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The onset of viscous fingering in the presence of a non monotonic viscosityprofile is investigated theoretically for two immiscible fluids. Classicalfluid dynamics predicts that no unstable behavior may be observed when aviscous fluid pushes a less viscous one in a Hele-Shaw cell. Here, we show thatthe presence of a viscosity gradient at the interface between both fluidsdestabilize the interface facilitating the spread of the perturbation. Theinfluence of the viscosity gradient on the dispersion relation is analyzed.

Linear stability analysis on the onset of viscous fingering due to a non monotonic viscosity profile for immiscible fluids