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This research focuses on the stability analysis of an odd viscosity-inducedshear-imposed Newtonian fluid flowing down an inclined slippery bed having aninsoluble surfactant at the top of the liquid surface. The Orr-Sommerfeldboundary value problem is developed by applying the normal mode approach to theinfinitesimal perturbed fluid flow and solved using the numerical methodChebyshev spectral collocation. The numerical results confirm the existence ofYih mode and Marangoni mode in the longwave zone. For the clean/contaminatedsurface of the film flow, the presence of an odd or Hall viscosity coefficientreduces the surface wave energy and delays the transition from laminar toperturbed flow. Also, it has stabilizing nature on the unstable Marangoni modeas well. The growth rate of both clean and contaminated liquid surfaces becomesmore/less when the stronger external shear acts along the downstream/upstreamdirection of fluid flow. Further, the slip parameter leads to a lower criticalReynolds number and makes the liquid surface more unstable. An increase in thecritical Reynolds number due to the stronger Marangoni force ensures that theinsoluble surfactant has the potential to dampen the Yih mode instability.Moreover, the unstable shear mode occurs in the finite wavenumber regime withvery high inertial force and a small angle of inclination. The two-foldvariation of the shear mode instability is possible with respect to the imposedshear. However, the inclusion of the odd viscosity coefficient in the viscousfalling film may advance the shear mode instability.

Odd-viscosity induced surfactant-laden shear-imposed viscous film over a slippery incline