Influence of the odd viscosity on the instability of a horizontal oscillating thin liquid film

This study establishes a stability analysis model for thin films of odd-viscosity fluids on laterally oscillating substrates using linear Floquet theory and the weighted residual method. To address the nonlinearity and periodic excitation characteristics of the thin-film dynamics equations, spectral methods and finite difference techniques are employed to derive a time-evolving Orr–Sommerfeld equation and a nonlinear governing equation for the free interface height. Numerical simulations are performed using a high-accuracy algorithm that combines Chebyshev spectral collocation with implicit time discretization. The results demonstrate that under strong streamwise oscillations, odd viscosity exerts a stabilizing effect by suppressing disturbance growth, whereas under weak oscillatory conditions, it promotes destabilization through enhanced modal coupling and significantly modulates gravity-dominated interfacial instability. Nonlinear simulations further reveal that odd viscosity induces lateral drifting of wave packets and dampens interface wave amplitudes. This mechanism provides a novel pathway for actively controlling interfacial stability via odd viscosity regulation.