Falling liquid film down a non-uniformly heated slippery inclined plane with odd viscosity effects

The study examines the impact of the odd component of the Cauchy stress tensor, linked to the breakdown of time-reversal symmetry, on the linear instability analysis of a viscous fluid layer flowing down a non-uniformly heated and slippery inclined plane. Using a long-wave series expansion within an Orr-Sommerfeld-type boundary value problem, the critical Reynolds number is derived. The results of the linear long wavelength instability in the case of infinitesimal wavenumbers reveal that odd viscosity stabilizes the flow, while wall slip destabilizes it. The noteworthy finding is that thermocapillarity significantly enhances stability, provided gas temperature matches wall temperature.