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.

当将柔软的，可变形的固体层附着到倾斜平面上时，将检查剪切施加的液膜流过倾斜平面的线性稳定性。流过刚性斜面的液膜表现出长波气液（GL）界面不稳定性，该不稳定性可以通过在气液界面处施加切变应力来修正。无论是否存在GL界面剪切，该GL界面模式在蠕变流动极限中都不会变得不稳定。我们证明，当施加剪切力的液膜流过一个覆盖有软固体层的倾斜平面时，即使在零雷诺数下，GL界面也会变得不稳定。仅当同时存在剪切和可变形的液-固（LS）界面时，才存在这种GL模式的不稳定性。对于非零雷诺数，我们显示，由于存在可变形的LS接口，因此存在多个起源的不稳定模式。这些不稳定的LS模式仅对于施加剪切力的液膜流变得重要并且在实践中可实现，并且在没有施加剪切力的情况下对于膜流变得无关紧要。我们还表明，这种LS界面不稳定性主导了低雷诺数条件下复合流体膜-固体系统的稳定性。我们的结果表明，通过在参数范围内使用可变形的固体涂层，可以使施加剪切力的薄膜流变得不稳定，否则该薄膜流在刚性壁的范围内保持稳定。最后，我们显示出可变形的固体层可用于获得稳定的膜流构型，用于参数方案，其中GL界面模式对于在刚性斜面上施加的剪切膜流是不稳定的。