The effect of odd-viscosity on Rayleigh–Taylor instability of a liquid film under a heated inclined substrate

Abstract

We discuss the effect of odd viscosity on Rayleigh–Taylor instability of a thin Newtonian liquid film with broken time-reversal symmetry as it flows down a uniformly heated, inclined substrate. Although considerable experimental and theoretical studies have been performed regarding Rayleigh–Taylor instability, there is still a need to understand the instability mechanism in the presence of odd viscosity, which creates nondissipative effects. Odd viscosity represents broken time reversal and parity symmetries in the two-dimensional active chiral fluid and characterizes deviation of the system from one that contains a passive fluid. Adopting the long-wave approach allows a nonlinear free surface evolution equation of the thin film that considers the influence of odd viscosity to be derived. New, interesting linear stability analysis results illustrate that larger odd viscosity leads to a lower perturbation growth rate ωr and cutoff wave number kc. In other words, odd viscosity has a stabilizing effect on the Rayleigh–Taylor instability. Numerical simulations are conducted using the method of lines to solve the nonlinear evolution equation. The numerical results show that enhancing the odd viscosity effect suppresses the disturbance amplitude and wave frequency. In addition, the numerical results show that the inclination angle and the Weber number have stabilizing effects on the Rayleigh–Taylor instability. However, the Biot number has the opposite effect when the thin liquid film conductivity is poor. Also, the oscillation tends to accumulate downstream of the inclined substrate if the evolution time is sufficiently long.