Shear-imposed thin film flow with variable fluid properties

Abstract

This study focuses on the stability of a thin liquid film on an inclined plane under the influence of external shear and thermal effects. The Navier–Stokes equation, coupled with the energy equation, is employed, considering temperature-dependent fluid properties that vary linearly with small temperature changes. The instability mechanisms are examined for shear acting in the same or opposite direction as the fluid flow, with temperature-dependent fluid properties. A fully nonlinear free surface evolution equation for the film thickness is derived to describe interfacial dynamics. Normal-mode analysis in linear stability analysis is conducted to explore the impact of temperature-dependent fluid properties and imposed shear direction on flow dynamics. Additionally, weakly nonlinear stability analysis is performed to identify supercritical or subcritical regions beyond the linear regime. Numerical simulations using the spectral method are carried out, confirming the theoretical model’s predictions of instability thresholds. In addition to the inclined plane configuration, the study also considers a thin liquid layer resting on a planar heated substrate. In this setting, where gravitational effects are negligible, rupture phenomena induced by van der Waals forces are analyzed. An evolution equation for the film profile is derived using lubrication theory, and numerical simulations reveal that externally applied shear can counteract the accelerated rupture driven by temperature dependent fluid properties.