Thermocapillary weak viscoelastic film flows on a rotating substrate

Abstract

We analyze the dynamics and stability of a thin viscoelastic film on a rotating, nonuniformly heated inclined plane, assuming weak rotation and a region far from the axis. The centrifugal force’s effect on instability is a key focus, with Walter’s B${}^{\prime \prime }$ rheology used for the viscoelastic liquid. By applying the long-wave approximation, we derive a nonlinear evolution equation for the local film thickness, capturing the interplay of viscoelasticity, rotation, thermocapillarity, and gravity in the low Reynolds number regime. Linear stability analysis shows that the linear growth rate of disturbances is influenced by the viscoelastic parameter, centrifugal force, and Marangoni stresses, while the linear wave speed is affected by rotation and thermocapillarity, but not viscoelasticity. A weakly nonlinear stability analysis reveals distinct instability regions, with both supercritical stable and subcritical unstable zones governed by rotation, thermocapillarity, and viscoelasticity. Numerical studies show that rotation enhances wave height, and viscoelasticity and thermal effects further amplify it. Additionally, viscoelasticity, rotation, and thermal effects impact nonlinear wave speed, though nonuniform heating reduces wave propagation. Full numerical simulations confirm the results from linear and weakly nonlinear analyses.