Effect of odd viscosity on the stability of thin viscoelastic liquid film flowing along an inclined plate

Abstract

A theory for the stability of a viscoelastic film flowing along an inclined wall which is considered the odd viscosity effect is investigated. Using the lubrication theory, a new liquid-gas interface evolution equation involving odd viscosity effect is derived. Linear stability analysis shows that the larger odd viscosity leads to the higher critical Reynolds number. While the higher viscoelastic parameter makes the critical Reynolds number lower. The weakly nonlinear study reveals that in the limited amplitude range, the supercritical stable region and the explosion region will decrease with the increase of the odd viscosity. Conversely, the unconditional stable region and the subcritical unstable region increase. Interestingly, the threshold of the supercritical stable region decreases with the increase of the odd viscosity. Therefore, by analysing the linear and non-linear stability of the evolution equation, we find that the odd viscosity stabilizes the flow, while the viscoelastic property destabilizes the flow.