Effect of wall deformability on the stability of shear-imposed film flow past an inclined plane

Abstract

The linear stability of shear-imposed liquid film flow past an inclined plane is examined when a soft, deformable solid layer is attached to the inclined plane. A liquid film flowing past a rigid inclined plane exhibits a long-wave gas–liquid (GL) interfacial instability which is modified by the presence of an imposed shear stress at gas–liquid interface. This GL interfacial mode does not become unstable in creeping flow limit whether a GL interfacial shear is present or not. We demonstrate that the GL interface becomes unstable even at zero Reynolds number when the shear-imposed liquid film flows past an inclined plane which is coated with soft solid layer. This GL mode instability exists only when both shear and a deformable liquid–solid (LS) interface are simultaneously present. For non-zero Reynolds number, we show that there exists multiple unstable modes originating because of the presence of deformable LS interface. These unstable LS modes become important and practically realizable only for shear-imposed liquid film flow and become irrelevant for film flows in absence of imposed shear. We also show that this LS interfacial instability dominate the stability behavior of the composite fluid film-solid system in low Reynolds number regime. Our results suggest that the shear-imposed film flow can be made unstable by using a deformable solid coating in parameter regime where the film flow otherwise remains stable in rigid wall limit. Finally, we show that a deformable solid layer can be used to obtain a stable film flow configuration for the parameter regime where the GL interfacial mode is unstable for shear imposed film flow over a rigid incline. Thus, we demonstrate the capability of a soft solid layer in manipulation and control of instabilities for shear-imposed film flows.