Instability of falling liquid films on inclined flexible substrates: Effects of odd viscosity and insoluble surfactants

This study examines the linear instability of liquid films flowing over flexible substrates, with a particular emphasis on how surfactant activity and odd viscosity independently induce mode competition and stability reversal through coupling with substrate dynamics. A unified spectral framework is proposed by constructing a modified Orr–Sommerfeld model that incorporates insoluble surfactant transport and odd-viscous stresses. The analysis demonstrates that interfacial surfactant gradients give rise to modal competition between surface and wall modes, thereby shifting critical stability thresholds. In contrast, odd viscosity modulates the spectral structure via its interaction with the flexible boundary, reversing the stabilizing effect observed in rigid systems. Further results show that both mechanisms can independently trigger short-wave instabilities even in the limit of zero Reynolds number, revealing strong non-inertial characteristics. These findings highlight the structural amplification role of substrate flexibility in shaping surface-driven and nondissipative effects, offering a theoretical foundation for controlling instabilities in multiphysics flows under complex boundary constraints.