Thermocapillary instability and wave formation on a viscous film flowing down an inclined plane with linear temperature variation: Effect of odd viscosity

Abstract

Thermocapillary instability and formation of waves for a thin viscous falling film with broken time-reversal-symmetry have been discussed in this present study. The film is flowing over a flat, rigid inclined plate with linear temperature variation. The presence of the odd part of the Cauchy stress tensor with odd viscosity coefficient brings new characteristics in thin film flow. The nonlinear evolution model, which tracks the free surface formation for this problem, has been developed using classical long-wave expansion method. Due to the presence of odd viscosity in the liquid, the evolution equation modified significantly. Both spatial and temporal analysis for linear stability has been performed along with the investigation of weakly nonlinear waves, leading the free-surface equation into the famous Kuramoto–Sivashinsky equation. Periodic stationary wave solutions of the full evolution equation confirm the existence of two significant wave families, γ1 and γ2, which are discussed in detail. Formation of the dynamical system and study of different bifurcation analysis and phases diagrams are also studied. The spatiotemporal evolution of the model has been analyzed numerically for different values of the odd viscosity parameter and Marangoni number. The odd viscosity gives stabilizing effect while the increase in Marangoni number increases the instability.