Impact of the odd viscosity on a falling film flow over topography plate with slip condition

This work examines the stability of a thin, viscous fluid with broken time-reversal symmetry (exhibiting odd viscosity) flowing over an inclined, slippery surface featuring weak corrugations. The nonlinear evolution equation, which incorporates the effects of odd viscosity, is derived using the integral boundary layer (IBL) approach based on the long-wave approximation. For the case of asymptotically small wall corrugations, the linear stability of the flow is analyzed using normal mode analysis to establish a dispersion relation. The temporal linear stability analysis reveals how the interplay between the corrugation substrate and the odd viscosity coefficient influence together the system’s stability characteristics in the presence of slippery property. The influence of other parameters including Reynolds number, Weber number, aspect ratio, and inclination angle on stability criteria is systematically investigated. The dispersion relation reveals that odd viscosity and Weber number exert stabilizing influences, whereas Reynolds number and slip length promote destabilization. The nonlinear evolution equation is reduced by imposing a constant flow rate constraint, and the resulting system is solved numerically using the fourth-order Runge-Kutta method in a finite spatial domain. A central finding of the present study is that substrate corrugation acts as a stabilizing mechanism: increasing the corrugation amplitude systematically suppresses free-surface instabilities, and this stabilizing effect is synergistically enhanced by the combined presence of odd viscosity and slip conditions. The nonlinear spatial analysis reveals that slip can act as a stabilizing mechanism in the fully nonlinear regime, particularly at moderate Reynolds numbers and in the combined presence of odd viscosity and substrate corrugation. These findings provide valuable insights for controlling thin film flows in industrial applications involving surfaces with broken time-reversal symmetry.