Falling liquid films on a uniformly heated compliant substrate with broken time-reversal symmetry

This study aims to analyze the dynamics of a thin Newtonian liquid film on a uniformly heated compliant substrate. We consider the violation of time-reversal symmetry in the liquid, resulting in an additional non-zero term in the liquid stress tensor. Using the long-wave expansion technique, we derive a set of coupled equations governing the film thickness and substrate deformation, accounting for inertia, surface tension, thermocapillarity, and odd viscosity. Through linear stability analysis and spatiotemporal simulations, we observe that the compliant substrate enhances instability, while wall heating exacerbates it. However, the introduction of odd viscosity effectively suppresses these instabilities, as confirmed by the agreement between simulation and theoretical predictions.