear stability analysis is ofgeneric type and it captures the early time diffusion dominated region whichwas never expressible through the quasi-steady state analysis (QSSA). Inaddition, it measures the onset of instability more accurately than the QSSAmethods. It is shown that the onset time depends non-monotonically on theretention parameter of the solute adsorption. This qualitative influence of theretention parameter on the onset of instability resemblances with the resultsobtained from direct numerical simulations of the nonlinear equations.Moreover, the present linear stability method helps for an appropriatecharacterisation of the linear and the nonlinear regimes of miscible VFinstability and also can be useful for the fluid flow problems with theunsteady base-state.

Onset of fingering instability in a finite slice of adsorbed solute