  This research focuses on the stability analysis of an odd viscosity-induced
shear-imposed Newtonian fluid flowing down an inclined slippery bed having an
insoluble surfactant at the top of the liquid surface. The Orr-Sommerfeld
boundary value problem is developed by applying the normal mode approach to the
infinitesimal perturbed fluid flow and solved using the numerical method
Chebyshev spectral collocation. The numerical results confirm the existence of
Yih mode and Marangoni mode in the longwave zone. For the clean/contaminated
surface of the film flow, the presence of an odd or Hall viscosity coefficient
reduces the surface wave energy and delays the transition from laminar to
perturbed flow. Also, it has stabilizing nature on the unstable Marangoni mode
as well. The growth rate of both clean and contaminated liquid surfaces becomes
more/less when the stronger external shear acts along the downstream/upstream
direction of fluid flow. Further, the slip parameter leads to a lower critical
Reynolds number and makes the liquid surface more unstable. An increase in the
critical Reynolds number due to the stronger Marangoni force ensures that the
insoluble surfactant has the potential to dampen the Yih mode instability.
Moreover, the unstable shear mode occurs in the finite wavenumber regime with
very high inertial force and a small angle of inclination. The two-fold
variation of the shear mode instability is possible with respect to the imposed
shear. However, the inclusion of the odd viscosity coefficient in the viscous
falling film may advance the shear mode instability.
