Role of odd viscosity in shear-imposed heated falling film down a slippery slope

We investigate the flow of a thin liquid film down a uniformly heated, slippery slope under the influence of gravity. The liquid-air interface is subjected to a constant imposed shear stress along the flow direction. Our model assumes that the time-reversal symmetry of the liquid is broken, introducing an additional viscosity coefficient known as odd viscosity. This study aims to explore the impact of odd viscosity on surface wave and shear wave dynamics in the presence of wall slippage, imposed shear stress, and thermal effects. To analyze the linear stability of this system, we have constructed an Orr-Sommerfeld type boundary value problem (OS BVP). The OS BVP is numerically solved using the Chebyshev spectral collocation method for a range of Reynolds numbers from low to high. We have found that while both the imposed shear and Marangoni number destabilize surface and shear modes, the instabilities can be mitigated by the odd viscosity coefficient.